1546593434.623 * [misc]progress: [Phase 1 of 3] Setting up. 1546593434.623 * * * [misc]progress: [1/2] Preparing points 1546593434.623 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1546593434.670 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.670 * * * * [misc]points: Sampling 197 additional inputs, on iter 1 have 59 / 256 1546593434.724 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.724 * * * * [misc]points: Sampling 149 additional inputs, on iter 2 have 107 / 256 1546593434.746 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.746 * * * * [misc]points: Sampling 122 additional inputs, on iter 3 have 134 / 256 1546593434.770 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.770 * * * * [misc]points: Sampling 88 additional inputs, on iter 4 have 168 / 256 1546593434.784 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.784 * * * * [misc]points: Sampling 56 additional inputs, on iter 5 have 200 / 256 1546593434.794 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.794 * * * * [misc]points: Sampling 45 additional inputs, on iter 6 have 211 / 256 1546593434.810 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.810 * * * * [misc]points: Sampling 37 additional inputs, on iter 7 have 219 / 256 1546593434.825 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.825 * * * * [misc]points: Sampling 25 additional inputs, on iter 8 have 231 / 256 1546593434.834 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.834 * * * * [misc]points: Sampling 21 additional inputs, on iter 9 have 235 / 256 1546593434.860 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.860 * * * * [misc]points: Sampling 16 additional inputs, on iter 10 have 240 / 256 1546593434.867 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.867 * * * * [misc]points: Sampling 14 additional inputs, on iter 11 have 242 / 256 1546593434.876 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.876 * * * * [misc]points: Sampling 8 additional inputs, on iter 12 have 248 / 256 1546593434.882 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.882 * * * * [misc]points: Sampling 5 additional inputs, on iter 13 have 251 / 256 1546593434.886 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.886 * * * * [misc]points: Sampling 4 additional inputs, on iter 14 have 252 / 256 1546593434.889 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.889 * * * * [misc]points: Sampling 4 additional inputs, on iter 15 have 253 / 256 1546593434.893 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.893 * * * * [misc]points: Sampling 4 additional inputs, on iter 16 have 253 / 256 1546593434.897 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.897 * * * * [misc]points: Sampling 4 additional inputs, on iter 17 have 253 / 256 1546593434.900 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.900 * * * * [misc]points: Sampling 4 additional inputs, on iter 18 have 255 / 256 1546593434.904 * * * * [misc]points: Filtering points with unrepresentable outputs 1546593434.904 * * * * [exit]points: Sampled 257 points with exact outputs 1546593434.904 * * * [misc]progress: [2/2] Setting up program. 1546593434.907 * [misc]progress: [Phase 2 of 3] Improving. 1546593434.907 * * * * [misc]progress: [ 1 / 1 ] simplifiying candidate # 1546593434.907 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1546593434.907 * * [misc]simplify: iters left: 6 (13 enodes) 1546593434.910 * * [misc]simplify: iters left: 5 (28 enodes) 1546593434.914 * * [misc]simplify: iters left: 4 (44 enodes) 1546593434.925 * * [misc]simplify: iters left: 3 (54 enodes) 1546593434.936 * * [misc]simplify: iters left: 2 (57 enodes) 1546593434.948 * * [misc]simplify: iters left: 1 (65 enodes) 1546593434.963 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546593434.963 * [misc]simplify: Simplified (2) to (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546593434.984 * * [misc]progress: iteration 1 / 4 1546593434.984 * * * [misc]progress: picking best candidate 1546593434.990 * * * * [misc]pick: Picked # 1546593434.990 * * * [misc]progress: localizing error 1546593435.018 * * * [misc]progress: generating rewritten candidates 1546593435.018 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1546593435.021 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1546593435.024 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1546593435.035 * * * [misc]progress: generating series expansions 1546593435.035 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1546593435.035 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546593435.035 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546593435.035 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593435.035 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593435.035 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593435.035 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593435.035 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.035 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.035 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593435.035 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.035 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.035 * [misc]taylor: Taking taylor expansion of k in k 1546593435.035 * [misc]backup-simplify: Simplify 0 into 0 1546593435.035 * [misc]backup-simplify: Simplify 1 into 1 1546593435.035 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593435.036 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593435.036 * [misc]taylor: Taking taylor expansion of 2 in k 1546593435.036 * [misc]backup-simplify: Simplify 2 into 2 1546593435.036 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593435.036 * [misc]taylor: Taking taylor expansion of n in k 1546593435.036 * [misc]backup-simplify: Simplify n into n 1546593435.036 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.036 * [misc]backup-simplify: Simplify PI into PI 1546593435.036 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593435.036 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593435.036 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593435.036 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593435.036 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.037 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593435.037 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593435.037 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593435.037 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593435.037 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593435.037 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593435.037 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593435.037 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.037 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.037 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593435.037 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.037 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.037 * [misc]taylor: Taking taylor expansion of k in n 1546593435.037 * [misc]backup-simplify: Simplify k into k 1546593435.037 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593435.037 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593435.037 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.037 * [misc]backup-simplify: Simplify 2 into 2 1546593435.037 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593435.037 * [misc]taylor: Taking taylor expansion of n in n 1546593435.037 * [misc]backup-simplify: Simplify 0 into 0 1546593435.037 * [misc]backup-simplify: Simplify 1 into 1 1546593435.037 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.037 * [misc]backup-simplify: Simplify PI into PI 1546593435.038 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593435.038 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593435.039 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593435.039 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593435.040 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.040 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593435.040 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593435.040 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593435.041 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.041 * [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)))) 1546593435.042 * [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))))) 1546593435.042 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593435.042 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593435.042 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593435.042 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593435.042 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.042 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.042 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593435.042 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.042 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.042 * [misc]taylor: Taking taylor expansion of k in n 1546593435.042 * [misc]backup-simplify: Simplify k into k 1546593435.042 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593435.042 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593435.042 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.042 * [misc]backup-simplify: Simplify 2 into 2 1546593435.042 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593435.042 * [misc]taylor: Taking taylor expansion of n in n 1546593435.042 * [misc]backup-simplify: Simplify 0 into 0 1546593435.043 * [misc]backup-simplify: Simplify 1 into 1 1546593435.043 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.043 * [misc]backup-simplify: Simplify PI into PI 1546593435.043 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593435.043 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593435.044 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593435.044 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593435.045 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.045 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593435.045 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593435.045 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593435.046 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.046 * [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)))) 1546593435.047 * [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))))) 1546593435.047 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546593435.047 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546593435.047 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593435.047 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.047 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.047 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593435.047 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.047 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.047 * [misc]taylor: Taking taylor expansion of k in k 1546593435.047 * [misc]backup-simplify: Simplify 0 into 0 1546593435.047 * [misc]backup-simplify: Simplify 1 into 1 1546593435.047 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546593435.047 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593435.047 * [misc]taylor: Taking taylor expansion of n in k 1546593435.047 * [misc]backup-simplify: Simplify n into n 1546593435.047 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593435.048 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593435.048 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593435.048 * [misc]taylor: Taking taylor expansion of 2 in k 1546593435.048 * [misc]backup-simplify: Simplify 2 into 2 1546593435.048 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.048 * [misc]backup-simplify: Simplify PI into PI 1546593435.048 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.048 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.049 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593435.049 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.049 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593435.049 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.050 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546593435.051 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593435.051 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593435.052 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593435.053 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593435.056 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593435.056 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546593435.056 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.057 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.057 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.058 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546593435.059 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593435.059 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.059 * [misc]backup-simplify: Simplify 0 into 0 1546593435.059 * [misc]backup-simplify: Simplify 0 into 0 1546593435.060 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546593435.061 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593435.063 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593435.064 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.064 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593435.064 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593435.064 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593435.065 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546593435.066 * [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))))))) 1546593435.068 * [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))))))) 1546593435.069 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.071 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593435.076 * [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 1546593435.076 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546593435.076 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.076 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.077 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.078 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593435.080 * [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 1546593435.080 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.080 * [misc]backup-simplify: Simplify 0 into 0 1546593435.080 * [misc]backup-simplify: Simplify 0 into 0 1546593435.080 * [misc]backup-simplify: Simplify 0 into 0 1546593435.082 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546593435.083 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593435.088 * [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 1546593435.088 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.089 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593435.089 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.089 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.090 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593435.092 * [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))))) 1546593435.094 * [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))))) 1546593435.106 * [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))))) 1546593435.106 * [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)))) 1546593435.106 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546593435.106 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593435.106 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593435.106 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593435.107 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593435.107 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.107 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.107 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593435.107 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.107 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.107 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.107 * [misc]taylor: Taking taylor expansion of k in k 1546593435.107 * [misc]backup-simplify: Simplify 0 into 0 1546593435.107 * [misc]backup-simplify: Simplify 1 into 1 1546593435.107 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.107 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593435.107 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593435.107 * [misc]taylor: Taking taylor expansion of 2 in k 1546593435.107 * [misc]backup-simplify: Simplify 2 into 2 1546593435.107 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593435.107 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.107 * [misc]backup-simplify: Simplify PI into PI 1546593435.107 * [misc]taylor: Taking taylor expansion of n in k 1546593435.107 * [misc]backup-simplify: Simplify n into n 1546593435.107 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593435.107 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593435.108 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593435.108 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593435.108 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593435.108 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593435.108 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593435.108 * [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)))) 1546593435.108 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593435.108 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593435.108 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593435.108 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593435.109 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.109 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.109 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593435.109 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.109 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.109 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.109 * [misc]taylor: Taking taylor expansion of k in n 1546593435.109 * [misc]backup-simplify: Simplify k into k 1546593435.109 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.109 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593435.109 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593435.109 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.109 * [misc]backup-simplify: Simplify 2 into 2 1546593435.109 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.109 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.109 * [misc]backup-simplify: Simplify PI into PI 1546593435.109 * [misc]taylor: Taking taylor expansion of n in n 1546593435.109 * [misc]backup-simplify: Simplify 0 into 0 1546593435.109 * [misc]backup-simplify: Simplify 1 into 1 1546593435.109 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.110 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.110 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.110 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593435.110 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593435.110 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593435.111 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.112 * [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))) 1546593435.112 * [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)))) 1546593435.112 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593435.112 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593435.112 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593435.112 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593435.112 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.113 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.113 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593435.113 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.113 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.113 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.113 * [misc]taylor: Taking taylor expansion of k in n 1546593435.113 * [misc]backup-simplify: Simplify k into k 1546593435.113 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.113 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593435.113 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593435.113 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.113 * [misc]backup-simplify: Simplify 2 into 2 1546593435.113 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.113 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.113 * [misc]backup-simplify: Simplify PI into PI 1546593435.113 * [misc]taylor: Taking taylor expansion of n in n 1546593435.113 * [misc]backup-simplify: Simplify 0 into 0 1546593435.113 * [misc]backup-simplify: Simplify 1 into 1 1546593435.114 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.114 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.114 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.114 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593435.114 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593435.115 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593435.115 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.116 * [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))) 1546593435.116 * [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)))) 1546593435.117 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546593435.117 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546593435.117 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593435.117 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.117 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.117 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593435.117 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.117 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.117 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.117 * [misc]taylor: Taking taylor expansion of k in k 1546593435.117 * [misc]backup-simplify: Simplify 0 into 0 1546593435.117 * [misc]backup-simplify: Simplify 1 into 1 1546593435.117 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.117 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546593435.117 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593435.117 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593435.117 * [misc]taylor: Taking taylor expansion of 2 in k 1546593435.117 * [misc]backup-simplify: Simplify 2 into 2 1546593435.117 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.117 * [misc]backup-simplify: Simplify PI into PI 1546593435.117 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.118 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.118 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593435.118 * [misc]taylor: Taking taylor expansion of n in k 1546593435.118 * [misc]backup-simplify: Simplify n into n 1546593435.118 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593435.118 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593435.118 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593435.118 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593435.119 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593435.119 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546593435.120 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546593435.120 * [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)))) 1546593435.121 * [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)))) 1546593435.122 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593435.123 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593435.125 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593435.126 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593435.126 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593435.126 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.126 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.127 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.127 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593435.129 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593435.129 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.129 * [misc]backup-simplify: Simplify 0 into 0 1546593435.129 * [misc]backup-simplify: Simplify 0 into 0 1546593435.129 * [misc]backup-simplify: Simplify 0 into 0 1546593435.131 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.132 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593435.137 * [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 1546593435.137 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.137 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593435.137 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.138 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.138 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.139 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546593435.141 * [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 1546593435.141 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.141 * [misc]backup-simplify: Simplify 0 into 0 1546593435.141 * [misc]backup-simplify: Simplify 0 into 0 1546593435.141 * [misc]backup-simplify: Simplify 0 into 0 1546593435.142 * [misc]backup-simplify: Simplify 0 into 0 1546593435.144 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.146 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.154 * [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 1546593435.154 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.154 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593435.155 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.155 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.155 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.156 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546593435.160 * [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 1546593435.160 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.160 * [misc]backup-simplify: Simplify 0 into 0 1546593435.160 * [misc]backup-simplify: Simplify 0 into 0 1546593435.161 * [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))))) 1546593435.161 * [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)) 1546593435.161 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546593435.161 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593435.161 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593435.161 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593435.161 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593435.161 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593435.161 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.162 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.162 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.162 * [misc]taylor: Taking taylor expansion of k in k 1546593435.162 * [misc]backup-simplify: Simplify 0 into 0 1546593435.162 * [misc]backup-simplify: Simplify 1 into 1 1546593435.162 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.162 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.162 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.162 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593435.162 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593435.162 * [misc]taylor: Taking taylor expansion of -2 in k 1546593435.162 * [misc]backup-simplify: Simplify -2 into -2 1546593435.162 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593435.162 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.162 * [misc]backup-simplify: Simplify PI into PI 1546593435.162 * [misc]taylor: Taking taylor expansion of n in k 1546593435.162 * [misc]backup-simplify: Simplify n into n 1546593435.162 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593435.162 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593435.162 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593435.163 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593435.163 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593435.163 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593435.163 * [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))) 1546593435.163 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593435.163 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593435.163 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593435.163 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593435.163 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593435.163 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.163 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.163 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.163 * [misc]taylor: Taking taylor expansion of k in n 1546593435.163 * [misc]backup-simplify: Simplify k into k 1546593435.163 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.163 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.163 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.164 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593435.164 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593435.164 * [misc]taylor: Taking taylor expansion of -2 in n 1546593435.164 * [misc]backup-simplify: Simplify -2 into -2 1546593435.164 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.164 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.164 * [misc]backup-simplify: Simplify PI into PI 1546593435.164 * [misc]taylor: Taking taylor expansion of n in n 1546593435.164 * [misc]backup-simplify: Simplify 0 into 0 1546593435.164 * [misc]backup-simplify: Simplify 1 into 1 1546593435.164 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.164 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593435.165 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593435.165 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593435.165 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593435.166 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.166 * [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))) 1546593435.167 * [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)))) 1546593435.167 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593435.167 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593435.167 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593435.167 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593435.167 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593435.167 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.167 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.167 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.167 * [misc]taylor: Taking taylor expansion of k in n 1546593435.167 * [misc]backup-simplify: Simplify k into k 1546593435.167 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.167 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.167 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.167 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593435.167 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593435.167 * [misc]taylor: Taking taylor expansion of -2 in n 1546593435.168 * [misc]backup-simplify: Simplify -2 into -2 1546593435.168 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.168 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.168 * [misc]backup-simplify: Simplify PI into PI 1546593435.168 * [misc]taylor: Taking taylor expansion of n in n 1546593435.168 * [misc]backup-simplify: Simplify 0 into 0 1546593435.168 * [misc]backup-simplify: Simplify 1 into 1 1546593435.168 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.168 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593435.169 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593435.169 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593435.169 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593435.169 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.170 * [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))) 1546593435.171 * [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)))) 1546593435.171 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546593435.171 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546593435.171 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593435.171 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593435.171 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.171 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.171 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.171 * [misc]taylor: Taking taylor expansion of k in k 1546593435.171 * [misc]backup-simplify: Simplify 0 into 0 1546593435.171 * [misc]backup-simplify: Simplify 1 into 1 1546593435.171 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.171 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.171 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.171 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546593435.171 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546593435.171 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546593435.171 * [misc]taylor: Taking taylor expansion of -2 in k 1546593435.171 * [misc]backup-simplify: Simplify -2 into -2 1546593435.172 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.172 * [misc]backup-simplify: Simplify PI into PI 1546593435.172 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593435.172 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593435.172 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593435.172 * [misc]taylor: Taking taylor expansion of n in k 1546593435.172 * [misc]backup-simplify: Simplify n into n 1546593435.172 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593435.173 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593435.173 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593435.173 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593435.173 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546593435.174 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546593435.174 * [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)))) 1546593435.175 * [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)))) 1546593435.176 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593435.176 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593435.178 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593435.178 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593435.178 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593435.178 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.179 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.179 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546593435.180 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593435.180 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.180 * [misc]backup-simplify: Simplify 0 into 0 1546593435.180 * [misc]backup-simplify: Simplify 0 into 0 1546593435.180 * [misc]backup-simplify: Simplify 0 into 0 1546593435.181 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.182 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593435.185 * [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 1546593435.185 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.185 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593435.185 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.185 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.186 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546593435.187 * [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 1546593435.187 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.187 * [misc]backup-simplify: Simplify 0 into 0 1546593435.187 * [misc]backup-simplify: Simplify 0 into 0 1546593435.187 * [misc]backup-simplify: Simplify 0 into 0 1546593435.187 * [misc]backup-simplify: Simplify 0 into 0 1546593435.188 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.189 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.194 * [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 1546593435.194 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.194 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593435.194 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.195 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.195 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546593435.197 * [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 1546593435.197 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.197 * [misc]backup-simplify: Simplify 0 into 0 1546593435.197 * [misc]backup-simplify: Simplify 0 into 0 1546593435.198 * [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))))) 1546593435.198 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1546593435.198 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546593435.198 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546593435.198 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593435.198 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.198 * [misc]backup-simplify: Simplify 2 into 2 1546593435.198 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593435.198 * [misc]taylor: Taking taylor expansion of n in n 1546593435.198 * [misc]backup-simplify: Simplify 0 into 0 1546593435.198 * [misc]backup-simplify: Simplify 1 into 1 1546593435.198 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.198 * [misc]backup-simplify: Simplify PI into PI 1546593435.198 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593435.198 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.198 * [misc]backup-simplify: Simplify 2 into 2 1546593435.198 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593435.198 * [misc]taylor: Taking taylor expansion of n in n 1546593435.198 * [misc]backup-simplify: Simplify 0 into 0 1546593435.198 * [misc]backup-simplify: Simplify 1 into 1 1546593435.198 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.198 * [misc]backup-simplify: Simplify PI into PI 1546593435.199 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593435.199 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593435.199 * [misc]backup-simplify: Simplify 0 into 0 1546593435.199 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593435.199 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593435.200 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.200 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593435.201 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593435.201 * [misc]backup-simplify: Simplify 0 into 0 1546593435.202 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.203 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593435.203 * [misc]backup-simplify: Simplify 0 into 0 1546593435.204 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593435.205 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546593435.205 * [misc]backup-simplify: Simplify 0 into 0 1546593435.207 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593435.208 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546593435.208 * [misc]backup-simplify: Simplify 0 into 0 1546593435.210 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593435.212 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546593435.212 * [misc]backup-simplify: Simplify 0 into 0 1546593435.214 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546593435.217 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546593435.217 * [misc]backup-simplify: Simplify 0 into 0 1546593435.217 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546593435.217 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546593435.217 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546593435.217 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593435.217 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.217 * [misc]backup-simplify: Simplify 2 into 2 1546593435.217 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.217 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.217 * [misc]backup-simplify: Simplify PI into PI 1546593435.217 * [misc]taylor: Taking taylor expansion of n in n 1546593435.217 * [misc]backup-simplify: Simplify 0 into 0 1546593435.217 * [misc]backup-simplify: Simplify 1 into 1 1546593435.217 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.217 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593435.217 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.217 * [misc]backup-simplify: Simplify 2 into 2 1546593435.217 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.217 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.217 * [misc]backup-simplify: Simplify PI into PI 1546593435.217 * [misc]taylor: Taking taylor expansion of n in n 1546593435.217 * [misc]backup-simplify: Simplify 0 into 0 1546593435.217 * [misc]backup-simplify: Simplify 1 into 1 1546593435.218 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.218 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.218 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.219 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593435.219 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593435.219 * [misc]backup-simplify: Simplify 0 into 0 1546593435.220 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.220 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593435.220 * [misc]backup-simplify: Simplify 0 into 0 1546593435.221 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.222 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.222 * [misc]backup-simplify: Simplify 0 into 0 1546593435.223 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.225 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593435.225 * [misc]backup-simplify: Simplify 0 into 0 1546593435.226 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.620 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593435.620 * [misc]backup-simplify: Simplify 0 into 0 1546593435.623 * [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 1546593435.625 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593435.625 * [misc]backup-simplify: Simplify 0 into 0 1546593435.625 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546593435.625 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546593435.625 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546593435.625 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593435.625 * [misc]taylor: Taking taylor expansion of -2 in n 1546593435.625 * [misc]backup-simplify: Simplify -2 into -2 1546593435.625 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.625 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.625 * [misc]backup-simplify: Simplify PI into PI 1546593435.625 * [misc]taylor: Taking taylor expansion of n in n 1546593435.625 * [misc]backup-simplify: Simplify 0 into 0 1546593435.625 * [misc]backup-simplify: Simplify 1 into 1 1546593435.626 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.626 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593435.626 * [misc]taylor: Taking taylor expansion of -2 in n 1546593435.626 * [misc]backup-simplify: Simplify -2 into -2 1546593435.626 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.626 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.626 * [misc]backup-simplify: Simplify PI into PI 1546593435.626 * [misc]taylor: Taking taylor expansion of n in n 1546593435.626 * [misc]backup-simplify: Simplify 0 into 0 1546593435.626 * [misc]backup-simplify: Simplify 1 into 1 1546593435.626 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.626 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593435.626 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593435.627 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593435.628 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593435.628 * [misc]backup-simplify: Simplify 0 into 0 1546593435.628 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.629 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593435.629 * [misc]backup-simplify: Simplify 0 into 0 1546593435.630 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.631 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.631 * [misc]backup-simplify: Simplify 0 into 0 1546593435.632 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.633 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593435.633 * [misc]backup-simplify: Simplify 0 into 0 1546593435.638 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.640 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593435.640 * [misc]backup-simplify: Simplify 0 into 0 1546593435.641 * [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 1546593435.643 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593435.643 * [misc]backup-simplify: Simplify 0 into 0 1546593435.644 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546593435.644 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1546593435.644 * [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)))) 1546593435.644 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1546593435.644 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593435.644 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593435.644 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.644 * [misc]taylor: Taking taylor expansion of k in k 1546593435.644 * [misc]backup-simplify: Simplify 0 into 0 1546593435.644 * [misc]backup-simplify: Simplify 1 into 1 1546593435.644 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.644 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593435.645 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593435.645 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593435.645 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593435.645 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593435.645 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593435.645 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.645 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.645 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593435.645 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.645 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.645 * [misc]taylor: Taking taylor expansion of k in k 1546593435.645 * [misc]backup-simplify: Simplify 0 into 0 1546593435.645 * [misc]backup-simplify: Simplify 1 into 1 1546593435.645 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593435.645 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593435.645 * [misc]taylor: Taking taylor expansion of 2 in k 1546593435.645 * [misc]backup-simplify: Simplify 2 into 2 1546593435.645 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593435.645 * [misc]taylor: Taking taylor expansion of n in k 1546593435.645 * [misc]backup-simplify: Simplify n into n 1546593435.645 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.645 * [misc]backup-simplify: Simplify PI into PI 1546593435.645 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593435.645 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593435.645 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593435.645 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593435.645 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.645 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593435.646 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593435.646 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593435.646 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of k in n 1546593435.646 * [misc]backup-simplify: Simplify k into k 1546593435.646 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.646 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546593435.646 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593435.646 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546593435.646 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.646 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.646 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.646 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.646 * [misc]taylor: Taking taylor expansion of k in n 1546593435.646 * [misc]backup-simplify: Simplify k into k 1546593435.646 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.646 * [misc]backup-simplify: Simplify 2 into 2 1546593435.646 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593435.646 * [misc]taylor: Taking taylor expansion of n in n 1546593435.646 * [misc]backup-simplify: Simplify 0 into 0 1546593435.646 * [misc]backup-simplify: Simplify 1 into 1 1546593435.646 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.646 * [misc]backup-simplify: Simplify PI into PI 1546593435.646 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593435.647 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593435.647 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593435.647 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593435.648 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.648 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593435.648 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593435.648 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593435.648 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.649 * [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)))) 1546593435.649 * [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))))) 1546593435.649 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of k in n 1546593435.649 * [misc]backup-simplify: Simplify k into k 1546593435.649 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.649 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546593435.649 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593435.649 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546593435.649 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.649 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.649 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.649 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.649 * [misc]taylor: Taking taylor expansion of k in n 1546593435.649 * [misc]backup-simplify: Simplify k into k 1546593435.649 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593435.649 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593435.650 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.650 * [misc]backup-simplify: Simplify 2 into 2 1546593435.650 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593435.650 * [misc]taylor: Taking taylor expansion of n in n 1546593435.650 * [misc]backup-simplify: Simplify 0 into 0 1546593435.650 * [misc]backup-simplify: Simplify 1 into 1 1546593435.650 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.650 * [misc]backup-simplify: Simplify PI into PI 1546593435.650 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593435.650 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593435.650 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593435.651 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593435.651 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.651 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593435.651 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593435.651 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593435.652 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.652 * [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)))) 1546593435.652 * [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))))) 1546593435.653 * [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))) 1546593435.653 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.653 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.653 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.653 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.653 * [misc]taylor: Taking taylor expansion of k in k 1546593435.653 * [misc]backup-simplify: Simplify 0 into 0 1546593435.653 * [misc]backup-simplify: Simplify 1 into 1 1546593435.653 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of n in k 1546593435.653 * [misc]backup-simplify: Simplify n into n 1546593435.653 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593435.653 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593435.653 * [misc]taylor: Taking taylor expansion of 2 in k 1546593435.653 * [misc]backup-simplify: Simplify 2 into 2 1546593435.653 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.653 * [misc]backup-simplify: Simplify PI into PI 1546593435.653 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.654 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.654 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593435.654 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.654 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593435.654 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.655 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546593435.655 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593435.655 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593435.655 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.655 * [misc]taylor: Taking taylor expansion of k in k 1546593435.655 * [misc]backup-simplify: Simplify 0 into 0 1546593435.655 * [misc]backup-simplify: Simplify 1 into 1 1546593435.655 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.655 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593435.656 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593435.656 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1546593435.656 * [misc]backup-simplify: Simplify 0 into 0 1546593435.657 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593435.657 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593435.659 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593435.659 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546593435.659 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.659 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.660 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.660 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546593435.661 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593435.661 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1546593435.661 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.661 * [misc]backup-simplify: Simplify 0 into 0 1546593435.662 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546593435.662 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593435.664 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593435.664 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.664 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593435.664 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593435.664 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593435.665 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546593435.666 * [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))))))) 1546593435.667 * [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))))))) 1546593435.667 * [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))))))) 1546593435.668 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.669 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593435.672 * [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 1546593435.672 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546593435.672 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.672 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.673 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.673 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593435.675 * [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 1546593435.675 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.676 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1546593435.676 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1546593435.676 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.676 * [misc]backup-simplify: Simplify 0 into 0 1546593435.677 * [misc]backup-simplify: Simplify 0 into 0 1546593435.677 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546593435.678 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593435.679 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546593435.680 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593435.685 * [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 1546593435.686 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.686 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593435.686 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.686 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.687 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593435.689 * [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))))) 1546593435.694 * [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)))))))) 1546593435.697 * [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)))))))) 1546593435.699 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593435.701 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546593435.707 * [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 1546593435.707 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1546593435.707 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.707 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.708 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593435.708 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546593435.710 * [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 1546593435.710 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.711 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1546593435.711 * [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 1546593435.711 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.711 * [misc]backup-simplify: Simplify 0 into 0 1546593435.711 * [misc]backup-simplify: Simplify 0 into 0 1546593435.712 * [misc]backup-simplify: Simplify 0 into 0 1546593435.712 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.712 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593435.714 * [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 1546593435.715 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.719 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1546593435.719 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.720 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546593435.720 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.720 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.720 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546593435.723 * [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))))))) 1546593435.729 * [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)))))))))))))) 1546593435.739 * [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)))))))))))))) 1546593435.750 * [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)))))))))))))))))))))) 1546593435.751 * [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))))) 1546593435.751 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1546593435.751 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593435.751 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593435.751 * [misc]taylor: Taking taylor expansion of k in k 1546593435.751 * [misc]backup-simplify: Simplify 0 into 0 1546593435.751 * [misc]backup-simplify: Simplify 1 into 1 1546593435.751 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593435.752 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593435.752 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.752 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.752 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of k in k 1546593435.752 * [misc]backup-simplify: Simplify 0 into 0 1546593435.752 * [misc]backup-simplify: Simplify 1 into 1 1546593435.752 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.752 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of 2 in k 1546593435.752 * [misc]backup-simplify: Simplify 2 into 2 1546593435.752 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593435.752 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.752 * [misc]backup-simplify: Simplify PI into PI 1546593435.752 * [misc]taylor: Taking taylor expansion of n in k 1546593435.752 * [misc]backup-simplify: Simplify n into n 1546593435.753 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593435.753 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593435.753 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593435.753 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593435.753 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593435.753 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593435.753 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593435.754 * [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)))) 1546593435.754 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of k in n 1546593435.754 * [misc]backup-simplify: Simplify k into k 1546593435.754 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546593435.754 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546593435.754 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.754 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.754 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.754 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.754 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of k in n 1546593435.754 * [misc]backup-simplify: Simplify k into k 1546593435.754 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.754 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.754 * [misc]backup-simplify: Simplify 2 into 2 1546593435.754 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.754 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.754 * [misc]backup-simplify: Simplify PI into PI 1546593435.754 * [misc]taylor: Taking taylor expansion of n in n 1546593435.754 * [misc]backup-simplify: Simplify 0 into 0 1546593435.755 * [misc]backup-simplify: Simplify 1 into 1 1546593435.755 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.755 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.756 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.756 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593435.756 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593435.756 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593435.757 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.757 * [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))) 1546593435.758 * [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)))) 1546593435.758 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593435.758 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546593435.758 * [misc]taylor: Taking taylor expansion of k in n 1546593435.758 * [misc]backup-simplify: Simplify k into k 1546593435.758 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546593435.758 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546593435.758 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593435.758 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593435.758 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593435.758 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593435.758 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.758 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.758 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593435.758 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.758 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.758 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.758 * [misc]taylor: Taking taylor expansion of k in n 1546593435.758 * [misc]backup-simplify: Simplify k into k 1546593435.758 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.759 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593435.759 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593435.759 * [misc]taylor: Taking taylor expansion of 2 in n 1546593435.759 * [misc]backup-simplify: Simplify 2 into 2 1546593435.759 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.759 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.759 * [misc]backup-simplify: Simplify PI into PI 1546593435.759 * [misc]taylor: Taking taylor expansion of n in n 1546593435.759 * [misc]backup-simplify: Simplify 0 into 0 1546593435.759 * [misc]backup-simplify: Simplify 1 into 1 1546593435.759 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.759 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.760 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.760 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593435.760 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593435.760 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593435.761 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.761 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1546593435.762 * [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)))) 1546593435.763 * [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)) 1546593435.763 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.763 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.763 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.763 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.763 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of k in k 1546593435.763 * [misc]backup-simplify: Simplify 0 into 0 1546593435.763 * [misc]backup-simplify: Simplify 1 into 1 1546593435.763 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.763 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593435.763 * [misc]taylor: Taking taylor expansion of 2 in k 1546593435.763 * [misc]backup-simplify: Simplify 2 into 2 1546593435.764 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.764 * [misc]backup-simplify: Simplify PI into PI 1546593435.764 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593435.764 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593435.764 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593435.764 * [misc]taylor: Taking taylor expansion of n in k 1546593435.764 * [misc]backup-simplify: Simplify n into n 1546593435.764 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593435.765 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593435.765 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593435.765 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593435.765 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593435.765 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546593435.766 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546593435.767 * [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)))) 1546593435.767 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593435.767 * [misc]taylor: Taking taylor expansion of k in k 1546593435.767 * [misc]backup-simplify: Simplify 0 into 0 1546593435.767 * [misc]backup-simplify: Simplify 1 into 1 1546593435.767 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593435.767 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593435.768 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1546593435.768 * [misc]backup-simplify: Simplify 0 into 0 1546593435.769 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593435.770 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593435.773 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593435.773 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593435.773 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593435.773 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.773 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.774 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.775 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593435.776 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593435.777 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546593435.777 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.777 * [misc]backup-simplify: Simplify 0 into 0 1546593435.777 * [misc]backup-simplify: Simplify 0 into 0 1546593435.778 * [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)))))) 1546593435.779 * [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)))))) 1546593435.781 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.782 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593435.785 * [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 1546593435.785 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.786 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593435.786 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.786 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.786 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.787 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546593435.788 * [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 1546593435.789 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1546593435.789 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546593435.789 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.789 * [misc]backup-simplify: Simplify 0 into 0 1546593435.789 * [misc]backup-simplify: Simplify 0 into 0 1546593435.789 * [misc]backup-simplify: Simplify 0 into 0 1546593435.790 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593435.791 * [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)))))) 1546593435.791 * [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)))))) 1546593435.792 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.793 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593435.797 * [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 1546593435.798 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.798 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593435.798 * [misc]backup-simplify: Simplify (- 0) into 0 1546593435.798 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.799 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593435.799 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546593435.801 * [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 1546593435.802 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1546593435.802 * [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 1546593435.802 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.802 * [misc]backup-simplify: Simplify 0 into 0 1546593435.802 * [misc]backup-simplify: Simplify 0 into 0 1546593435.802 * [misc]backup-simplify: Simplify 0 into 0 1546593435.802 * [misc]backup-simplify: Simplify 0 into 0 1546593435.803 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593435.804 * [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)))))) 1546593435.804 * [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)))))) 1546593435.806 * [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)))))))) 1546593435.806 * [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))) 1546593435.806 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1546593435.806 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.806 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.806 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of k in k 1546593435.806 * [misc]backup-simplify: Simplify 0 into 0 1546593435.806 * [misc]backup-simplify: Simplify 1 into 1 1546593435.806 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.806 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.806 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.806 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of -2 in k 1546593435.806 * [misc]backup-simplify: Simplify -2 into -2 1546593435.806 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593435.806 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.806 * [misc]backup-simplify: Simplify PI into PI 1546593435.806 * [misc]taylor: Taking taylor expansion of n in k 1546593435.806 * [misc]backup-simplify: Simplify n into n 1546593435.806 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593435.806 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593435.806 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593435.807 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593435.807 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593435.807 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593435.807 * [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))) 1546593435.807 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593435.807 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593435.807 * [misc]taylor: Taking taylor expansion of -1 in k 1546593435.807 * [misc]backup-simplify: Simplify -1 into -1 1546593435.807 * [misc]taylor: Taking taylor expansion of k in k 1546593435.807 * [misc]backup-simplify: Simplify 0 into 0 1546593435.807 * [misc]backup-simplify: Simplify 1 into 1 1546593435.807 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593435.807 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593435.808 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593435.808 * [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)))) 1546593435.808 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.808 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.808 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of k in n 1546593435.808 * [misc]backup-simplify: Simplify k into k 1546593435.808 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.808 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.808 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.808 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of -2 in n 1546593435.808 * [misc]backup-simplify: Simplify -2 into -2 1546593435.808 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.808 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.808 * [misc]backup-simplify: Simplify PI into PI 1546593435.808 * [misc]taylor: Taking taylor expansion of n in n 1546593435.808 * [misc]backup-simplify: Simplify 0 into 0 1546593435.808 * [misc]backup-simplify: Simplify 1 into 1 1546593435.808 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.809 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593435.809 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593435.809 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593435.809 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593435.809 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.810 * [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))) 1546593435.810 * [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)))) 1546593435.810 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546593435.810 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546593435.810 * [misc]taylor: Taking taylor expansion of -1 in n 1546593435.810 * [misc]backup-simplify: Simplify -1 into -1 1546593435.810 * [misc]taylor: Taking taylor expansion of k in n 1546593435.810 * [misc]backup-simplify: Simplify k into k 1546593435.810 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546593435.810 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546593435.811 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546593435.811 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546593435.811 * [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))) 1546593435.811 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.811 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.811 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of k in n 1546593435.811 * [misc]backup-simplify: Simplify k into k 1546593435.811 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593435.811 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593435.811 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.811 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of -2 in n 1546593435.811 * [misc]backup-simplify: Simplify -2 into -2 1546593435.811 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593435.811 * [misc]taylor: Taking taylor expansion of PI in n 1546593435.812 * [misc]backup-simplify: Simplify PI into PI 1546593435.812 * [misc]taylor: Taking taylor expansion of n in n 1546593435.812 * [misc]backup-simplify: Simplify 0 into 0 1546593435.812 * [misc]backup-simplify: Simplify 1 into 1 1546593435.812 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593435.812 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593435.812 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593435.812 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593435.812 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593435.813 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.813 * [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))) 1546593435.814 * [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)))) 1546593435.814 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546593435.814 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546593435.814 * [misc]taylor: Taking taylor expansion of -1 in n 1546593435.814 * [misc]backup-simplify: Simplify -1 into -1 1546593435.814 * [misc]taylor: Taking taylor expansion of k in n 1546593435.814 * [misc]backup-simplify: Simplify k into k 1546593435.814 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546593435.814 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546593435.814 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546593435.814 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546593435.814 * [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))) 1546593435.814 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.815 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.815 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of k in k 1546593435.815 * [misc]backup-simplify: Simplify 0 into 0 1546593435.815 * [misc]backup-simplify: Simplify 1 into 1 1546593435.815 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593435.815 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593435.815 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593435.815 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546593435.815 * [misc]taylor: Taking taylor expansion of -2 in k 1546593435.815 * [misc]backup-simplify: Simplify -2 into -2 1546593435.815 * [misc]taylor: Taking taylor expansion of PI in k 1546593435.815 * [misc]backup-simplify: Simplify PI into PI 1546593435.815 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593435.816 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593435.816 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593435.816 * [misc]taylor: Taking taylor expansion of n in k 1546593435.816 * [misc]backup-simplify: Simplify n into n 1546593435.816 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593435.816 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593435.816 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593435.816 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593435.817 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546593435.817 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546593435.818 * [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)))) 1546593435.818 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593435.818 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593435.818 * [misc]taylor: Taking taylor expansion of -1 in k 1546593435.818 * [misc]backup-simplify: Simplify -1 into -1 1546593435.818 * [misc]taylor: Taking taylor expansion of k in k 1546593435.818 * [misc]backup-simplify: Simplify 0 into 0 1546593435.818 * [misc]backup-simplify: Simplify 1 into 1 1546593435.818 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593435.818 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593435.819 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593435.820 * [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))))) 1546593435.820 * [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))))) 1546593435.821 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593435.822 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593435.825 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593435.825 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593435.825 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593435.825 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.826 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.827 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546593435.829 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593435.830 * [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 1546593435.830 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.830 * [misc]backup-simplify: Simplify 0 into 0 1546593435.830 * [misc]backup-simplify: Simplify 0 into 0 1546593435.830 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593435.831 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593435.832 * [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)))))) 1546593435.833 * [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)))))) 1546593435.835 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.836 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593435.841 * [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 1546593435.841 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.842 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593435.842 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593435.842 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593435.843 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546593435.846 * [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 1546593435.846 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593435.847 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1546593435.848 * [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 1546593435.848 * [misc]taylor: Taking taylor expansion of 0 in k 1546593435.848 * [misc]backup-simplify: Simplify 0 into 0 1546593435.848 * [misc]backup-simplify: Simplify 0 into 0 1546593435.848 * [misc]backup-simplify: Simplify 0 into 0 1546593435.848 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593435.849 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593435.851 * [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)))))) 1546593435.852 * [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)))))) 1546593435.854 * [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))))))))))) 1546593435.855 * * * [misc]progress: simplifying candidates 1546593435.855 * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # 1546593435.855 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546593435.855 * * [misc]simplify: iters left: 6 (11 enodes) 1546593435.859 * * [misc]simplify: iters left: 5 (21 enodes) 1546593435.865 * * [misc]simplify: iters left: 4 (47 enodes) 1546593435.878 * * [misc]simplify: iters left: 3 (109 enodes) 1546593435.902 * * [misc]simplify: iters left: 2 (300 enodes) 1546593436.117 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546593436.118 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1546593436.118 * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # 1546593436.118 * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # 1546593436.118 * [enter]simplify: Simplifying (* PI (* n 2)) 1546593436.118 * * [misc]simplify: iters left: 4 (5 enodes) 1546593436.120 * * [misc]simplify: iters left: 3 (9 enodes) 1546593436.122 * * [misc]simplify: iters left: 2 (15 enodes) 1546593436.126 * * [misc]simplify: iters left: 1 (17 enodes) 1546593436.130 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546593436.130 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1546593436.131 * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # 1546593436.131 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546593436.131 * * [misc]simplify: iters left: 5 (8 enodes) 1546593436.133 * * [misc]simplify: iters left: 4 (12 enodes) 1546593436.137 * * [misc]simplify: iters left: 3 (18 enodes) 1546593436.140 * * [misc]simplify: iters left: 2 (20 enodes) 1546593436.143 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546593436.143 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1546593436.143 * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # 1546593436.143 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546593436.143 * * [misc]simplify: iters left: 5 (6 enodes) 1546593436.144 * * [misc]simplify: iters left: 4 (8 enodes) 1546593436.145 * * [misc]simplify: iters left: 3 (11 enodes) 1546593436.149 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546593436.149 * [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))) 1546593436.149 * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # 1546593436.149 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546593436.149 * * [misc]simplify: iters left: 5 (6 enodes) 1546593436.150 * * [misc]simplify: iters left: 4 (8 enodes) 1546593436.151 * * [misc]simplify: iters left: 3 (11 enodes) 1546593436.152 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546593436.152 * [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))) 1546593436.152 * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # 1546593436.153 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546593436.153 * * [misc]simplify: iters left: 4 (5 enodes) 1546593436.154 * * [misc]simplify: iters left: 3 (7 enodes) 1546593436.155 * * [misc]simplify: iters left: 2 (10 enodes) 1546593436.156 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546593436.156 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1546593436.156 * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # 1546593436.157 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546593436.157 * * [misc]simplify: iters left: 5 (9 enodes) 1546593436.158 * * [misc]simplify: iters left: 4 (15 enodes) 1546593436.160 * * [misc]simplify: iters left: 3 (21 enodes) 1546593436.163 * * [misc]simplify: iters left: 2 (22 enodes) 1546593436.165 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546593436.166 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1546593436.166 * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # 1546593436.166 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546593436.166 * * [misc]simplify: iters left: 5 (9 enodes) 1546593436.167 * * [misc]simplify: iters left: 4 (15 enodes) 1546593436.169 * * [misc]simplify: iters left: 3 (21 enodes) 1546593436.172 * * [misc]simplify: iters left: 2 (22 enodes) 1546593436.175 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546593436.175 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1546593436.175 * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # 1546593436.175 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546593436.175 * * [misc]simplify: iters left: 5 (7 enodes) 1546593436.176 * * [misc]simplify: iters left: 4 (9 enodes) 1546593436.177 * * [misc]simplify: iters left: 3 (12 enodes) 1546593436.179 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546593436.179 * [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))) 1546593436.179 * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # 1546593436.179 * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # 1546593436.180 * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # 1546593436.180 * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # 1546593436.180 * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # 1546593436.180 * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # 1546593436.180 * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # 1546593436.180 * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # 1546593436.180 * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # 1546593436.180 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546593436.180 * * [misc]simplify: iters left: 6 (14 enodes) 1546593436.182 * * [misc]simplify: iters left: 5 (26 enodes) 1546593436.186 * * [misc]simplify: iters left: 4 (53 enodes) 1546593436.197 * * [misc]simplify: iters left: 3 (137 enodes) 1546593436.279 * * [misc]simplify: iters left: 2 (487 enodes) 1546593436.784 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1546593436.784 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1546593436.784 * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # 1546593436.784 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546593436.784 * * [misc]simplify: iters left: 6 (14 enodes) 1546593436.786 * * [misc]simplify: iters left: 5 (26 enodes) 1546593436.790 * * [misc]simplify: iters left: 4 (53 enodes) 1546593436.801 * * [misc]simplify: iters left: 3 (137 enodes) 1546593436.884 * * [misc]simplify: iters left: 2 (487 enodes) 1546593437.418 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1546593437.418 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1546593437.418 * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # 1546593437.418 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1546593437.418 * * [misc]simplify: iters left: 6 (14 enodes) 1546593437.423 * * [misc]simplify: iters left: 5 (24 enodes) 1546593437.430 * * [misc]simplify: iters left: 4 (42 enodes) 1546593437.442 * * [misc]simplify: iters left: 3 (71 enodes) 1546593437.472 * * [misc]simplify: iters left: 2 (208 enodes) 1546593437.646 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546593437.646 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546593437.646 * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # 1546593437.646 * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # 1546593437.646 * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # 1546593437.647 * [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))) 1546593437.647 * * [misc]simplify: iters left: 6 (16 enodes) 1546593437.649 * * [misc]simplify: iters left: 5 (31 enodes) 1546593437.654 * * [misc]simplify: iters left: 4 (67 enodes) 1546593437.665 * * [misc]simplify: iters left: 3 (124 enodes) 1546593437.689 * * [misc]simplify: iters left: 2 (195 enodes) 1546593437.770 * * [misc]simplify: iters left: 1 (309 enodes) 1546593437.913 * [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)))) 1546593437.914 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))))) 1546593437.914 * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # 1546593437.914 * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # 1546593437.914 * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # 1546593437.914 * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # 1546593437.914 * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # 1546593437.914 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593437.914 * * [misc]simplify: iters left: 6 (12 enodes) 1546593437.917 * * [misc]simplify: iters left: 5 (19 enodes) 1546593437.922 * * [misc]simplify: iters left: 4 (25 enodes) 1546593437.926 * * [misc]simplify: iters left: 3 (26 enodes) 1546593437.929 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593437.929 * [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))))) 1546593437.929 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1546593437.929 * * [misc]simplify: iters left: 6 (12 enodes) 1546593437.931 * * [misc]simplify: iters left: 5 (18 enodes) 1546593437.934 * * [misc]simplify: iters left: 4 (24 enodes) 1546593437.938 * * [misc]simplify: iters left: 3 (25 enodes) 1546593437.941 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1546593437.941 * [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))))) 1546593437.941 * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # 1546593437.942 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1546593437.942 * * [misc]simplify: iters left: 6 (11 enodes) 1546593437.944 * * [misc]simplify: iters left: 5 (16 enodes) 1546593437.946 * * [misc]simplify: iters left: 4 (22 enodes) 1546593437.950 * * [misc]simplify: iters left: 3 (24 enodes) 1546593437.956 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1546593437.956 * [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))))) 1546593437.956 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546593437.956 * * [misc]simplify: iters left: 6 (12 enodes) 1546593437.960 * * [misc]simplify: iters left: 5 (18 enodes) 1546593437.965 * * [misc]simplify: iters left: 4 (24 enodes) 1546593437.971 * * [misc]simplify: iters left: 3 (25 enodes) 1546593437.978 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546593437.978 * [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))))) 1546593437.978 * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # 1546593437.978 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546593437.978 * * [misc]simplify: iters left: 6 (9 enodes) 1546593437.981 * * [misc]simplify: iters left: 5 (16 enodes) 1546593437.986 * * [misc]simplify: iters left: 4 (24 enodes) 1546593437.992 * * [misc]simplify: iters left: 3 (26 enodes) 1546593437.998 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546593437.998 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1546593437.998 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1546593437.998 * * [misc]simplify: iters left: 6 (11 enodes) 1546593438.002 * * [misc]simplify: iters left: 5 (17 enodes) 1546593438.006 * * [misc]simplify: iters left: 4 (23 enodes) 1546593438.013 * * [misc]simplify: iters left: 3 (24 enodes) 1546593438.019 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1546593438.019 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1546593438.019 * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # 1546593438.019 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593438.019 * * [misc]simplify: iters left: 6 (12 enodes) 1546593438.023 * * [misc]simplify: iters left: 5 (19 enodes) 1546593438.028 * * [misc]simplify: iters left: 4 (25 enodes) 1546593438.035 * * [misc]simplify: iters left: 3 (26 enodes) 1546593438.041 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593438.041 * [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))))) 1546593438.041 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1546593438.042 * * [misc]simplify: iters left: 6 (12 enodes) 1546593438.045 * * [misc]simplify: iters left: 5 (18 enodes) 1546593438.050 * * [misc]simplify: iters left: 4 (24 enodes) 1546593438.057 * * [misc]simplify: iters left: 3 (25 enodes) 1546593438.063 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1546593438.063 * [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))))) 1546593438.063 * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # 1546593438.064 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1546593438.064 * * [misc]simplify: iters left: 6 (11 enodes) 1546593438.067 * * [misc]simplify: iters left: 5 (16 enodes) 1546593438.071 * * [misc]simplify: iters left: 4 (22 enodes) 1546593438.077 * * [misc]simplify: iters left: 3 (24 enodes) 1546593438.084 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1546593438.084 * [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))))) 1546593438.085 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546593438.085 * * [misc]simplify: iters left: 6 (12 enodes) 1546593438.088 * * [misc]simplify: iters left: 5 (18 enodes) 1546593438.094 * * [misc]simplify: iters left: 4 (24 enodes) 1546593438.099 * * [misc]simplify: iters left: 3 (25 enodes) 1546593438.105 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546593438.105 * [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))))) 1546593438.105 * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # 1546593438.106 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546593438.106 * * [misc]simplify: iters left: 6 (9 enodes) 1546593438.109 * * [misc]simplify: iters left: 5 (16 enodes) 1546593438.113 * * [misc]simplify: iters left: 4 (24 enodes) 1546593438.119 * * [misc]simplify: iters left: 3 (26 enodes) 1546593438.124 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546593438.124 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1546593438.124 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1546593438.125 * * [misc]simplify: iters left: 6 (11 enodes) 1546593438.128 * * [misc]simplify: iters left: 5 (17 enodes) 1546593438.133 * * [misc]simplify: iters left: 4 (23 enodes) 1546593438.138 * * [misc]simplify: iters left: 3 (24 enodes) 1546593438.144 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1546593438.144 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1546593438.144 * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # 1546593438.145 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593438.145 * * [misc]simplify: iters left: 6 (11 enodes) 1546593438.148 * * [misc]simplify: iters left: 5 (15 enodes) 1546593438.152 * * [misc]simplify: iters left: 4 (18 enodes) 1546593438.157 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593438.157 * [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))))) 1546593438.158 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546593438.158 * * [misc]simplify: iters left: 6 (11 enodes) 1546593438.161 * * [misc]simplify: iters left: 5 (14 enodes) 1546593438.165 * * [misc]simplify: iters left: 4 (17 enodes) 1546593438.169 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546593438.169 * [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))))) 1546593438.170 * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # 1546593438.170 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593438.170 * * [misc]simplify: iters left: 6 (10 enodes) 1546593438.173 * * [misc]simplify: iters left: 5 (12 enodes) 1546593438.176 * * [misc]simplify: iters left: 4 (15 enodes) 1546593438.180 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593438.180 * [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))))) 1546593438.181 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593438.181 * * [misc]simplify: iters left: 6 (11 enodes) 1546593438.184 * * [misc]simplify: iters left: 5 (14 enodes) 1546593438.188 * * [misc]simplify: iters left: 4 (17 enodes) 1546593438.193 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593438.193 * [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))))) 1546593438.193 * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # 1546593438.193 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1546593438.193 * * [misc]simplify: iters left: 6 (9 enodes) 1546593438.196 * * [misc]simplify: iters left: 5 (13 enodes) 1546593438.200 * * [misc]simplify: iters left: 4 (18 enodes) 1546593438.205 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546593438.205 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546593438.205 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546593438.205 * * [misc]simplify: iters left: 6 (10 enodes) 1546593438.208 * * [misc]simplify: iters left: 5 (13 enodes) 1546593438.212 * * [misc]simplify: iters left: 4 (16 enodes) 1546593438.216 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546593438.216 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546593438.216 * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # 1546593438.217 * [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)))) 1546593438.217 * * [misc]simplify: iters left: 6 (16 enodes) 1546593438.222 * * [misc]simplify: iters left: 5 (28 enodes) 1546593438.232 * * [misc]simplify: iters left: 4 (46 enodes) 1546593438.240 * * [misc]simplify: iters left: 3 (50 enodes) 1546593438.246 * * [misc]simplify: iters left: 2 (53 enodes) 1546593438.252 * [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)))) 1546593438.253 * [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))))) 1546593438.253 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546593438.253 * * [misc]simplify: iters left: 6 (14 enodes) 1546593438.255 * * [misc]simplify: iters left: 5 (20 enodes) 1546593438.258 * * [misc]simplify: iters left: 4 (29 enodes) 1546593438.262 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.268 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546593438.268 * [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))))) 1546593438.268 * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # 1546593438.269 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1546593438.269 * * [misc]simplify: iters left: 6 (15 enodes) 1546593438.273 * * [misc]simplify: iters left: 5 (23 enodes) 1546593438.280 * * [misc]simplify: iters left: 4 (34 enodes) 1546593438.288 * * [misc]simplify: iters left: 3 (37 enodes) 1546593438.293 * [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)))))) 1546593438.293 * [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))))) 1546593438.293 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593438.293 * * [misc]simplify: iters left: 6 (14 enodes) 1546593438.295 * * [misc]simplify: iters left: 5 (20 enodes) 1546593438.298 * * [misc]simplify: iters left: 4 (29 enodes) 1546593438.302 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.306 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593438.306 * [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))))) 1546593438.306 * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # 1546593438.306 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1546593438.306 * * [misc]simplify: iters left: 6 (14 enodes) 1546593438.308 * * [misc]simplify: iters left: 5 (24 enodes) 1546593438.312 * * [misc]simplify: iters left: 4 (39 enodes) 1546593438.319 * * [misc]simplify: iters left: 3 (54 enodes) 1546593438.334 * * [misc]simplify: iters left: 2 (80 enodes) 1546593438.354 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1546593438.354 * [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)))) 1546593438.354 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1546593438.354 * * [misc]simplify: iters left: 6 (13 enodes) 1546593438.358 * * [misc]simplify: iters left: 5 (19 enodes) 1546593438.364 * * [misc]simplify: iters left: 4 (28 enodes) 1546593438.371 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.375 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1546593438.375 * [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)))) 1546593438.375 * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # 1546593438.376 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593438.376 * * [misc]simplify: iters left: 6 (15 enodes) 1546593438.378 * * [misc]simplify: iters left: 5 (23 enodes) 1546593438.381 * * [misc]simplify: iters left: 4 (32 enodes) 1546593438.385 * * [misc]simplify: iters left: 3 (34 enodes) 1546593438.390 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593438.390 * [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))))) 1546593438.390 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546593438.390 * * [misc]simplify: iters left: 6 (14 enodes) 1546593438.392 * * [misc]simplify: iters left: 5 (20 enodes) 1546593438.395 * * [misc]simplify: iters left: 4 (29 enodes) 1546593438.399 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.407 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546593438.407 * [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))))) 1546593438.407 * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # 1546593438.407 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593438.407 * * [misc]simplify: iters left: 6 (14 enodes) 1546593438.409 * * [misc]simplify: iters left: 5 (20 enodes) 1546593438.412 * * [misc]simplify: iters left: 4 (29 enodes) 1546593438.416 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.420 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593438.420 * [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))))) 1546593438.420 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593438.420 * * [misc]simplify: iters left: 6 (14 enodes) 1546593438.422 * * [misc]simplify: iters left: 5 (20 enodes) 1546593438.425 * * [misc]simplify: iters left: 4 (29 enodes) 1546593438.430 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.433 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593438.433 * [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))))) 1546593438.434 * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # 1546593438.434 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1546593438.434 * * [misc]simplify: iters left: 6 (13 enodes) 1546593438.436 * * [misc]simplify: iters left: 5 (21 enodes) 1546593438.439 * * [misc]simplify: iters left: 4 (32 enodes) 1546593438.447 * * [misc]simplify: iters left: 3 (33 enodes) 1546593438.454 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1546593438.454 * [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)))) 1546593438.454 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1546593438.454 * * [misc]simplify: iters left: 6 (13 enodes) 1546593438.457 * * [misc]simplify: iters left: 5 (19 enodes) 1546593438.459 * * [misc]simplify: iters left: 4 (28 enodes) 1546593438.463 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.467 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1546593438.467 * [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)))) 1546593438.467 * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # 1546593438.467 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593438.467 * * [misc]simplify: iters left: 6 (6 enodes) 1546593438.468 * * [misc]simplify: iters left: 5 (10 enodes) 1546593438.470 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1546593438.470 * [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))))) 1546593438.470 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546593438.470 * * [misc]simplify: iters left: 6 (13 enodes) 1546593438.472 * * [misc]simplify: iters left: 5 (19 enodes) 1546593438.475 * * [misc]simplify: iters left: 4 (28 enodes) 1546593438.478 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.482 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546593438.482 * [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))))) 1546593438.482 * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # 1546593438.482 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1546593438.482 * * [misc]simplify: iters left: 4 (5 enodes) 1546593438.483 * * [misc]simplify: iters left: 3 (7 enodes) 1546593438.485 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1546593438.485 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546593438.485 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593438.485 * * [misc]simplify: iters left: 6 (13 enodes) 1546593438.489 * * [misc]simplify: iters left: 5 (19 enodes) 1546593438.494 * * [misc]simplify: iters left: 4 (28 enodes) 1546593438.501 * * [misc]simplify: iters left: 3 (30 enodes) 1546593438.505 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593438.505 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546593438.505 * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # 1546593438.505 * [enter]simplify: Simplifying (/ 1 1) 1546593438.505 * * [misc]simplify: iters left: 2 (2 enodes) 1546593438.505 * * [misc]simplify: iters left: 1 (4 enodes) 1546593438.506 * [exit]simplify: Simplified to 1 1546593438.506 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546593438.506 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546593438.506 * * [misc]simplify: iters left: 6 (12 enodes) 1546593438.508 * * [misc]simplify: iters left: 5 (18 enodes) 1546593438.510 * * [misc]simplify: iters left: 4 (27 enodes) 1546593438.514 * * [misc]simplify: iters left: 3 (29 enodes) 1546593438.517 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1546593438.518 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546593438.518 * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # 1546593438.518 * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # 1546593438.518 * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # 1546593438.518 * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # 1546593438.518 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1546593438.518 * * [misc]simplify: iters left: 2 (3 enodes) 1546593438.518 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1546593438.518 * [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)))) 1546593438.518 * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # 1546593438.519 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546593438.519 * * [misc]simplify: iters left: 2 (3 enodes) 1546593438.520 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546593438.520 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1546593438.520 * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # 1546593438.520 * [enter]simplify: Simplifying (sqrt k) 1546593438.520 * * [misc]simplify: iters left: 1 (2 enodes) 1546593438.520 * [exit]simplify: Simplified to (sqrt k) 1546593438.520 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1546593438.520 * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # 1546593438.520 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546593438.521 * * [misc]simplify: iters left: 5 (7 enodes) 1546593438.522 * * [misc]simplify: iters left: 4 (12 enodes) 1546593438.523 * * [misc]simplify: iters left: 3 (18 enodes) 1546593438.526 * * [misc]simplify: iters left: 2 (20 enodes) 1546593438.528 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546593438.528 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1546593438.528 * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # 1546593438.529 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546593438.529 * * [misc]simplify: iters left: 5 (7 enodes) 1546593438.531 * * [misc]simplify: iters left: 4 (12 enodes) 1546593438.534 * * [misc]simplify: iters left: 3 (18 enodes) 1546593438.538 * * [misc]simplify: iters left: 2 (20 enodes) 1546593438.542 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546593438.542 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1546593438.542 * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # 1546593438.542 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546593438.542 * * [misc]simplify: iters left: 5 (7 enodes) 1546593438.544 * * [misc]simplify: iters left: 4 (9 enodes) 1546593438.545 * * [misc]simplify: iters left: 3 (12 enodes) 1546593438.547 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546593438.547 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546593438.547 * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # 1546593438.547 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593438.547 * * [misc]simplify: iters left: 6 (12 enodes) 1546593438.549 * * [misc]simplify: iters left: 5 (18 enodes) 1546593438.552 * * [misc]simplify: iters left: 4 (27 enodes) 1546593438.555 * * [misc]simplify: iters left: 3 (29 enodes) 1546593438.559 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593438.559 * [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))))))) 1546593438.559 * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # 1546593438.559 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593438.559 * * [misc]simplify: iters left: 6 (11 enodes) 1546593438.561 * * [misc]simplify: iters left: 5 (17 enodes) 1546593438.563 * * [misc]simplify: iters left: 4 (26 enodes) 1546593438.567 * * [misc]simplify: iters left: 3 (27 enodes) 1546593438.570 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546593438.570 * [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))))))) 1546593438.570 * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # 1546593438.570 * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # 1546593438.570 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546593438.571 * * [misc]simplify: iters left: 5 (7 enodes) 1546593438.572 * * [misc]simplify: iters left: 4 (12 enodes) 1546593438.575 * * [misc]simplify: iters left: 3 (18 enodes) 1546593438.580 * * [misc]simplify: iters left: 2 (20 enodes) 1546593438.584 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546593438.584 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1546593438.584 * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # 1546593438.588 * [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))))) 1546593438.588 * * [misc]simplify: iters left: 6 (37 enodes) 1546593438.603 * * [misc]simplify: iters left: 5 (105 enodes) 1546593438.629 * * [misc]simplify: iters left: 4 (339 enodes) 1546593438.869 * [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))))) 1546593438.869 * [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))) 1546593438.870 * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # 1546593438.870 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546593438.870 * * [misc]simplify: iters left: 6 (15 enodes) 1546593438.876 * * [misc]simplify: iters left: 5 (33 enodes) 1546593438.886 * * [misc]simplify: iters left: 4 (64 enodes) 1546593438.901 * * [misc]simplify: iters left: 3 (171 enodes) 1546593438.996 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546593438.996 * [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))) 1546593438.996 * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # 1546593438.996 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546593438.996 * * [misc]simplify: iters left: 6 (15 enodes) 1546593439.002 * * [misc]simplify: iters left: 5 (30 enodes) 1546593439.012 * * [misc]simplify: iters left: 4 (65 enodes) 1546593439.037 * * [misc]simplify: iters left: 3 (200 enodes) 1546593439.143 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546593439.143 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1546593439.143 * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # 1546593439.143 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593439.143 * * [misc]simplify: iters left: 4 (5 enodes) 1546593439.145 * * [misc]simplify: iters left: 3 (9 enodes) 1546593439.148 * * [misc]simplify: iters left: 2 (15 enodes) 1546593439.152 * * [misc]simplify: iters left: 1 (17 enodes) 1546593439.156 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593439.156 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546593439.156 * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # 1546593439.156 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593439.156 * * [misc]simplify: iters left: 4 (5 enodes) 1546593439.158 * * [misc]simplify: iters left: 3 (9 enodes) 1546593439.161 * * [misc]simplify: iters left: 2 (15 enodes) 1546593439.164 * * [misc]simplify: iters left: 1 (17 enodes) 1546593439.168 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593439.169 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546593439.169 * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # 1546593439.169 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593439.169 * * [misc]simplify: iters left: 4 (5 enodes) 1546593439.171 * * [misc]simplify: iters left: 3 (9 enodes) 1546593439.173 * * [misc]simplify: iters left: 2 (15 enodes) 1546593439.176 * * [misc]simplify: iters left: 1 (17 enodes) 1546593439.181 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593439.182 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546593439.182 * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # 1546593439.182 * [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)))))))))))))))))))))) 1546593439.182 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593439.182 * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # 1546593439.182 * [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)))))))) 1546593439.182 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593439.182 * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # 1546593439.182 * [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))))))))))) 1546593439.182 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593439.182 * * * [misc]progress: adding candidates to table 1546593439.974 * * [misc]progress: iteration 2 / 4 1546593439.974 * * * [misc]progress: picking best candidate 1546593440.001 * * * * [misc]pick: Picked # 1546593440.001 * * * [misc]progress: localizing error 1546593440.011 * * * [misc]progress: generating rewritten candidates 1546593440.011 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2) 1546593440.015 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1) 1546593440.017 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1546593440.025 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1546593440.032 * * * [misc]progress: generating series expansions 1546593440.032 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2) 1546593440.032 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546593440.032 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546593440.032 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593440.032 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593440.032 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593440.032 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593440.032 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.032 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.032 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593440.032 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.032 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.032 * [misc]taylor: Taking taylor expansion of k in k 1546593440.032 * [misc]backup-simplify: Simplify 0 into 0 1546593440.032 * [misc]backup-simplify: Simplify 1 into 1 1546593440.032 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593440.032 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593440.032 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.032 * [misc]backup-simplify: Simplify 2 into 2 1546593440.032 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593440.032 * [misc]taylor: Taking taylor expansion of n in k 1546593440.032 * [misc]backup-simplify: Simplify n into n 1546593440.032 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.032 * [misc]backup-simplify: Simplify PI into PI 1546593440.032 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593440.032 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593440.033 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593440.033 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593440.033 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.033 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.033 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593440.033 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593440.033 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593440.033 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593440.033 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593440.033 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593440.033 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.033 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.033 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593440.033 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.033 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.033 * [misc]taylor: Taking taylor expansion of k in n 1546593440.033 * [misc]backup-simplify: Simplify k into k 1546593440.033 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593440.033 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.033 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.033 * [misc]backup-simplify: Simplify 2 into 2 1546593440.033 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.034 * [misc]taylor: Taking taylor expansion of n in n 1546593440.034 * [misc]backup-simplify: Simplify 0 into 0 1546593440.034 * [misc]backup-simplify: Simplify 1 into 1 1546593440.034 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.034 * [misc]backup-simplify: Simplify PI into PI 1546593440.034 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.034 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.034 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.035 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.035 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.035 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593440.035 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593440.035 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593440.036 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.036 * [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)))) 1546593440.037 * [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))))) 1546593440.037 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593440.037 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593440.037 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593440.037 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593440.037 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.037 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.037 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593440.037 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.037 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.037 * [misc]taylor: Taking taylor expansion of k in n 1546593440.037 * [misc]backup-simplify: Simplify k into k 1546593440.037 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593440.037 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.037 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.037 * [misc]backup-simplify: Simplify 2 into 2 1546593440.037 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.037 * [misc]taylor: Taking taylor expansion of n in n 1546593440.037 * [misc]backup-simplify: Simplify 0 into 0 1546593440.037 * [misc]backup-simplify: Simplify 1 into 1 1546593440.037 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.037 * [misc]backup-simplify: Simplify PI into PI 1546593440.037 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.037 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.038 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.038 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.038 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.038 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593440.038 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593440.038 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593440.039 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.039 * [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)))) 1546593440.040 * [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))))) 1546593440.040 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546593440.040 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546593440.040 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593440.040 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.040 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.040 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593440.040 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.040 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.040 * [misc]taylor: Taking taylor expansion of k in k 1546593440.040 * [misc]backup-simplify: Simplify 0 into 0 1546593440.040 * [misc]backup-simplify: Simplify 1 into 1 1546593440.040 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546593440.040 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593440.040 * [misc]taylor: Taking taylor expansion of n in k 1546593440.040 * [misc]backup-simplify: Simplify n into n 1546593440.040 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593440.040 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593440.040 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593440.040 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.040 * [misc]backup-simplify: Simplify 2 into 2 1546593440.040 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.040 * [misc]backup-simplify: Simplify PI into PI 1546593440.040 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.041 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.041 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593440.041 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.041 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.041 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.041 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546593440.042 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593440.042 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593440.043 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593440.043 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593440.045 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593440.045 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546593440.045 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.045 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.046 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.046 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546593440.047 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593440.047 * [misc]taylor: Taking taylor expansion of 0 in k 1546593440.047 * [misc]backup-simplify: Simplify 0 into 0 1546593440.047 * [misc]backup-simplify: Simplify 0 into 0 1546593440.048 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546593440.048 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593440.050 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593440.050 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.050 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593440.050 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.050 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.053 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546593440.055 * [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))))))) 1546593440.055 * [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))))))) 1546593440.056 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593440.057 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593440.060 * [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 1546593440.060 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546593440.060 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.060 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.061 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.061 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593440.063 * [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 1546593440.063 * [misc]taylor: Taking taylor expansion of 0 in k 1546593440.063 * [misc]backup-simplify: Simplify 0 into 0 1546593440.063 * [misc]backup-simplify: Simplify 0 into 0 1546593440.063 * [misc]backup-simplify: Simplify 0 into 0 1546593440.064 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546593440.065 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593440.069 * [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 1546593440.069 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.069 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593440.069 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.069 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.070 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593440.071 * [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))))) 1546593440.073 * [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))))) 1546593440.076 * [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))))) 1546593440.076 * [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)))) 1546593440.076 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546593440.076 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.076 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.076 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.076 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.076 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of k in k 1546593440.076 * [misc]backup-simplify: Simplify 0 into 0 1546593440.076 * [misc]backup-simplify: Simplify 1 into 1 1546593440.076 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.076 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.076 * [misc]backup-simplify: Simplify 2 into 2 1546593440.076 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.076 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.076 * [misc]backup-simplify: Simplify PI into PI 1546593440.076 * [misc]taylor: Taking taylor expansion of n in k 1546593440.076 * [misc]backup-simplify: Simplify n into n 1546593440.076 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.077 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593440.077 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593440.077 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.077 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.077 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.077 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593440.077 * [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)))) 1546593440.077 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.077 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.077 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.077 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.077 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of k in n 1546593440.077 * [misc]backup-simplify: Simplify k into k 1546593440.077 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.077 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.077 * [misc]backup-simplify: Simplify 2 into 2 1546593440.077 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.077 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.077 * [misc]backup-simplify: Simplify PI into PI 1546593440.078 * [misc]taylor: Taking taylor expansion of n in n 1546593440.078 * [misc]backup-simplify: Simplify 0 into 0 1546593440.078 * [misc]backup-simplify: Simplify 1 into 1 1546593440.078 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.078 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.078 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.078 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.078 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.078 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.079 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.079 * [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))) 1546593440.080 * [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)))) 1546593440.080 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.080 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.080 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.080 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.080 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of k in n 1546593440.080 * [misc]backup-simplify: Simplify k into k 1546593440.080 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.080 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.080 * [misc]backup-simplify: Simplify 2 into 2 1546593440.080 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.080 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.080 * [misc]backup-simplify: Simplify PI into PI 1546593440.080 * [misc]taylor: Taking taylor expansion of n in n 1546593440.080 * [misc]backup-simplify: Simplify 0 into 0 1546593440.080 * [misc]backup-simplify: Simplify 1 into 1 1546593440.080 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.080 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.081 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.081 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.081 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.081 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.081 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.082 * [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))) 1546593440.082 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1546593440.082 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546593440.082 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546593440.082 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593440.082 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.082 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.082 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.082 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.082 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.082 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.082 * [misc]taylor: Taking taylor expansion of k in k 1546593440.082 * [misc]backup-simplify: Simplify 0 into 0 1546593440.082 * [misc]backup-simplify: Simplify 1 into 1 1546593440.082 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.082 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546593440.082 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593440.082 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593440.082 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.083 * [misc]backup-simplify: Simplify 2 into 2 1546593440.083 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.083 * [misc]backup-simplify: Simplify PI into PI 1546593440.083 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.083 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.083 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593440.083 * [misc]taylor: Taking taylor expansion of n in k 1546593440.083 * [misc]backup-simplify: Simplify n into n 1546593440.083 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593440.083 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.083 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.083 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.083 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593440.084 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546593440.084 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546593440.085 * [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)))) 1546593440.085 * [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)))) 1546593440.086 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593440.086 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593440.088 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593440.088 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593440.088 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593440.088 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.088 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.088 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.089 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593440.090 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593440.090 * [misc]taylor: Taking taylor expansion of 0 in k 1546593440.090 * [misc]backup-simplify: Simplify 0 into 0 1546593440.090 * [misc]backup-simplify: Simplify 0 into 0 1546593440.090 * [misc]backup-simplify: Simplify 0 into 0 1546593440.091 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.091 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593440.094 * [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 1546593440.094 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593440.095 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593440.095 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.095 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.095 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.096 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546593440.097 * [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 1546593440.097 * [misc]taylor: Taking taylor expansion of 0 in k 1546593440.097 * [misc]backup-simplify: Simplify 0 into 0 1546593440.097 * [misc]backup-simplify: Simplify 0 into 0 1546593440.097 * [misc]backup-simplify: Simplify 0 into 0 1546593440.097 * [misc]backup-simplify: Simplify 0 into 0 1546593440.098 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.099 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593440.104 * [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 1546593440.104 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593440.104 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593440.104 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.104 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.105 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.105 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546593440.108 * [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 1546593440.108 * [misc]taylor: Taking taylor expansion of 0 in k 1546593440.108 * [misc]backup-simplify: Simplify 0 into 0 1546593440.108 * [misc]backup-simplify: Simplify 0 into 0 1546593440.109 * [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))))) 1546593440.109 * [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)) 1546593440.109 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546593440.109 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.109 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.109 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of k in k 1546593440.109 * [misc]backup-simplify: Simplify 0 into 0 1546593440.109 * [misc]backup-simplify: Simplify 1 into 1 1546593440.109 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.109 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.109 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.109 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of -2 in k 1546593440.109 * [misc]backup-simplify: Simplify -2 into -2 1546593440.109 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.109 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.109 * [misc]backup-simplify: Simplify PI into PI 1546593440.109 * [misc]taylor: Taking taylor expansion of n in k 1546593440.109 * [misc]backup-simplify: Simplify n into n 1546593440.109 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.109 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593440.109 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593440.110 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.110 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.110 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593440.110 * [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))) 1546593440.110 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.110 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.110 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of k in n 1546593440.110 * [misc]backup-simplify: Simplify k into k 1546593440.110 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.110 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.110 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.110 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.110 * [misc]backup-simplify: Simplify -2 into -2 1546593440.110 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.110 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.110 * [misc]backup-simplify: Simplify PI into PI 1546593440.110 * [misc]taylor: Taking taylor expansion of n in n 1546593440.110 * [misc]backup-simplify: Simplify 0 into 0 1546593440.110 * [misc]backup-simplify: Simplify 1 into 1 1546593440.111 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.111 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.111 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.111 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.111 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.112 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.112 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593440.112 * [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)))) 1546593440.112 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.112 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593440.112 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593440.112 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.112 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.112 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.113 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.113 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.113 * [misc]taylor: Taking taylor expansion of k in n 1546593440.113 * [misc]backup-simplify: Simplify k into k 1546593440.113 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.113 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.113 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.113 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.113 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.113 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.113 * [misc]backup-simplify: Simplify -2 into -2 1546593440.113 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.113 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.113 * [misc]backup-simplify: Simplify PI into PI 1546593440.113 * [misc]taylor: Taking taylor expansion of n in n 1546593440.113 * [misc]backup-simplify: Simplify 0 into 0 1546593440.113 * [misc]backup-simplify: Simplify 1 into 1 1546593440.113 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.113 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.113 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.113 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.114 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.114 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.114 * [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))) 1546593440.115 * [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)))) 1546593440.115 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546593440.115 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546593440.115 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593440.115 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.115 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.115 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.115 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.115 * [misc]taylor: Taking taylor expansion of k in k 1546593440.115 * [misc]backup-simplify: Simplify 0 into 0 1546593440.115 * [misc]backup-simplify: Simplify 1 into 1 1546593440.115 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.115 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.115 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.115 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546593440.115 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546593440.115 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546593440.115 * [misc]taylor: Taking taylor expansion of -2 in k 1546593440.115 * [misc]backup-simplify: Simplify -2 into -2 1546593440.115 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.115 * [misc]backup-simplify: Simplify PI into PI 1546593440.115 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.116 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.116 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593440.116 * [misc]taylor: Taking taylor expansion of n in k 1546593440.116 * [misc]backup-simplify: Simplify n into n 1546593440.116 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593440.116 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.116 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.116 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593440.116 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546593440.117 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546593440.117 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593440.118 * [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)))) 1546593440.118 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593440.119 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593440.120 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593440.120 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593440.121 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593440.121 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.121 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.121 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546593440.122 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593440.122 * [misc]taylor: Taking taylor expansion of 0 in k 1546593440.122 * [misc]backup-simplify: Simplify 0 into 0 1546593440.122 * [misc]backup-simplify: Simplify 0 into 0 1546593440.123 * [misc]backup-simplify: Simplify 0 into 0 1546593440.123 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.124 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593440.127 * [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 1546593440.127 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593440.127 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593440.127 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.128 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.128 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546593440.130 * [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 1546593440.130 * [misc]taylor: Taking taylor expansion of 0 in k 1546593440.130 * [misc]backup-simplify: Simplify 0 into 0 1546593440.130 * [misc]backup-simplify: Simplify 0 into 0 1546593440.130 * [misc]backup-simplify: Simplify 0 into 0 1546593440.130 * [misc]backup-simplify: Simplify 0 into 0 1546593440.131 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.132 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593440.136 * [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 1546593440.136 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593440.137 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593440.137 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.137 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.138 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546593440.140 * [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 1546593440.140 * [misc]taylor: Taking taylor expansion of 0 in k 1546593440.140 * [misc]backup-simplify: Simplify 0 into 0 1546593440.140 * [misc]backup-simplify: Simplify 0 into 0 1546593440.141 * [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))))) 1546593440.141 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1) 1546593440.141 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546593440.141 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546593440.141 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.141 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.141 * [misc]backup-simplify: Simplify 2 into 2 1546593440.142 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.142 * [misc]taylor: Taking taylor expansion of n in n 1546593440.142 * [misc]backup-simplify: Simplify 0 into 0 1546593440.142 * [misc]backup-simplify: Simplify 1 into 1 1546593440.142 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.142 * [misc]backup-simplify: Simplify PI into PI 1546593440.142 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.142 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.142 * [misc]backup-simplify: Simplify 2 into 2 1546593440.142 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.142 * [misc]taylor: Taking taylor expansion of n in n 1546593440.142 * [misc]backup-simplify: Simplify 0 into 0 1546593440.142 * [misc]backup-simplify: Simplify 1 into 1 1546593440.142 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.142 * [misc]backup-simplify: Simplify PI into PI 1546593440.142 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.142 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.143 * [misc]backup-simplify: Simplify 0 into 0 1546593440.143 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.144 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.144 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.145 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593440.146 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593440.146 * [misc]backup-simplify: Simplify 0 into 0 1546593440.148 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593440.149 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593440.149 * [misc]backup-simplify: Simplify 0 into 0 1546593440.151 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593440.153 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546593440.153 * [misc]backup-simplify: Simplify 0 into 0 1546593440.155 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593440.158 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546593440.158 * [misc]backup-simplify: Simplify 0 into 0 1546593440.163 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593440.167 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546593440.167 * [misc]backup-simplify: Simplify 0 into 0 1546593440.171 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546593440.175 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546593440.175 * [misc]backup-simplify: Simplify 0 into 0 1546593440.175 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546593440.176 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546593440.176 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546593440.176 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.176 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.176 * [misc]backup-simplify: Simplify 2 into 2 1546593440.176 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.176 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.176 * [misc]backup-simplify: Simplify PI into PI 1546593440.176 * [misc]taylor: Taking taylor expansion of n in n 1546593440.176 * [misc]backup-simplify: Simplify 0 into 0 1546593440.176 * [misc]backup-simplify: Simplify 1 into 1 1546593440.176 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.176 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.176 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.176 * [misc]backup-simplify: Simplify 2 into 2 1546593440.176 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.176 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.176 * [misc]backup-simplify: Simplify PI into PI 1546593440.176 * [misc]taylor: Taking taylor expansion of n in n 1546593440.176 * [misc]backup-simplify: Simplify 0 into 0 1546593440.176 * [misc]backup-simplify: Simplify 1 into 1 1546593440.177 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.177 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.177 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.178 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593440.179 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593440.179 * [misc]backup-simplify: Simplify 0 into 0 1546593440.181 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.182 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593440.182 * [misc]backup-simplify: Simplify 0 into 0 1546593440.183 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.185 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593440.185 * [misc]backup-simplify: Simplify 0 into 0 1546593440.187 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.189 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593440.189 * [misc]backup-simplify: Simplify 0 into 0 1546593440.191 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.194 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593440.194 * [misc]backup-simplify: Simplify 0 into 0 1546593440.196 * [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 1546593440.199 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593440.199 * [misc]backup-simplify: Simplify 0 into 0 1546593440.200 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546593440.200 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546593440.200 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546593440.200 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.200 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.200 * [misc]backup-simplify: Simplify -2 into -2 1546593440.200 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.200 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.200 * [misc]backup-simplify: Simplify PI into PI 1546593440.200 * [misc]taylor: Taking taylor expansion of n in n 1546593440.200 * [misc]backup-simplify: Simplify 0 into 0 1546593440.200 * [misc]backup-simplify: Simplify 1 into 1 1546593440.200 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.201 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.201 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.201 * [misc]backup-simplify: Simplify -2 into -2 1546593440.201 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.201 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.201 * [misc]backup-simplify: Simplify PI into PI 1546593440.201 * [misc]taylor: Taking taylor expansion of n in n 1546593440.201 * [misc]backup-simplify: Simplify 0 into 0 1546593440.201 * [misc]backup-simplify: Simplify 1 into 1 1546593440.201 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.201 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.202 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.203 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593440.203 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593440.203 * [misc]backup-simplify: Simplify 0 into 0 1546593440.205 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.206 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593440.206 * [misc]backup-simplify: Simplify 0 into 0 1546593440.207 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.209 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593440.209 * [misc]backup-simplify: Simplify 0 into 0 1546593440.211 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.213 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593440.213 * [misc]backup-simplify: Simplify 0 into 0 1546593440.215 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.217 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593440.217 * [misc]backup-simplify: Simplify 0 into 0 1546593440.218 * [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 1546593440.221 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593440.221 * [misc]backup-simplify: Simplify 0 into 0 1546593440.221 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546593440.221 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1546593440.221 * [misc]backup-simplify: Simplify (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 1546593440.221 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 1546593440.221 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 1546593440.221 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546593440.221 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593440.221 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593440.221 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593440.221 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593440.221 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.221 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.221 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593440.221 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.221 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.221 * [misc]taylor: Taking taylor expansion of k in n 1546593440.221 * [misc]backup-simplify: Simplify k into k 1546593440.221 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593440.221 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.222 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.222 * [misc]backup-simplify: Simplify 2 into 2 1546593440.222 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.222 * [misc]taylor: Taking taylor expansion of n in n 1546593440.222 * [misc]backup-simplify: Simplify 0 into 0 1546593440.222 * [misc]backup-simplify: Simplify 1 into 1 1546593440.222 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.222 * [misc]backup-simplify: Simplify PI into PI 1546593440.222 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.222 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.222 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.223 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.223 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.223 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593440.223 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593440.223 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593440.224 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.224 * [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)))) 1546593440.224 * [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))))) 1546593440.225 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546593440.225 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546593440.225 * [misc]taylor: Taking taylor expansion of k in n 1546593440.225 * [misc]backup-simplify: Simplify k into k 1546593440.225 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546593440.225 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546593440.225 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.225 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.225 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.225 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.225 * [misc]taylor: Taking taylor expansion of k in k 1546593440.225 * [misc]backup-simplify: Simplify 0 into 0 1546593440.225 * [misc]backup-simplify: Simplify 1 into 1 1546593440.225 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.225 * [misc]backup-simplify: Simplify 2 into 2 1546593440.225 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593440.225 * [misc]taylor: Taking taylor expansion of n in k 1546593440.225 * [misc]backup-simplify: Simplify n into n 1546593440.225 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.225 * [misc]backup-simplify: Simplify PI into PI 1546593440.225 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593440.225 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593440.225 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593440.226 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593440.226 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.226 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.226 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593440.226 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593440.226 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546593440.226 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593440.226 * [misc]taylor: Taking taylor expansion of k in k 1546593440.226 * [misc]backup-simplify: Simplify 0 into 0 1546593440.226 * [misc]backup-simplify: Simplify 1 into 1 1546593440.226 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.226 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593440.226 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.227 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.227 * [misc]taylor: Taking taylor expansion of k in k 1546593440.227 * [misc]backup-simplify: Simplify 0 into 0 1546593440.227 * [misc]backup-simplify: Simplify 1 into 1 1546593440.227 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.227 * [misc]backup-simplify: Simplify 2 into 2 1546593440.227 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593440.227 * [misc]taylor: Taking taylor expansion of n in k 1546593440.227 * [misc]backup-simplify: Simplify n into n 1546593440.227 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.227 * [misc]backup-simplify: Simplify PI into PI 1546593440.227 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593440.227 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593440.227 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593440.227 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593440.227 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.227 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.227 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593440.227 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593440.228 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546593440.228 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593440.228 * [misc]taylor: Taking taylor expansion of k in k 1546593440.228 * [misc]backup-simplify: Simplify 0 into 0 1546593440.228 * [misc]backup-simplify: Simplify 1 into 1 1546593440.228 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.228 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593440.228 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 1546593440.228 * [misc]taylor: Taking taylor expansion of 0 in n 1546593440.228 * [misc]backup-simplify: Simplify 0 into 0 1546593440.228 * [misc]backup-simplify: Simplify 0 into 0 1546593440.228 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546593440.229 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546593440.229 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546593440.229 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593440.229 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.230 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.230 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546593440.230 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546593440.230 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 1546593440.231 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 1546593440.231 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546593440.231 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546593440.231 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.231 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.231 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546593440.231 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546593440.231 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546593440.231 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.231 * [misc]taylor: Taking taylor expansion of n in n 1546593440.231 * [misc]backup-simplify: Simplify 0 into 0 1546593440.231 * [misc]backup-simplify: Simplify 1 into 1 1546593440.231 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.231 * [misc]backup-simplify: Simplify PI into PI 1546593440.231 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.232 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.232 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546593440.232 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.232 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546593440.232 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546593440.232 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.232 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.233 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546593440.233 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546593440.233 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593440.234 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546593440.235 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593440.236 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593440.236 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593440.236 * [misc]backup-simplify: Simplify 0 into 0 1546593440.237 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593440.237 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546593440.238 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546593440.239 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1546593440.239 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593440.239 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.239 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.239 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546593440.240 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546593440.241 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 1546593440.243 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 1546593440.243 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 1546593440.243 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 1546593440.243 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 1546593440.244 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.244 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.244 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 1546593440.244 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 1546593440.244 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593440.244 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.244 * [misc]backup-simplify: Simplify 2 into 2 1546593440.244 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593440.244 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593440.244 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 1546593440.244 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593440.244 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.244 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.244 * [misc]backup-simplify: Simplify 2 into 2 1546593440.244 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.244 * [misc]taylor: Taking taylor expansion of n in n 1546593440.244 * [misc]backup-simplify: Simplify 0 into 0 1546593440.244 * [misc]backup-simplify: Simplify 1 into 1 1546593440.244 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.244 * [misc]backup-simplify: Simplify PI into PI 1546593440.244 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.244 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.245 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.245 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.246 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.246 * [misc]taylor: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 1546593440.246 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546593440.246 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.246 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.246 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546593440.246 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546593440.246 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546593440.246 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546593440.246 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.246 * [misc]taylor: Taking taylor expansion of n in n 1546593440.246 * [misc]backup-simplify: Simplify 0 into 0 1546593440.246 * [misc]backup-simplify: Simplify 1 into 1 1546593440.246 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.246 * [misc]backup-simplify: Simplify PI into PI 1546593440.246 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.247 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.247 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546593440.247 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.247 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546593440.247 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546593440.247 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546593440.247 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.247 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.247 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546593440.247 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546593440.247 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546593440.247 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.248 * [misc]taylor: Taking taylor expansion of n in n 1546593440.248 * [misc]backup-simplify: Simplify 0 into 0 1546593440.248 * [misc]backup-simplify: Simplify 1 into 1 1546593440.248 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.248 * [misc]backup-simplify: Simplify PI into PI 1546593440.248 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.248 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.248 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546593440.248 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.249 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546593440.249 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546593440.249 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.249 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546593440.249 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546593440.250 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.250 * [misc]backup-simplify: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 1546593440.251 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 1546593440.251 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 1546593440.252 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.252 * [misc]backup-simplify: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 1546593440.253 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593440.253 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593440.255 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593440.256 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 1546593440.256 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 1546593440.257 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546593440.258 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 1546593440.261 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546593440.262 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593440.262 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546593440.263 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593440.264 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593440.267 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546593440.271 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546593440.274 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546593440.275 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 1546593440.276 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593440.277 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1546593440.279 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1546593440.281 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546593440.283 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546593440.285 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546593440.286 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546593440.296 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546593440.297 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 1546593440.297 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 1546593440.297 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.297 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.297 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.297 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.297 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of k in n 1546593440.297 * [misc]backup-simplify: Simplify k into k 1546593440.297 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.297 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.297 * [misc]backup-simplify: Simplify 2 into 2 1546593440.297 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.297 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.297 * [misc]backup-simplify: Simplify PI into PI 1546593440.297 * [misc]taylor: Taking taylor expansion of n in n 1546593440.297 * [misc]backup-simplify: Simplify 0 into 0 1546593440.298 * [misc]backup-simplify: Simplify 1 into 1 1546593440.298 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.298 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.299 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.299 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.299 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.299 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.300 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.301 * [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))) 1546593440.301 * [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)))) 1546593440.302 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593440.302 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546593440.302 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.302 * [misc]taylor: Taking taylor expansion of k in n 1546593440.302 * [misc]backup-simplify: Simplify k into k 1546593440.302 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.302 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546593440.302 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593440.302 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546593440.302 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546593440.302 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593440.302 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.303 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.303 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of k in k 1546593440.303 * [misc]backup-simplify: Simplify 0 into 0 1546593440.303 * [misc]backup-simplify: Simplify 1 into 1 1546593440.303 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.303 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.303 * [misc]backup-simplify: Simplify 2 into 2 1546593440.303 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.303 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.303 * [misc]backup-simplify: Simplify PI into PI 1546593440.303 * [misc]taylor: Taking taylor expansion of n in k 1546593440.303 * [misc]backup-simplify: Simplify n into n 1546593440.303 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.303 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593440.304 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593440.304 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.304 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.304 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.304 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593440.304 * [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)))) 1546593440.305 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546593440.305 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593440.305 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.305 * [misc]taylor: Taking taylor expansion of k in k 1546593440.305 * [misc]backup-simplify: Simplify 0 into 0 1546593440.305 * [misc]backup-simplify: Simplify 1 into 1 1546593440.305 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.305 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.305 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593440.306 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.306 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.306 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.306 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.306 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of k in k 1546593440.306 * [misc]backup-simplify: Simplify 0 into 0 1546593440.306 * [misc]backup-simplify: Simplify 1 into 1 1546593440.306 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.306 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.306 * [misc]backup-simplify: Simplify 2 into 2 1546593440.306 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.306 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.306 * [misc]backup-simplify: Simplify PI into PI 1546593440.306 * [misc]taylor: Taking taylor expansion of n in k 1546593440.306 * [misc]backup-simplify: Simplify n into n 1546593440.306 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.306 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593440.307 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593440.307 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.307 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.307 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.307 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593440.307 * [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)))) 1546593440.308 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546593440.308 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593440.308 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.308 * [misc]taylor: Taking taylor expansion of k in k 1546593440.308 * [misc]backup-simplify: Simplify 0 into 0 1546593440.308 * [misc]backup-simplify: Simplify 1 into 1 1546593440.308 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.308 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.309 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593440.309 * [misc]backup-simplify: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1546593440.309 * [misc]taylor: Taking taylor expansion of 0 in n 1546593440.309 * [misc]backup-simplify: Simplify 0 into 0 1546593440.309 * [misc]backup-simplify: Simplify 0 into 0 1546593440.309 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546593440.310 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546593440.310 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.310 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.310 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.310 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.310 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.310 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.310 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of k in n 1546593440.310 * [misc]backup-simplify: Simplify k into k 1546593440.310 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.310 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.310 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.311 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.311 * [misc]backup-simplify: Simplify 2 into 2 1546593440.311 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.311 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.311 * [misc]backup-simplify: Simplify PI into PI 1546593440.311 * [misc]taylor: Taking taylor expansion of n in n 1546593440.311 * [misc]backup-simplify: Simplify 0 into 0 1546593440.311 * [misc]backup-simplify: Simplify 1 into 1 1546593440.311 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.311 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.312 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.312 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.312 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.312 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.313 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.313 * [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))) 1546593440.314 * [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)))) 1546593440.315 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593440.315 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593440.316 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593440.317 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593440.317 * [misc]backup-simplify: Simplify 0 into 0 1546593440.317 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546593440.318 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593440.319 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546593440.319 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546593440.319 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546593440.319 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593440.319 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.319 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.319 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593440.319 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.319 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.319 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.319 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.319 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.319 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.319 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.319 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.319 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.320 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.320 * [misc]taylor: Taking taylor expansion of k in n 1546593440.320 * [misc]backup-simplify: Simplify k into k 1546593440.320 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.320 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.320 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.320 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.320 * [misc]backup-simplify: Simplify 2 into 2 1546593440.320 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.320 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.320 * [misc]backup-simplify: Simplify PI into PI 1546593440.320 * [misc]taylor: Taking taylor expansion of n in n 1546593440.320 * [misc]backup-simplify: Simplify 0 into 0 1546593440.320 * [misc]backup-simplify: Simplify 1 into 1 1546593440.320 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.320 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.320 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.320 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.320 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.321 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.321 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.321 * [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))) 1546593440.322 * [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)))) 1546593440.322 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593440.323 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593440.323 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593440.323 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593440.324 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593440.325 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593440.326 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593440.326 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593440.326 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593440.326 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.327 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.327 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.327 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593440.328 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593440.330 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546593440.330 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546593440.330 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.330 * [misc]backup-simplify: Simplify 0 into 0 1546593440.330 * [misc]backup-simplify: Simplify 0 into 0 1546593440.331 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.331 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593440.332 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546593440.332 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546593440.332 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.332 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.332 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.332 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.332 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.332 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.332 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.332 * [misc]taylor: Taking taylor expansion of k in n 1546593440.332 * [misc]backup-simplify: Simplify k into k 1546593440.332 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.333 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.333 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.333 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.333 * [misc]backup-simplify: Simplify 2 into 2 1546593440.333 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.333 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.333 * [misc]backup-simplify: Simplify PI into PI 1546593440.333 * [misc]taylor: Taking taylor expansion of n in n 1546593440.333 * [misc]backup-simplify: Simplify 0 into 0 1546593440.333 * [misc]backup-simplify: Simplify 1 into 1 1546593440.333 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.333 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.333 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.333 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.333 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.334 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.334 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.334 * [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))) 1546593440.335 * [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)))) 1546593440.335 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593440.336 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593440.336 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593440.337 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593440.338 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546593440.338 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1546593440.338 * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 1546593440.338 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593440.338 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546593440.338 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546593440.338 * [misc]taylor: Taking taylor expansion of -1 in n 1546593440.338 * [misc]backup-simplify: Simplify -1 into -1 1546593440.338 * [misc]taylor: Taking taylor expansion of k in n 1546593440.338 * [misc]backup-simplify: Simplify k into k 1546593440.338 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546593440.338 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546593440.339 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546593440.339 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546593440.339 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.339 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.339 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of k in n 1546593440.339 * [misc]backup-simplify: Simplify k into k 1546593440.339 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.339 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.339 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.339 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.339 * [misc]backup-simplify: Simplify -2 into -2 1546593440.339 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.339 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.339 * [misc]backup-simplify: Simplify PI into PI 1546593440.339 * [misc]taylor: Taking taylor expansion of n in n 1546593440.339 * [misc]backup-simplify: Simplify 0 into 0 1546593440.339 * [misc]backup-simplify: Simplify 1 into 1 1546593440.339 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.339 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.340 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.340 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.340 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.340 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.341 * [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))) 1546593440.341 * [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)))) 1546593440.341 * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593440.341 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of -1 in k 1546593440.342 * [misc]backup-simplify: Simplify -1 into -1 1546593440.342 * [misc]taylor: Taking taylor expansion of k in k 1546593440.342 * [misc]backup-simplify: Simplify 0 into 0 1546593440.342 * [misc]backup-simplify: Simplify 1 into 1 1546593440.342 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593440.342 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.342 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593440.342 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.342 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.342 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of k in k 1546593440.342 * [misc]backup-simplify: Simplify 0 into 0 1546593440.342 * [misc]backup-simplify: Simplify 1 into 1 1546593440.342 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.342 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.342 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.342 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593440.342 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593440.343 * [misc]taylor: Taking taylor expansion of -2 in k 1546593440.343 * [misc]backup-simplify: Simplify -2 into -2 1546593440.343 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.343 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.343 * [misc]backup-simplify: Simplify PI into PI 1546593440.343 * [misc]taylor: Taking taylor expansion of n in k 1546593440.343 * [misc]backup-simplify: Simplify n into n 1546593440.343 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.343 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593440.343 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593440.343 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.343 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.343 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593440.343 * [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))) 1546593440.343 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546593440.343 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546593440.343 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593440.343 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593440.343 * [misc]taylor: Taking taylor expansion of -1 in k 1546593440.343 * [misc]backup-simplify: Simplify -1 into -1 1546593440.343 * [misc]taylor: Taking taylor expansion of k in k 1546593440.343 * [misc]backup-simplify: Simplify 0 into 0 1546593440.343 * [misc]backup-simplify: Simplify 1 into 1 1546593440.344 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593440.344 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.344 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593440.344 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.344 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.344 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of k in k 1546593440.344 * [misc]backup-simplify: Simplify 0 into 0 1546593440.344 * [misc]backup-simplify: Simplify 1 into 1 1546593440.344 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.344 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.344 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.344 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of -2 in k 1546593440.344 * [misc]backup-simplify: Simplify -2 into -2 1546593440.344 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.344 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.344 * [misc]backup-simplify: Simplify PI into PI 1546593440.344 * [misc]taylor: Taking taylor expansion of n in k 1546593440.344 * [misc]backup-simplify: Simplify n into n 1546593440.345 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.345 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593440.345 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593440.345 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.345 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.345 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593440.345 * [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))) 1546593440.345 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546593440.345 * [misc]taylor: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593440.345 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.345 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.345 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593440.345 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.345 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.345 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.345 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.345 * [misc]backup-simplify: Simplify -2 into -2 1546593440.345 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.345 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.345 * [misc]backup-simplify: Simplify PI into PI 1546593440.345 * [misc]taylor: Taking taylor expansion of n in n 1546593440.345 * [misc]backup-simplify: Simplify 0 into 0 1546593440.346 * [misc]backup-simplify: Simplify 1 into 1 1546593440.346 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.346 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.346 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.346 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.346 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.346 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.346 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.346 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.346 * [misc]taylor: Taking taylor expansion of k in n 1546593440.346 * [misc]backup-simplify: Simplify k into k 1546593440.346 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.346 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.346 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.347 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.347 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.347 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.347 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593440.348 * [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)))) 1546593440.348 * [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))))) 1546593440.348 * [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))))) 1546593440.349 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593440.349 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593440.350 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546593440.350 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546593440.350 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546593440.350 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.350 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.350 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593440.350 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593440.350 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.350 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.350 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.350 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.350 * [misc]backup-simplify: Simplify -2 into -2 1546593440.350 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.350 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.350 * [misc]backup-simplify: Simplify PI into PI 1546593440.350 * [misc]taylor: Taking taylor expansion of n in n 1546593440.350 * [misc]backup-simplify: Simplify 0 into 0 1546593440.350 * [misc]backup-simplify: Simplify 1 into 1 1546593440.350 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.350 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.351 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.351 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.351 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.351 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.351 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.351 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.351 * [misc]taylor: Taking taylor expansion of k in n 1546593440.351 * [misc]backup-simplify: Simplify k into k 1546593440.351 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.351 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.351 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.351 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.351 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.352 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.352 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593440.353 * [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)))) 1546593440.354 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593440.354 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593440.355 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546593440.356 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546593440.356 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.356 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593440.357 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593440.357 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.358 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593440.359 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593440.361 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593440.362 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546593440.364 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593440.366 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546593440.366 * [misc]backup-simplify: Simplify 0 into 0 1546593440.366 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.367 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593440.368 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546593440.369 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546593440.369 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546593440.369 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.369 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.369 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593440.369 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593440.369 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.369 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.369 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.369 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.369 * [misc]backup-simplify: Simplify -2 into -2 1546593440.369 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.369 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.369 * [misc]backup-simplify: Simplify PI into PI 1546593440.369 * [misc]taylor: Taking taylor expansion of n in n 1546593440.369 * [misc]backup-simplify: Simplify 0 into 0 1546593440.369 * [misc]backup-simplify: Simplify 1 into 1 1546593440.369 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.370 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.370 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.370 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.370 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.370 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.370 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.370 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.370 * [misc]taylor: Taking taylor expansion of k in n 1546593440.370 * [misc]backup-simplify: Simplify k into k 1546593440.370 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.370 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.370 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.371 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.371 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.371 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.372 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593440.373 * [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)))) 1546593440.373 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593440.374 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593440.375 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546593440.375 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546593440.378 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546593440.378 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1546593440.378 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1546593440.379 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 1546593440.379 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546593440.379 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546593440.379 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.379 * [misc]taylor: Taking taylor expansion of k in n 1546593440.379 * [misc]backup-simplify: Simplify k into k 1546593440.379 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.379 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546593440.379 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593440.379 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546593440.379 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593440.380 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593440.380 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593440.380 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593440.380 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.380 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.380 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593440.380 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.380 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.380 * [misc]taylor: Taking taylor expansion of k in n 1546593440.380 * [misc]backup-simplify: Simplify k into k 1546593440.380 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593440.380 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.381 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.381 * [misc]backup-simplify: Simplify 2 into 2 1546593440.381 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.381 * [misc]taylor: Taking taylor expansion of n in n 1546593440.381 * [misc]backup-simplify: Simplify 0 into 0 1546593440.381 * [misc]backup-simplify: Simplify 1 into 1 1546593440.381 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.381 * [misc]backup-simplify: Simplify PI into PI 1546593440.381 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.381 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.382 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.383 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.383 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.383 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593440.383 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593440.384 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593440.384 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.385 * [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)))) 1546593440.385 * [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))))) 1546593440.385 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593440.386 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593440.386 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.386 * [misc]taylor: Taking taylor expansion of k in k 1546593440.386 * [misc]backup-simplify: Simplify 0 into 0 1546593440.386 * [misc]backup-simplify: Simplify 1 into 1 1546593440.386 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.386 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.386 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593440.386 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593440.386 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593440.387 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593440.387 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593440.387 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.387 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.387 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593440.387 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.387 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.387 * [misc]taylor: Taking taylor expansion of k in k 1546593440.387 * [misc]backup-simplify: Simplify 0 into 0 1546593440.387 * [misc]backup-simplify: Simplify 1 into 1 1546593440.387 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593440.387 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593440.387 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.387 * [misc]backup-simplify: Simplify 2 into 2 1546593440.387 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593440.387 * [misc]taylor: Taking taylor expansion of n in k 1546593440.387 * [misc]backup-simplify: Simplify n into n 1546593440.387 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.387 * [misc]backup-simplify: Simplify PI into PI 1546593440.387 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593440.387 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593440.387 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593440.388 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593440.388 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.388 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.388 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593440.388 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593440.388 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593440.388 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593440.388 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.388 * [misc]taylor: Taking taylor expansion of k in k 1546593440.388 * [misc]backup-simplify: Simplify 0 into 0 1546593440.388 * [misc]backup-simplify: Simplify 1 into 1 1546593440.389 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.389 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.390 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593440.390 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593440.390 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593440.390 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593440.390 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593440.390 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.390 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.390 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593440.390 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.390 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.390 * [misc]taylor: Taking taylor expansion of k in k 1546593440.390 * [misc]backup-simplify: Simplify 0 into 0 1546593440.390 * [misc]backup-simplify: Simplify 1 into 1 1546593440.390 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593440.390 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593440.390 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.390 * [misc]backup-simplify: Simplify 2 into 2 1546593440.390 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593440.390 * [misc]taylor: Taking taylor expansion of n in k 1546593440.390 * [misc]backup-simplify: Simplify n into n 1546593440.390 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.390 * [misc]backup-simplify: Simplify PI into PI 1546593440.391 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593440.391 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593440.391 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593440.391 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593440.391 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.391 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.391 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593440.391 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593440.392 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 1546593440.392 * [misc]taylor: Taking taylor expansion of 0 in n 1546593440.392 * [misc]backup-simplify: Simplify 0 into 0 1546593440.392 * [misc]backup-simplify: Simplify 0 into 0 1546593440.392 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546593440.392 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546593440.393 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546593440.394 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593440.394 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.394 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.394 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546593440.394 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546593440.395 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1546593440.395 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546593440.395 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546593440.395 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.395 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.395 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546593440.395 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593440.395 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.395 * [misc]backup-simplify: Simplify 2 into 2 1546593440.395 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593440.395 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593440.395 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593440.395 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.396 * [misc]taylor: Taking taylor expansion of n in n 1546593440.396 * [misc]backup-simplify: Simplify 0 into 0 1546593440.396 * [misc]backup-simplify: Simplify 1 into 1 1546593440.396 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.396 * [misc]backup-simplify: Simplify PI into PI 1546593440.396 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.397 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.397 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.397 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593440.397 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546593440.397 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593440.398 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.398 * [misc]backup-simplify: Simplify 0 into 0 1546593440.398 * [misc]backup-simplify: Simplify 0 into 0 1546593440.398 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546593440.399 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546593440.400 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1546593440.401 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593440.401 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.401 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.401 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546593440.402 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546593440.403 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546593440.404 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593440.405 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1546593440.405 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1546593440.405 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1546593440.405 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1546593440.405 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.405 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.405 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1546593440.405 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1546593440.405 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593440.405 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.405 * [misc]backup-simplify: Simplify 2 into 2 1546593440.405 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593440.405 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593440.405 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593440.405 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.405 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.406 * [misc]backup-simplify: Simplify 2 into 2 1546593440.406 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.406 * [misc]taylor: Taking taylor expansion of n in n 1546593440.406 * [misc]backup-simplify: Simplify 0 into 0 1546593440.406 * [misc]backup-simplify: Simplify 1 into 1 1546593440.406 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.406 * [misc]backup-simplify: Simplify PI into PI 1546593440.406 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.406 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.407 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.407 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.408 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.408 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593440.408 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.408 * [misc]taylor: Taking taylor expansion of n in n 1546593440.408 * [misc]backup-simplify: Simplify 0 into 0 1546593440.408 * [misc]backup-simplify: Simplify 1 into 1 1546593440.408 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.408 * [misc]backup-simplify: Simplify PI into PI 1546593440.408 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.409 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.409 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.410 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593440.410 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546593440.410 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546593440.410 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.410 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.410 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546593440.410 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593440.410 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.410 * [misc]backup-simplify: Simplify 2 into 2 1546593440.410 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593440.410 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593440.410 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593440.410 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.410 * [misc]taylor: Taking taylor expansion of n in n 1546593440.410 * [misc]backup-simplify: Simplify 0 into 0 1546593440.410 * [misc]backup-simplify: Simplify 1 into 1 1546593440.410 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.410 * [misc]backup-simplify: Simplify PI into PI 1546593440.411 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.411 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.412 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.412 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593440.413 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.413 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1546593440.414 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1546593440.414 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593440.414 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546593440.415 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593440.415 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.415 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.415 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.415 * [misc]backup-simplify: Simplify 0 into 0 1546593440.416 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593440.417 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593440.418 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593440.418 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593440.418 * [misc]backup-simplify: Simplify 0 into 0 1546593440.419 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593440.419 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1546593440.421 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 1546593440.421 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546593440.421 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.421 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.422 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1546593440.424 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 1546593440.424 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.425 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593440.425 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 1546593440.425 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 1546593440.425 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 1546593440.425 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1546593440.425 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.425 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.425 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1546593440.425 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1546593440.426 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593440.426 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.426 * [misc]backup-simplify: Simplify 2 into 2 1546593440.426 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593440.426 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593440.426 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593440.426 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.426 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.426 * [misc]backup-simplify: Simplify 2 into 2 1546593440.426 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.426 * [misc]taylor: Taking taylor expansion of n in n 1546593440.426 * [misc]backup-simplify: Simplify 0 into 0 1546593440.426 * [misc]backup-simplify: Simplify 1 into 1 1546593440.426 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.426 * [misc]backup-simplify: Simplify PI into PI 1546593440.426 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.426 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.427 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.427 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.427 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.428 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593440.428 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.428 * [misc]taylor: Taking taylor expansion of n in n 1546593440.428 * [misc]backup-simplify: Simplify 0 into 0 1546593440.428 * [misc]backup-simplify: Simplify 1 into 1 1546593440.428 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.428 * [misc]backup-simplify: Simplify PI into PI 1546593440.428 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.428 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.428 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.429 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593440.429 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.429 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.429 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.429 * [misc]backup-simplify: Simplify 2 into 2 1546593440.429 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593440.429 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593440.429 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.429 * [misc]backup-simplify: Simplify 2 into 2 1546593440.429 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.429 * [misc]taylor: Taking taylor expansion of n in n 1546593440.429 * [misc]backup-simplify: Simplify 0 into 0 1546593440.429 * [misc]backup-simplify: Simplify 1 into 1 1546593440.429 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.429 * [misc]backup-simplify: Simplify PI into PI 1546593440.429 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.429 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593440.430 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.430 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593440.431 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.431 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.431 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593440.431 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.431 * [misc]taylor: Taking taylor expansion of n in n 1546593440.431 * [misc]backup-simplify: Simplify 0 into 0 1546593440.431 * [misc]backup-simplify: Simplify 1 into 1 1546593440.431 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.431 * [misc]backup-simplify: Simplify PI into PI 1546593440.431 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.432 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.432 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.432 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593440.432 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546593440.432 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546593440.432 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.432 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.432 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546593440.432 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593440.432 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.432 * [misc]backup-simplify: Simplify 2 into 2 1546593440.432 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593440.432 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593440.432 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593440.432 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593440.432 * [misc]taylor: Taking taylor expansion of n in n 1546593440.432 * [misc]backup-simplify: Simplify 0 into 0 1546593440.432 * [misc]backup-simplify: Simplify 1 into 1 1546593440.432 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.433 * [misc]backup-simplify: Simplify PI into PI 1546593440.433 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593440.433 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593440.433 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.433 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593440.434 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.434 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1546593440.435 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1546593440.435 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593440.435 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.436 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.436 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1546593440.437 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1546593440.437 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1546593440.437 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593440.437 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546593440.438 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593440.438 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.438 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.438 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.438 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.438 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.438 * [misc]backup-simplify: Simplify 0 into 0 1546593440.439 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593440.440 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593440.441 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593440.442 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593440.442 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546593440.443 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1546593440.444 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1546593440.445 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593440.446 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593440.447 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593440.450 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 1546593440.454 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546593440.456 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546593440.457 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593440.458 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1546593440.459 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1546593440.460 * [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)))) 1546593440.462 * [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)))) 1546593440.464 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546593440.464 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546593440.468 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1546593440.468 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546593440.468 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 1546593440.468 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593440.468 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546593440.468 * [misc]taylor: Taking taylor expansion of k in n 1546593440.468 * [misc]backup-simplify: Simplify k into k 1546593440.468 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546593440.468 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546593440.468 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.468 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.468 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.468 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.468 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.468 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.469 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.469 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.469 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.469 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.469 * [misc]taylor: Taking taylor expansion of k in n 1546593440.469 * [misc]backup-simplify: Simplify k into k 1546593440.469 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.469 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.469 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.469 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.469 * [misc]backup-simplify: Simplify 2 into 2 1546593440.469 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.469 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.469 * [misc]backup-simplify: Simplify PI into PI 1546593440.469 * [misc]taylor: Taking taylor expansion of n in n 1546593440.469 * [misc]backup-simplify: Simplify 0 into 0 1546593440.469 * [misc]backup-simplify: Simplify 1 into 1 1546593440.469 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.469 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.470 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.470 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.470 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.470 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.470 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.471 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1546593440.471 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1546593440.471 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593440.471 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593440.471 * [misc]taylor: Taking taylor expansion of k in k 1546593440.471 * [misc]backup-simplify: Simplify 0 into 0 1546593440.471 * [misc]backup-simplify: Simplify 1 into 1 1546593440.471 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.471 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593440.471 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593440.471 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593440.471 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593440.472 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593440.472 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.472 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.472 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.472 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.472 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.472 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.472 * [misc]taylor: Taking taylor expansion of k in k 1546593440.472 * [misc]backup-simplify: Simplify 0 into 0 1546593440.472 * [misc]backup-simplify: Simplify 1 into 1 1546593440.472 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.472 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593440.472 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593440.472 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.472 * [misc]backup-simplify: Simplify 2 into 2 1546593440.472 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.472 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.472 * [misc]backup-simplify: Simplify PI into PI 1546593440.472 * [misc]taylor: Taking taylor expansion of n in k 1546593440.472 * [misc]backup-simplify: Simplify n into n 1546593440.472 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.472 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593440.472 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593440.472 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.472 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.472 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.472 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593440.473 * [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)))) 1546593440.473 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of k in k 1546593440.473 * [misc]backup-simplify: Simplify 0 into 0 1546593440.473 * [misc]backup-simplify: Simplify 1 into 1 1546593440.473 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.473 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593440.473 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.473 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.473 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.473 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.473 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of k in k 1546593440.473 * [misc]backup-simplify: Simplify 0 into 0 1546593440.473 * [misc]backup-simplify: Simplify 1 into 1 1546593440.473 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.473 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of 2 in k 1546593440.473 * [misc]backup-simplify: Simplify 2 into 2 1546593440.473 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.473 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.473 * [misc]backup-simplify: Simplify PI into PI 1546593440.474 * [misc]taylor: Taking taylor expansion of n in k 1546593440.474 * [misc]backup-simplify: Simplify n into n 1546593440.474 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.474 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593440.474 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593440.474 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.474 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593440.474 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593440.474 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593440.474 * [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)))) 1546593440.474 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 1546593440.474 * [misc]taylor: Taking taylor expansion of 0 in n 1546593440.474 * [misc]backup-simplify: Simplify 0 into 0 1546593440.474 * [misc]backup-simplify: Simplify 0 into 0 1546593440.475 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546593440.475 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.475 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.475 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.475 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.475 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.475 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.475 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of k in n 1546593440.475 * [misc]backup-simplify: Simplify k into k 1546593440.475 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.475 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.475 * [misc]backup-simplify: Simplify 2 into 2 1546593440.475 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.475 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.475 * [misc]backup-simplify: Simplify PI into PI 1546593440.475 * [misc]taylor: Taking taylor expansion of n in n 1546593440.475 * [misc]backup-simplify: Simplify 0 into 0 1546593440.475 * [misc]backup-simplify: Simplify 1 into 1 1546593440.475 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.476 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.476 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.476 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.476 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.476 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.476 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.477 * [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))) 1546593440.477 * [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)))) 1546593440.478 * [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))))) 1546593440.478 * [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)))))) 1546593440.478 * [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)))))) 1546593440.478 * [misc]backup-simplify: Simplify 0 into 0 1546593440.479 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593440.479 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546593440.479 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.480 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.480 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.480 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.480 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.480 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.480 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of k in n 1546593440.480 * [misc]backup-simplify: Simplify k into k 1546593440.480 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.480 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.480 * [misc]backup-simplify: Simplify 2 into 2 1546593440.480 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.480 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.480 * [misc]backup-simplify: Simplify PI into PI 1546593440.480 * [misc]taylor: Taking taylor expansion of n in n 1546593440.480 * [misc]backup-simplify: Simplify 0 into 0 1546593440.480 * [misc]backup-simplify: Simplify 1 into 1 1546593440.480 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.480 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.481 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.481 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.481 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.481 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.481 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.482 * [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))) 1546593440.482 * [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)))) 1546593440.482 * [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))))) 1546593440.483 * [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)))))) 1546593440.483 * [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)))))) 1546593440.484 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593440.485 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593440.488 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593440.488 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593440.488 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593440.488 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.488 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.489 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.490 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593440.491 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593440.492 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546593440.493 * [misc]backup-simplify: Simplify (- 0) into 0 1546593440.493 * [misc]backup-simplify: Simplify 0 into 0 1546593440.493 * [misc]backup-simplify: Simplify 0 into 0 1546593440.494 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593440.495 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546593440.495 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.495 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.495 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.495 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.495 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.495 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.495 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of k in n 1546593440.495 * [misc]backup-simplify: Simplify k into k 1546593440.495 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.495 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of 2 in n 1546593440.495 * [misc]backup-simplify: Simplify 2 into 2 1546593440.495 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.495 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.495 * [misc]backup-simplify: Simplify PI into PI 1546593440.495 * [misc]taylor: Taking taylor expansion of n in n 1546593440.495 * [misc]backup-simplify: Simplify 0 into 0 1546593440.496 * [misc]backup-simplify: Simplify 1 into 1 1546593440.496 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.496 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593440.497 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593440.497 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.497 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593440.497 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593440.498 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593440.498 * [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))) 1546593440.499 * [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)))) 1546593440.500 * [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))))) 1546593440.501 * [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)))))) 1546593440.501 * [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)))))) 1546593440.504 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1546593440.505 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1546593440.505 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 1546593440.505 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.505 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.505 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of k in n 1546593440.505 * [misc]backup-simplify: Simplify k into k 1546593440.505 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.505 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.505 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.505 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.505 * [misc]backup-simplify: Simplify -2 into -2 1546593440.505 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.505 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.505 * [misc]backup-simplify: Simplify PI into PI 1546593440.505 * [misc]taylor: Taking taylor expansion of n in n 1546593440.505 * [misc]backup-simplify: Simplify 0 into 0 1546593440.505 * [misc]backup-simplify: Simplify 1 into 1 1546593440.506 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.506 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.507 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.507 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.507 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.507 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.508 * [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))) 1546593440.509 * [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)))) 1546593440.509 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546593440.509 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546593440.509 * [misc]taylor: Taking taylor expansion of -1 in n 1546593440.509 * [misc]backup-simplify: Simplify -1 into -1 1546593440.509 * [misc]taylor: Taking taylor expansion of k in n 1546593440.509 * [misc]backup-simplify: Simplify k into k 1546593440.509 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546593440.509 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546593440.509 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546593440.509 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546593440.510 * [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))) 1546593440.510 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546593440.510 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593440.510 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593440.510 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593440.510 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593440.510 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.510 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.510 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.510 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.510 * [misc]taylor: Taking taylor expansion of k in k 1546593440.510 * [misc]backup-simplify: Simplify 0 into 0 1546593440.510 * [misc]backup-simplify: Simplify 1 into 1 1546593440.511 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.511 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.511 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.511 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593440.511 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593440.511 * [misc]taylor: Taking taylor expansion of -2 in k 1546593440.511 * [misc]backup-simplify: Simplify -2 into -2 1546593440.511 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.511 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.511 * [misc]backup-simplify: Simplify PI into PI 1546593440.511 * [misc]taylor: Taking taylor expansion of n in k 1546593440.511 * [misc]backup-simplify: Simplify n into n 1546593440.511 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.511 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593440.511 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593440.511 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.512 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.512 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593440.512 * [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))) 1546593440.512 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593440.512 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593440.512 * [misc]taylor: Taking taylor expansion of -1 in k 1546593440.512 * [misc]backup-simplify: Simplify -1 into -1 1546593440.512 * [misc]taylor: Taking taylor expansion of k in k 1546593440.512 * [misc]backup-simplify: Simplify 0 into 0 1546593440.512 * [misc]backup-simplify: Simplify 1 into 1 1546593440.512 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593440.512 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.513 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593440.513 * [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)))) 1546593440.513 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546593440.513 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593440.513 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593440.513 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593440.513 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593440.513 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593440.513 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.513 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.513 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593440.513 * [misc]taylor: Taking taylor expansion of k in k 1546593440.513 * [misc]backup-simplify: Simplify 0 into 0 1546593440.513 * [misc]backup-simplify: Simplify 1 into 1 1546593440.514 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593440.514 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593440.514 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.514 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593440.514 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593440.514 * [misc]taylor: Taking taylor expansion of -2 in k 1546593440.514 * [misc]backup-simplify: Simplify -2 into -2 1546593440.514 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593440.514 * [misc]taylor: Taking taylor expansion of PI in k 1546593440.514 * [misc]backup-simplify: Simplify PI into PI 1546593440.514 * [misc]taylor: Taking taylor expansion of n in k 1546593440.514 * [misc]backup-simplify: Simplify n into n 1546593440.514 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593440.514 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593440.514 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593440.514 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593440.515 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593440.515 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593440.515 * [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))) 1546593440.515 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593440.515 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593440.515 * [misc]taylor: Taking taylor expansion of -1 in k 1546593440.515 * [misc]backup-simplify: Simplify -1 into -1 1546593440.515 * [misc]taylor: Taking taylor expansion of k in k 1546593440.515 * [misc]backup-simplify: Simplify 0 into 0 1546593440.515 * [misc]backup-simplify: Simplify 1 into 1 1546593440.515 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593440.515 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593440.516 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593440.516 * [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)))) 1546593440.516 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593440.516 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.516 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.516 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593440.516 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.516 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.516 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.516 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.516 * [misc]backup-simplify: Simplify -2 into -2 1546593440.517 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.517 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.517 * [misc]backup-simplify: Simplify PI into PI 1546593440.517 * [misc]taylor: Taking taylor expansion of n in n 1546593440.517 * [misc]backup-simplify: Simplify 0 into 0 1546593440.517 * [misc]backup-simplify: Simplify 1 into 1 1546593440.517 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.517 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.518 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.518 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.518 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.518 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.518 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.518 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.518 * [misc]taylor: Taking taylor expansion of k in n 1546593440.518 * [misc]backup-simplify: Simplify k into k 1546593440.518 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.518 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.518 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.519 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.519 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.519 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.519 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593440.520 * [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)))) 1546593440.520 * [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))))) 1546593440.521 * [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))))) 1546593440.521 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593440.522 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593440.522 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1546593440.522 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546593440.522 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593440.522 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.522 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.522 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593440.522 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.522 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.522 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.522 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.522 * [misc]backup-simplify: Simplify -2 into -2 1546593440.522 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.522 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.522 * [misc]backup-simplify: Simplify PI into PI 1546593440.522 * [misc]taylor: Taking taylor expansion of n in n 1546593440.522 * [misc]backup-simplify: Simplify 0 into 0 1546593440.522 * [misc]backup-simplify: Simplify 1 into 1 1546593440.522 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.523 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.523 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.523 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.523 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.523 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.523 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.523 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.523 * [misc]taylor: Taking taylor expansion of k in n 1546593440.523 * [misc]backup-simplify: Simplify k into k 1546593440.523 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.523 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.523 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.523 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.524 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.524 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.524 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593440.524 * [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)))) 1546593440.525 * [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))))) 1546593440.525 * [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)))))) 1546593440.526 * [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)))))) 1546593440.526 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.526 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593440.526 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593440.526 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593440.527 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593440.527 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593440.529 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593440.529 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546593440.530 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593440.531 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 1546593440.531 * [misc]backup-simplify: Simplify 0 into 0 1546593440.531 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593440.532 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593440.532 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1546593440.532 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546593440.532 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593440.532 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593440.532 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593440.532 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593440.533 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593440.533 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593440.533 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593440.533 * [misc]taylor: Taking taylor expansion of -2 in n 1546593440.533 * [misc]backup-simplify: Simplify -2 into -2 1546593440.533 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593440.533 * [misc]taylor: Taking taylor expansion of PI in n 1546593440.533 * [misc]backup-simplify: Simplify PI into PI 1546593440.533 * [misc]taylor: Taking taylor expansion of n in n 1546593440.533 * [misc]backup-simplify: Simplify 0 into 0 1546593440.533 * [misc]backup-simplify: Simplify 1 into 1 1546593440.533 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593440.533 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593440.533 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593440.533 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593440.533 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593440.533 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.533 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593440.533 * [misc]taylor: Taking taylor expansion of k in n 1546593440.533 * [misc]backup-simplify: Simplify k into k 1546593440.533 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593440.534 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593440.534 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593440.534 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593440.534 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593440.534 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593440.534 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593440.535 * [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)))) 1546593440.535 * [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))))) 1546593440.536 * [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)))))) 1546593440.536 * [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)))))) 1546593440.538 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1546593440.538 * * * [misc]progress: simplifying candidates 1546593440.538 * * * * [misc]progress: [ 1 / 120 ] simplifiying candidate # 1546593440.538 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546593440.538 * * [misc]simplify: iters left: 6 (11 enodes) 1546593440.540 * * [misc]simplify: iters left: 5 (21 enodes) 1546593440.545 * * [misc]simplify: iters left: 4 (47 enodes) 1546593440.553 * * [misc]simplify: iters left: 3 (109 enodes) 1546593440.590 * * [misc]simplify: iters left: 2 (300 enodes) 1546593440.826 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546593440.826 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))))))) 1546593440.826 * * * * [misc]progress: [ 2 / 120 ] simplifiying candidate # 1546593440.826 * * * * [misc]progress: [ 3 / 120 ] simplifiying candidate # 1546593440.827 * [enter]simplify: Simplifying (* PI (* n 2)) 1546593440.827 * * [misc]simplify: iters left: 4 (5 enodes) 1546593440.828 * * [misc]simplify: iters left: 3 (9 enodes) 1546593440.831 * * [misc]simplify: iters left: 2 (15 enodes) 1546593440.835 * * [misc]simplify: iters left: 1 (17 enodes) 1546593440.839 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546593440.839 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2))))))) 1546593440.839 * * * * [misc]progress: [ 4 / 120 ] simplifiying candidate # 1546593440.839 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546593440.840 * * [misc]simplify: iters left: 5 (8 enodes) 1546593440.842 * * [misc]simplify: iters left: 4 (12 enodes) 1546593440.849 * * [misc]simplify: iters left: 3 (18 enodes) 1546593440.853 * * [misc]simplify: iters left: 2 (20 enodes) 1546593440.858 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546593440.858 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2)))))) 1546593440.858 * * * * [misc]progress: [ 5 / 120 ] simplifiying candidate # 1546593440.859 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546593440.859 * * [misc]simplify: iters left: 5 (6 enodes) 1546593440.861 * * [misc]simplify: iters left: 4 (8 enodes) 1546593440.863 * * [misc]simplify: iters left: 3 (11 enodes) 1546593440.866 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546593440.866 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))))) 1546593440.866 * * * * [misc]progress: [ 6 / 120 ] simplifiying candidate # 1546593440.866 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546593440.866 * * [misc]simplify: iters left: 5 (6 enodes) 1546593440.868 * * [misc]simplify: iters left: 4 (8 enodes) 1546593440.870 * * [misc]simplify: iters left: 3 (11 enodes) 1546593440.873 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546593440.873 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))))) 1546593440.874 * * * * [misc]progress: [ 7 / 120 ] simplifiying candidate # 1546593440.874 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546593440.874 * * [misc]simplify: iters left: 4 (5 enodes) 1546593440.875 * * [misc]simplify: iters left: 3 (7 enodes) 1546593440.877 * * [misc]simplify: iters left: 2 (10 enodes) 1546593440.880 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546593440.880 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2)))))) 1546593440.880 * * * * [misc]progress: [ 8 / 120 ] simplifiying candidate # 1546593440.881 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546593440.881 * * [misc]simplify: iters left: 5 (9 enodes) 1546593440.884 * * [misc]simplify: iters left: 4 (15 enodes) 1546593440.888 * * [misc]simplify: iters left: 3 (21 enodes) 1546593440.894 * * [misc]simplify: iters left: 2 (22 enodes) 1546593440.899 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546593440.900 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546593440.900 * * * * [misc]progress: [ 9 / 120 ] simplifiying candidate # 1546593440.900 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546593440.900 * * [misc]simplify: iters left: 5 (9 enodes) 1546593440.903 * * [misc]simplify: iters left: 4 (15 enodes) 1546593440.907 * * [misc]simplify: iters left: 3 (21 enodes) 1546593440.913 * * [misc]simplify: iters left: 2 (22 enodes) 1546593440.917 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546593440.917 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546593440.917 * * * * [misc]progress: [ 10 / 120 ] simplifiying candidate # 1546593440.917 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546593440.917 * * [misc]simplify: iters left: 5 (7 enodes) 1546593440.918 * * [misc]simplify: iters left: 4 (9 enodes) 1546593440.920 * * [misc]simplify: iters left: 3 (12 enodes) 1546593440.921 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546593440.921 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546593440.921 * * * * [misc]progress: [ 11 / 120 ] simplifiying candidate # 1546593440.921 * * * * [misc]progress: [ 12 / 120 ] simplifiying candidate # 1546593440.921 * * * * [misc]progress: [ 13 / 120 ] simplifiying candidate # 1546593440.921 * * * * [misc]progress: [ 14 / 120 ] simplifiying candidate # 1546593440.921 * * * * [misc]progress: [ 15 / 120 ] simplifiying candidate # 1546593440.921 * * * * [misc]progress: [ 16 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 17 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 18 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 19 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 20 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 21 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 22 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 23 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 24 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 25 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 26 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 27 / 120 ] simplifiying candidate # 1546593440.922 * * * * [misc]progress: [ 28 / 120 ] simplifiying candidate # 1546593440.922 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1546593440.922 * * [misc]simplify: iters left: 6 (14 enodes) 1546593440.924 * * [misc]simplify: iters left: 5 (26 enodes) 1546593440.929 * * [misc]simplify: iters left: 4 (59 enodes) 1546593440.944 * * [misc]simplify: iters left: 3 (164 enodes) 1546593440.996 * * [misc]simplify: iters left: 2 (488 enodes) 1546593441.260 * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n)))) 1546593441.260 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n))))))) 1546593441.260 * * * * [misc]progress: [ 29 / 120 ] simplifiying candidate # 1546593441.260 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1546593441.260 * * [misc]simplify: iters left: 6 (14 enodes) 1546593441.263 * * [misc]simplify: iters left: 5 (26 enodes) 1546593441.267 * * [misc]simplify: iters left: 4 (59 enodes) 1546593441.284 * * [misc]simplify: iters left: 3 (164 enodes) 1546593441.343 * * [misc]simplify: iters left: 2 (488 enodes) 1546593441.605 * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n)))) 1546593441.605 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n))))))) 1546593441.605 * * * * [misc]progress: [ 30 / 120 ] simplifiying candidate # 1546593441.605 * [enter]simplify: Simplifying (- (log (sqrt k)) (log (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593441.605 * * [misc]simplify: iters left: 6 (14 enodes) 1546593441.607 * * [misc]simplify: iters left: 5 (24 enodes) 1546593441.611 * * [misc]simplify: iters left: 4 (46 enodes) 1546593441.618 * * [misc]simplify: iters left: 3 (103 enodes) 1546593441.653 * * [misc]simplify: iters left: 2 (336 enodes) 1546593441.864 * [exit]simplify: Simplified to (+ (* (log (* n (* PI 2))) (+ (/ k 2) -1/2)) (log (sqrt k))) 1546593441.864 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (* (log (* n (* PI 2))) (+ (/ k 2) -1/2)) (log (sqrt k)))))) 1546593441.864 * * * * [misc]progress: [ 31 / 120 ] simplifiying candidate # 1546593441.864 * * * * [misc]progress: [ 32 / 120 ] simplifiying candidate # 1546593441.864 * * * * [misc]progress: [ 33 / 120 ] simplifiying candidate # 1546593441.864 * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593441.864 * * [misc]simplify: iters left: 6 (16 enodes) 1546593441.870 * * [misc]simplify: iters left: 5 (31 enodes) 1546593441.880 * * [misc]simplify: iters left: 4 (70 enodes) 1546593441.907 * * [misc]simplify: iters left: 3 (130 enodes) 1546593441.944 * * [misc]simplify: iters left: 2 (206 enodes) 1546593441.988 * * [misc]simplify: iters left: 1 (288 enodes) 1546593442.072 * [exit]simplify: Simplified to (/ (/ (* k (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) 1546593442.072 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* k (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))))) 1546593442.072 * * * * [misc]progress: [ 34 / 120 ] simplifiying candidate # 1546593442.072 * * * * [misc]progress: [ 35 / 120 ] simplifiying candidate # 1546593442.072 * * * * [misc]progress: [ 36 / 120 ] simplifiying candidate # 1546593442.072 * * * * [misc]progress: [ 37 / 120 ] simplifiying candidate # 1546593442.072 * * * * [misc]progress: [ 38 / 120 ] simplifiying candidate # 1546593442.073 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1546593442.073 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.074 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.079 * * [misc]simplify: iters left: 4 (27 enodes) 1546593442.086 * * [misc]simplify: iters left: 3 (29 enodes) 1546593442.093 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1546593442.093 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546593442.093 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.093 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.097 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.102 * * [misc]simplify: iters left: 4 (24 enodes) 1546593442.108 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.114 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546593442.114 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546593442.115 * * * * [misc]progress: [ 39 / 120 ] simplifiying candidate # 1546593442.115 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1546593442.115 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.119 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.124 * * [misc]simplify: iters left: 4 (27 enodes) 1546593442.133 * * [misc]simplify: iters left: 3 (29 enodes) 1546593442.141 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1546593442.141 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546593442.141 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.141 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.145 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.150 * * [misc]simplify: iters left: 4 (24 enodes) 1546593442.156 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.162 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546593442.163 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546593442.163 * * * * [misc]progress: [ 40 / 120 ] simplifiying candidate # 1546593442.163 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) 1546593442.163 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.166 * * [misc]simplify: iters left: 5 (15 enodes) 1546593442.171 * * [misc]simplify: iters left: 4 (20 enodes) 1546593442.176 * * [misc]simplify: iters left: 3 (21 enodes) 1546593442.182 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) 1546593442.182 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546593442.182 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.183 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.186 * * [misc]simplify: iters left: 5 (14 enodes) 1546593442.190 * * [misc]simplify: iters left: 4 (17 enodes) 1546593442.194 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.194 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546593442.195 * * * * [misc]progress: [ 41 / 120 ] simplifiying candidate # 1546593442.195 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546593442.195 * * [misc]simplify: iters left: 6 (16 enodes) 1546593442.200 * * [misc]simplify: iters left: 5 (28 enodes) 1546593442.209 * * [misc]simplify: iters left: 4 (46 enodes) 1546593442.222 * * [misc]simplify: iters left: 3 (50 enodes) 1546593442.234 * * [misc]simplify: iters left: 2 (53 enodes) 1546593442.248 * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546593442.248 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546593442.248 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.248 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.250 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.253 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.257 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.260 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.261 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546593442.261 * * * * [misc]progress: [ 42 / 120 ] simplifiying candidate # 1546593442.261 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.261 * * [misc]simplify: iters left: 6 (15 enodes) 1546593442.264 * * [misc]simplify: iters left: 5 (23 enodes) 1546593442.267 * * [misc]simplify: iters left: 4 (34 enodes) 1546593442.272 * * [misc]simplify: iters left: 3 (36 enodes) 1546593442.277 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.278 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546593442.278 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.278 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.283 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.288 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.296 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.303 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.303 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546593442.303 * * * * [misc]progress: [ 43 / 120 ] simplifiying candidate # 1546593442.303 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) 1546593442.304 * * [misc]simplify: iters left: 6 (6 enodes) 1546593442.305 * * [misc]simplify: iters left: 5 (10 enodes) 1546593442.309 * * [misc]simplify: iters left: 4 (16 enodes) 1546593442.312 * * [misc]simplify: iters left: 3 (18 enodes) 1546593442.316 * * [misc]simplify: iters left: 2 (23 enodes) 1546593442.321 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546593442.321 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546593442.322 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593442.322 * * [misc]simplify: iters left: 6 (13 enodes) 1546593442.326 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.331 * * [misc]simplify: iters left: 4 (28 enodes) 1546593442.339 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.346 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546593442.346 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546593442.346 * * * * [misc]progress: [ 44 / 120 ] simplifiying candidate # 1546593442.347 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1546593442.347 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.350 * * [misc]simplify: iters left: 5 (16 enodes) 1546593442.354 * * [misc]simplify: iters left: 4 (22 enodes) 1546593442.360 * * [misc]simplify: iters left: 3 (23 enodes) 1546593442.362 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1546593442.363 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546593442.363 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.363 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.365 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.367 * * [misc]simplify: iters left: 4 (24 enodes) 1546593442.370 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.373 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546593442.373 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546593442.373 * * * * [misc]progress: [ 45 / 120 ] simplifiying candidate # 1546593442.373 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1546593442.373 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.375 * * [misc]simplify: iters left: 5 (16 enodes) 1546593442.377 * * [misc]simplify: iters left: 4 (22 enodes) 1546593442.381 * * [misc]simplify: iters left: 3 (23 enodes) 1546593442.384 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1546593442.384 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546593442.384 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.384 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.386 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.389 * * [misc]simplify: iters left: 4 (24 enodes) 1546593442.392 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.395 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546593442.395 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546593442.395 * * * * [misc]progress: [ 46 / 120 ] simplifiying candidate # 1546593442.395 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) 1546593442.395 * * [misc]simplify: iters left: 6 (10 enodes) 1546593442.397 * * [misc]simplify: iters left: 5 (12 enodes) 1546593442.398 * * [misc]simplify: iters left: 4 (15 enodes) 1546593442.400 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) 1546593442.400 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546593442.400 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.401 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.402 * * [misc]simplify: iters left: 5 (14 enodes) 1546593442.404 * * [misc]simplify: iters left: 4 (17 enodes) 1546593442.406 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.406 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546593442.406 * * * * [misc]progress: [ 47 / 120 ] simplifiying candidate # 1546593442.406 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546593442.407 * * [misc]simplify: iters left: 6 (15 enodes) 1546593442.409 * * [misc]simplify: iters left: 5 (23 enodes) 1546593442.412 * * [misc]simplify: iters left: 4 (32 enodes) 1546593442.416 * * [misc]simplify: iters left: 3 (34 enodes) 1546593442.422 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546593442.422 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546593442.422 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.422 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.426 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.432 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.440 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.447 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.447 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546593442.447 * * * * [misc]progress: [ 48 / 120 ] simplifiying candidate # 1546593442.447 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.447 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.452 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.458 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.465 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.473 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.473 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546593442.473 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.473 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.477 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.483 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.492 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.499 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.499 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546593442.499 * * * * [misc]progress: [ 49 / 120 ] simplifiying candidate # 1546593442.500 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) 1) 1546593442.500 * * [misc]simplify: iters left: 4 (5 enodes) 1546593442.501 * * [misc]simplify: iters left: 3 (7 enodes) 1546593442.503 * * [misc]simplify: iters left: 2 (9 enodes) 1546593442.505 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546593442.505 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546593442.505 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593442.506 * * [misc]simplify: iters left: 6 (13 enodes) 1546593442.509 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.515 * * [misc]simplify: iters left: 4 (28 enodes) 1546593442.522 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.530 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546593442.530 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546593442.530 * * * * [misc]progress: [ 50 / 120 ] simplifiying candidate # 1546593442.531 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1546593442.531 * * [misc]simplify: iters left: 6 (9 enodes) 1546593442.534 * * [misc]simplify: iters left: 5 (16 enodes) 1546593442.538 * * [misc]simplify: iters left: 4 (22 enodes) 1546593442.541 * * [misc]simplify: iters left: 3 (23 enodes) 1546593442.544 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1546593442.544 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546593442.544 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.544 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.546 * * [misc]simplify: iters left: 5 (17 enodes) 1546593442.548 * * [misc]simplify: iters left: 4 (23 enodes) 1546593442.551 * * [misc]simplify: iters left: 3 (24 enodes) 1546593442.554 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546593442.554 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1546593442.554 * * * * [misc]progress: [ 51 / 120 ] simplifiying candidate # 1546593442.554 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1546593442.554 * * [misc]simplify: iters left: 6 (9 enodes) 1546593442.556 * * [misc]simplify: iters left: 5 (16 enodes) 1546593442.558 * * [misc]simplify: iters left: 4 (22 enodes) 1546593442.561 * * [misc]simplify: iters left: 3 (23 enodes) 1546593442.563 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1546593442.563 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546593442.563 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.563 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.565 * * [misc]simplify: iters left: 5 (17 enodes) 1546593442.567 * * [misc]simplify: iters left: 4 (23 enodes) 1546593442.570 * * [misc]simplify: iters left: 3 (24 enodes) 1546593442.573 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546593442.573 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1546593442.573 * * * * [misc]progress: [ 52 / 120 ] simplifiying candidate # 1546593442.573 * [enter]simplify: Simplifying (/ 1 (pow PI (- 1/2 (/ k 2)))) 1546593442.574 * * [misc]simplify: iters left: 6 (9 enodes) 1546593442.575 * * [misc]simplify: iters left: 5 (13 enodes) 1546593442.578 * * [misc]simplify: iters left: 4 (16 enodes) 1546593442.582 * [exit]simplify: Simplified to (/ 1 (pow PI (- 1/2 (/ k 2)))) 1546593442.582 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546593442.582 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.582 * * [misc]simplify: iters left: 6 (10 enodes) 1546593442.585 * * [misc]simplify: iters left: 5 (13 enodes) 1546593442.589 * * [misc]simplify: iters left: 4 (16 enodes) 1546593442.593 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.594 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546593442.594 * * * * [misc]progress: [ 53 / 120 ] simplifiying candidate # 1546593442.594 * [enter]simplify: Simplifying (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546593442.594 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.598 * * [misc]simplify: iters left: 5 (24 enodes) 1546593442.606 * * [misc]simplify: iters left: 4 (33 enodes) 1546593442.615 * * [misc]simplify: iters left: 3 (34 enodes) 1546593442.623 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593442.623 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546593442.624 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.624 * * [misc]simplify: iters left: 6 (13 enodes) 1546593442.626 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.628 * * [misc]simplify: iters left: 4 (28 enodes) 1546593442.632 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.636 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546593442.636 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))))) 1546593442.636 * * * * [misc]progress: [ 54 / 120 ] simplifiying candidate # 1546593442.637 * [enter]simplify: Simplifying (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.637 * * [misc]simplify: iters left: 6 (13 enodes) 1546593442.639 * * [misc]simplify: iters left: 5 (21 enodes) 1546593442.642 * * [misc]simplify: iters left: 4 (30 enodes) 1546593442.646 * * [misc]simplify: iters left: 3 (31 enodes) 1546593442.649 * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1546593442.649 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546593442.650 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.650 * * [misc]simplify: iters left: 6 (13 enodes) 1546593442.652 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.654 * * [misc]simplify: iters left: 4 (28 enodes) 1546593442.658 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.662 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546593442.662 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))))) 1546593442.662 * * * * [misc]progress: [ 55 / 120 ] simplifiying candidate # 1546593442.662 * [enter]simplify: Simplifying (/ 1 1) 1546593442.662 * * [misc]simplify: iters left: 2 (2 enodes) 1546593442.662 * * [misc]simplify: iters left: 1 (4 enodes) 1546593442.663 * [exit]simplify: Simplified to 1 1546593442.663 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546593442.663 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593442.663 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.665 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.667 * * [misc]simplify: iters left: 4 (27 enodes) 1546593442.671 * * [misc]simplify: iters left: 3 (29 enodes) 1546593442.674 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593442.674 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546593442.674 * * * * [misc]progress: [ 56 / 120 ] simplifiying candidate # 1546593442.675 * * * * [misc]progress: [ 57 / 120 ] simplifiying candidate # 1546593442.675 * * * * [misc]progress: [ 58 / 120 ] simplifiying candidate # 1546593442.675 * * * * [misc]progress: [ 59 / 120 ] simplifiying candidate # 1546593442.675 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546593442.675 * * [misc]simplify: iters left: 5 (9 enodes) 1546593442.677 * * [misc]simplify: iters left: 4 (15 enodes) 1546593442.682 * * [misc]simplify: iters left: 3 (21 enodes) 1546593442.687 * * [misc]simplify: iters left: 2 (22 enodes) 1546593442.693 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546593442.693 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546593442.693 * * * * [misc]progress: [ 60 / 120 ] simplifiying candidate # 1546593442.693 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546593442.693 * * [misc]simplify: iters left: 5 (9 enodes) 1546593442.696 * * [misc]simplify: iters left: 4 (15 enodes) 1546593442.700 * * [misc]simplify: iters left: 3 (21 enodes) 1546593442.707 * * [misc]simplify: iters left: 2 (22 enodes) 1546593442.712 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546593442.712 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546593442.712 * * * * [misc]progress: [ 61 / 120 ] simplifiying candidate # 1546593442.713 * [enter]simplify: Simplifying (pow (* n 2) (- 1/2 (/ k 2))) 1546593442.713 * * [misc]simplify: iters left: 5 (8 enodes) 1546593442.715 * * [misc]simplify: iters left: 4 (11 enodes) 1546593442.718 * * [misc]simplify: iters left: 3 (14 enodes) 1546593442.722 * [exit]simplify: Simplified to (pow (* n 2) (- 1/2 (/ k 2))) 1546593442.722 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546593442.722 * * * * [misc]progress: [ 62 / 120 ] simplifiying candidate # 1546593442.723 * [enter]simplify: Simplifying (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593442.723 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.726 * * [misc]simplify: iters left: 5 (17 enodes) 1546593442.731 * * [misc]simplify: iters left: 4 (26 enodes) 1546593442.738 * * [misc]simplify: iters left: 3 (27 enodes) 1546593442.745 * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546593442.745 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546593442.745 * * * * [misc]progress: [ 63 / 120 ] simplifiying candidate # 1546593442.745 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593442.745 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.749 * * [misc]simplify: iters left: 5 (17 enodes) 1546593442.752 * * [misc]simplify: iters left: 4 (26 enodes) 1546593442.756 * * [misc]simplify: iters left: 3 (27 enodes) 1546593442.759 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546593442.759 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546593442.759 * * * * [misc]progress: [ 64 / 120 ] simplifiying candidate # 1546593442.759 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546593442.759 * * [misc]simplify: iters left: 5 (10 enodes) 1546593442.761 * * [misc]simplify: iters left: 4 (16 enodes) 1546593442.763 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.766 * * [misc]simplify: iters left: 2 (26 enodes) 1546593442.769 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546593442.769 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546593442.770 * * * * [misc]progress: [ 65 / 120 ] simplifiying candidate # 1546593442.770 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546593442.770 * * [misc]simplify: iters left: 4 (4 enodes) 1546593442.770 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546593442.770 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546593442.770 * * * * [misc]progress: [ 66 / 120 ] simplifiying candidate # 1546593442.771 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546593442.771 * * [misc]simplify: iters left: 2 (3 enodes) 1546593442.771 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546593442.771 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546593442.771 * * * * [misc]progress: [ 67 / 120 ] simplifiying candidate # 1546593442.771 * * * * [misc]progress: [ 68 / 120 ] simplifiying candidate # 1546593442.771 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546593442.771 * * [misc]simplify: iters left: 5 (8 enodes) 1546593442.772 * * [misc]simplify: iters left: 4 (12 enodes) 1546593442.774 * * [misc]simplify: iters left: 3 (18 enodes) 1546593442.777 * * [misc]simplify: iters left: 2 (20 enodes) 1546593442.779 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546593442.779 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* 2 n) PI) (/ k 2))))) 1546593442.779 * * * * [misc]progress: [ 69 / 120 ] simplifiying candidate # 1546593442.779 * * * * [misc]progress: [ 70 / 120 ] simplifiying candidate # 1546593442.779 * [enter]simplify: Simplifying (- 1) 1546593442.779 * * [misc]simplify: iters left: 2 (2 enodes) 1546593442.780 * * [misc]simplify: iters left: 1 (5 enodes) 1546593442.781 * [exit]simplify: Simplified to -1 1546593442.781 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) -1)) 1546593442.781 * * * * [misc]progress: [ 71 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 72 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 73 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 74 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 75 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 76 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 77 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 78 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 79 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 80 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 81 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 82 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 83 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 84 / 120 ] simplifiying candidate # 1546593442.781 * * * * [misc]progress: [ 85 / 120 ] simplifiying candidate # 1546593442.781 * [enter]simplify: Simplifying (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.781 * * [misc]simplify: iters left: 6 (13 enodes) 1546593442.783 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.786 * * [misc]simplify: iters left: 4 (28 enodes) 1546593442.790 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.793 * [exit]simplify: Simplified to (cbrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546593442.794 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (cbrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546593442.794 * * * * [misc]progress: [ 86 / 120 ] simplifiying candidate # 1546593442.794 * [enter]simplify: Simplifying (sqrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.794 * * [misc]simplify: iters left: 6 (13 enodes) 1546593442.796 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.799 * * [misc]simplify: iters left: 4 (28 enodes) 1546593442.805 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.814 * [exit]simplify: Simplified to (sqrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546593442.814 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546593442.814 * * * * [misc]progress: [ 87 / 120 ] simplifiying candidate # 1546593442.814 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.814 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.818 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.823 * * [misc]simplify: iters left: 4 (24 enodes) 1546593442.830 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.836 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546593442.836 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546593442.836 * * * * [misc]progress: [ 88 / 120 ] simplifiying candidate # 1546593442.837 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.837 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.841 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.846 * * [misc]simplify: iters left: 4 (24 enodes) 1546593442.852 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.859 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546593442.859 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546593442.859 * * * * [misc]progress: [ 89 / 120 ] simplifiying candidate # 1546593442.859 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.859 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.863 * * [misc]simplify: iters left: 5 (14 enodes) 1546593442.867 * * [misc]simplify: iters left: 4 (17 enodes) 1546593442.871 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.871 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546593442.872 * * * * [misc]progress: [ 90 / 120 ] simplifiying candidate # 1546593442.872 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.872 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.876 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.882 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.889 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.897 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.897 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546593442.897 * * * * [misc]progress: [ 91 / 120 ] simplifiying candidate # 1546593442.898 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.898 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.901 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.904 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.908 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.911 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.911 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546593442.911 * * * * [misc]progress: [ 92 / 120 ] simplifiying candidate # 1546593442.912 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593442.912 * * [misc]simplify: iters left: 6 (13 enodes) 1546593442.914 * * [misc]simplify: iters left: 5 (19 enodes) 1546593442.916 * * [misc]simplify: iters left: 4 (28 enodes) 1546593442.920 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.924 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546593442.924 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))) 1546593442.924 * * * * [misc]progress: [ 93 / 120 ] simplifiying candidate # 1546593442.924 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.924 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.926 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.930 * * [misc]simplify: iters left: 4 (24 enodes) 1546593442.937 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.943 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546593442.943 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546593442.943 * * * * [misc]progress: [ 94 / 120 ] simplifiying candidate # 1546593442.944 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593442.944 * * [misc]simplify: iters left: 6 (12 enodes) 1546593442.948 * * [misc]simplify: iters left: 5 (18 enodes) 1546593442.953 * * [misc]simplify: iters left: 4 (24 enodes) 1546593442.957 * * [misc]simplify: iters left: 3 (25 enodes) 1546593442.960 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546593442.960 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546593442.960 * * * * [misc]progress: [ 95 / 120 ] simplifiying candidate # 1546593442.960 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.960 * * [misc]simplify: iters left: 6 (11 enodes) 1546593442.962 * * [misc]simplify: iters left: 5 (14 enodes) 1546593442.964 * * [misc]simplify: iters left: 4 (17 enodes) 1546593442.966 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593442.966 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546593442.966 * * * * [misc]progress: [ 96 / 120 ] simplifiying candidate # 1546593442.966 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.966 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.968 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.971 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.975 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.979 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.979 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546593442.979 * * * * [misc]progress: [ 97 / 120 ] simplifiying candidate # 1546593442.979 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593442.979 * * [misc]simplify: iters left: 6 (14 enodes) 1546593442.981 * * [misc]simplify: iters left: 5 (20 enodes) 1546593442.984 * * [misc]simplify: iters left: 4 (29 enodes) 1546593442.988 * * [misc]simplify: iters left: 3 (30 enodes) 1546593442.995 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593442.995 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546593442.995 * * * * [misc]progress: [ 98 / 120 ] simplifiying candidate # 1546593442.996 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593442.996 * * [misc]simplify: iters left: 6 (13 enodes) 1546593443.000 * * [misc]simplify: iters left: 5 (19 enodes) 1546593443.005 * * [misc]simplify: iters left: 4 (28 enodes) 1546593443.013 * * [misc]simplify: iters left: 3 (30 enodes) 1546593443.018 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546593443.018 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))) 1546593443.018 * * * * [misc]progress: [ 99 / 120 ] simplifiying candidate # 1546593443.018 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593443.018 * * [misc]simplify: iters left: 6 (11 enodes) 1546593443.020 * * [misc]simplify: iters left: 5 (17 enodes) 1546593443.022 * * [misc]simplify: iters left: 4 (23 enodes) 1546593443.025 * * [misc]simplify: iters left: 3 (24 enodes) 1546593443.028 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546593443.028 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1546593443.028 * * * * [misc]progress: [ 100 / 120 ] simplifiying candidate # 1546593443.029 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546593443.029 * * [misc]simplify: iters left: 6 (11 enodes) 1546593443.030 * * [misc]simplify: iters left: 5 (17 enodes) 1546593443.033 * * [misc]simplify: iters left: 4 (23 enodes) 1546593443.036 * * [misc]simplify: iters left: 3 (24 enodes) 1546593443.039 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546593443.039 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1546593443.040 * * * * [misc]progress: [ 101 / 120 ] simplifiying candidate # 1546593443.040 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593443.040 * * [misc]simplify: iters left: 6 (10 enodes) 1546593443.041 * * [misc]simplify: iters left: 5 (13 enodes) 1546593443.043 * * [misc]simplify: iters left: 4 (16 enodes) 1546593443.047 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546593443.048 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546593443.048 * * * * [misc]progress: [ 102 / 120 ] simplifiying candidate # 1546593443.048 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593443.048 * * [misc]simplify: iters left: 6 (13 enodes) 1546593443.052 * * [misc]simplify: iters left: 5 (19 enodes) 1546593443.057 * * [misc]simplify: iters left: 4 (28 enodes) 1546593443.065 * * [misc]simplify: iters left: 3 (30 enodes) 1546593443.070 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546593443.070 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546593443.070 * * * * [misc]progress: [ 103 / 120 ] simplifiying candidate # 1546593443.070 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593443.070 * * [misc]simplify: iters left: 6 (13 enodes) 1546593443.072 * * [misc]simplify: iters left: 5 (19 enodes) 1546593443.075 * * [misc]simplify: iters left: 4 (28 enodes) 1546593443.078 * * [misc]simplify: iters left: 3 (30 enodes) 1546593443.082 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546593443.082 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546593443.082 * * * * [misc]progress: [ 104 / 120 ] simplifiying candidate # 1546593443.082 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593443.082 * * [misc]simplify: iters left: 6 (12 enodes) 1546593443.084 * * [misc]simplify: iters left: 5 (18 enodes) 1546593443.087 * * [misc]simplify: iters left: 4 (27 enodes) 1546593443.091 * * [misc]simplify: iters left: 3 (29 enodes) 1546593443.094 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593443.094 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546593443.094 * * * * [misc]progress: [ 105 / 120 ] simplifiying candidate # 1546593443.094 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593443.095 * * [misc]simplify: iters left: 6 (12 enodes) 1546593443.098 * * [misc]simplify: iters left: 5 (18 enodes) 1546593443.103 * * [misc]simplify: iters left: 4 (27 enodes) 1546593443.110 * * [misc]simplify: iters left: 3 (29 enodes) 1546593443.117 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593443.117 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546593443.118 * * * * [misc]progress: [ 106 / 120 ] simplifiying candidate # 1546593443.118 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593443.118 * * [misc]simplify: iters left: 6 (12 enodes) 1546593443.122 * * [misc]simplify: iters left: 5 (20 enodes) 1546593443.127 * * [misc]simplify: iters left: 4 (29 enodes) 1546593443.135 * * [misc]simplify: iters left: 3 (30 enodes) 1546593443.142 * [exit]simplify: Simplified to (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1546593443.142 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))) 1546593443.142 * * * * [misc]progress: [ 107 / 120 ] simplifiying candidate # 1546593443.142 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546593443.142 * * [misc]simplify: iters left: 5 (8 enodes) 1546593443.146 * * [misc]simplify: iters left: 4 (12 enodes) 1546593443.150 * * [misc]simplify: iters left: 3 (18 enodes) 1546593443.155 * * [misc]simplify: iters left: 2 (20 enodes) 1546593443.159 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546593443.160 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) 1/2))) (pow (* (* 2 n) PI) (/ k 2)))) 1546593443.160 * * * * [misc]progress: [ 108 / 120 ] simplifiying candidate # 1546593443.160 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546593443.160 * * [misc]simplify: iters left: 5 (10 enodes) 1546593443.161 * * [misc]simplify: iters left: 4 (16 enodes) 1546593443.164 * * [misc]simplify: iters left: 3 (25 enodes) 1546593443.167 * * [misc]simplify: iters left: 2 (26 enodes) 1546593443.170 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546593443.170 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593443.170 * * * * [misc]progress: [ 109 / 120 ] simplifiying candidate # 1546593443.171 * [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))))) 1546593443.171 * * [misc]simplify: iters left: 6 (37 enodes) 1546593443.181 * * [misc]simplify: iters left: 5 (105 enodes) 1546593443.222 * * [misc]simplify: iters left: 4 (339 enodes) 1546593443.420 * [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))))) 1546593443.420 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)))))))) 1546593443.420 * * * * [misc]progress: [ 110 / 120 ] simplifiying candidate # 1546593443.420 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546593443.420 * * [misc]simplify: iters left: 6 (15 enodes) 1546593443.424 * * [misc]simplify: iters left: 5 (33 enodes) 1546593443.429 * * [misc]simplify: iters left: 4 (64 enodes) 1546593443.451 * * [misc]simplify: iters left: 3 (171 enodes) 1546593443.545 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546593443.545 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))))))) 1546593443.545 * * * * [misc]progress: [ 111 / 120 ] simplifiying candidate # 1546593443.546 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546593443.546 * * [misc]simplify: iters left: 6 (15 enodes) 1546593443.552 * * [misc]simplify: iters left: 5 (30 enodes) 1546593443.562 * * [misc]simplify: iters left: 4 (65 enodes) 1546593443.586 * * [misc]simplify: iters left: 3 (200 enodes) 1546593443.713 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546593443.713 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))))) 1546593443.713 * * * * [misc]progress: [ 112 / 120 ] simplifiying candidate # 1546593443.714 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593443.714 * * [misc]simplify: iters left: 4 (5 enodes) 1546593443.715 * * [misc]simplify: iters left: 3 (9 enodes) 1546593443.718 * * [misc]simplify: iters left: 2 (15 enodes) 1546593443.722 * * [misc]simplify: iters left: 1 (17 enodes) 1546593443.726 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593443.726 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546593443.726 * * * * [misc]progress: [ 113 / 120 ] simplifiying candidate # 1546593443.726 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593443.726 * * [misc]simplify: iters left: 4 (5 enodes) 1546593443.728 * * [misc]simplify: iters left: 3 (9 enodes) 1546593443.730 * * [misc]simplify: iters left: 2 (15 enodes) 1546593443.734 * * [misc]simplify: iters left: 1 (17 enodes) 1546593443.738 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593443.738 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546593443.738 * * * * [misc]progress: [ 114 / 120 ] simplifiying candidate # 1546593443.739 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593443.739 * * [misc]simplify: iters left: 4 (5 enodes) 1546593443.740 * * [misc]simplify: iters left: 3 (9 enodes) 1546593443.743 * * [misc]simplify: iters left: 2 (15 enodes) 1546593443.745 * * [misc]simplify: iters left: 1 (17 enodes) 1546593443.747 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593443.747 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546593443.747 * * * * [misc]progress: [ 115 / 120 ] simplifiying candidate # 1546593443.748 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546593443.748 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546593443.748 * * * * [misc]progress: [ 116 / 120 ] simplifiying candidate # 1546593443.748 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546593443.748 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546593443.748 * * * * [misc]progress: [ 117 / 120 ] simplifiying candidate # 1546593443.748 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546593443.748 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546593443.748 * * * * [misc]progress: [ 118 / 120 ] simplifiying candidate # 1546593443.748 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1546593443.748 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593443.749 * * * * [misc]progress: [ 119 / 120 ] simplifiying candidate # 1546593443.749 * [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)))))))) 1546593443.749 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593443.749 * * * * [misc]progress: [ 120 / 120 ] simplifiying candidate # 1546593443.749 * [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))))))))))) 1546593443.749 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593443.749 * * * [misc]progress: adding candidates to table 1546593445.248 * * [misc]progress: iteration 3 / 4 1546593445.248 * * * [misc]progress: picking best candidate 1546593445.271 * * * * [misc]pick: Picked # 1546593445.271 * * * [misc]progress: localizing error 1546593445.302 * * * [misc]progress: generating rewritten candidates 1546593445.302 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2) 1546593445.305 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1 2) 1546593445.306 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1546593445.314 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1546593445.321 * * * [misc]progress: generating series expansions 1546593445.321 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2) 1546593445.322 * [misc]backup-simplify: Simplify (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546593445.322 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546593445.322 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593445.322 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593445.322 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593445.322 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593445.322 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.322 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.322 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593445.322 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.322 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.322 * [misc]taylor: Taking taylor expansion of k in k 1546593445.322 * [misc]backup-simplify: Simplify 0 into 0 1546593445.322 * [misc]backup-simplify: Simplify 1 into 1 1546593445.322 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593445.322 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593445.322 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.322 * [misc]backup-simplify: Simplify 2 into 2 1546593445.322 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593445.322 * [misc]taylor: Taking taylor expansion of n in k 1546593445.322 * [misc]backup-simplify: Simplify n into n 1546593445.322 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.322 * [misc]backup-simplify: Simplify PI into PI 1546593445.322 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593445.322 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593445.323 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593445.323 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593445.323 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.323 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.323 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593445.323 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593445.323 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593445.324 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593445.324 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593445.324 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593445.324 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.324 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.324 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593445.324 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.324 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.324 * [misc]taylor: Taking taylor expansion of k in n 1546593445.324 * [misc]backup-simplify: Simplify k into k 1546593445.324 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593445.324 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593445.324 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.324 * [misc]backup-simplify: Simplify 2 into 2 1546593445.324 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.324 * [misc]taylor: Taking taylor expansion of n in n 1546593445.324 * [misc]backup-simplify: Simplify 0 into 0 1546593445.324 * [misc]backup-simplify: Simplify 1 into 1 1546593445.324 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.324 * [misc]backup-simplify: Simplify PI into PI 1546593445.325 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.325 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593445.325 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.326 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593445.326 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.327 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593445.327 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593445.327 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593445.327 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.328 * [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)))) 1546593445.329 * [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))))) 1546593445.329 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593445.329 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593445.329 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593445.329 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593445.329 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.329 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.329 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593445.329 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.329 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.329 * [misc]taylor: Taking taylor expansion of k in n 1546593445.329 * [misc]backup-simplify: Simplify k into k 1546593445.329 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593445.329 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593445.329 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.329 * [misc]backup-simplify: Simplify 2 into 2 1546593445.329 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.329 * [misc]taylor: Taking taylor expansion of n in n 1546593445.329 * [misc]backup-simplify: Simplify 0 into 0 1546593445.329 * [misc]backup-simplify: Simplify 1 into 1 1546593445.329 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.329 * [misc]backup-simplify: Simplify PI into PI 1546593445.329 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.330 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593445.330 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.331 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593445.331 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.331 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593445.332 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593445.332 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593445.332 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.333 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1546593445.333 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1546593445.334 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546593445.334 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546593445.334 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593445.337 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.338 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.338 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593445.338 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.338 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.338 * [misc]taylor: Taking taylor expansion of k in k 1546593445.338 * [misc]backup-simplify: Simplify 0 into 0 1546593445.338 * [misc]backup-simplify: Simplify 1 into 1 1546593445.338 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546593445.338 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593445.338 * [misc]taylor: Taking taylor expansion of n in k 1546593445.338 * [misc]backup-simplify: Simplify n into n 1546593445.338 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593445.338 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593445.338 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593445.338 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.338 * [misc]backup-simplify: Simplify 2 into 2 1546593445.338 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.338 * [misc]backup-simplify: Simplify PI into PI 1546593445.339 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.339 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.339 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593445.340 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.340 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.340 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.341 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546593445.341 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593445.342 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593445.343 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593445.344 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593445.347 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593445.347 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546593445.347 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.347 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.348 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.348 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546593445.350 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593445.350 * [misc]taylor: Taking taylor expansion of 0 in k 1546593445.350 * [misc]backup-simplify: Simplify 0 into 0 1546593445.350 * [misc]backup-simplify: Simplify 0 into 0 1546593445.351 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546593445.352 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593445.354 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593445.355 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.355 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593445.355 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.355 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.356 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546593445.357 * [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))))))) 1546593445.359 * [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))))))) 1546593445.360 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593445.362 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593445.367 * [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 1546593445.367 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546593445.367 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.367 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.368 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.369 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593445.371 * [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 1546593445.371 * [misc]taylor: Taking taylor expansion of 0 in k 1546593445.371 * [misc]backup-simplify: Simplify 0 into 0 1546593445.371 * [misc]backup-simplify: Simplify 0 into 0 1546593445.371 * [misc]backup-simplify: Simplify 0 into 0 1546593445.373 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546593445.374 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593445.379 * [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 1546593445.379 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.379 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593445.380 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.381 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.382 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593445.384 * [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))))) 1546593445.386 * [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))))) 1546593445.392 * [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))))) 1546593445.392 * [misc]backup-simplify: Simplify (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1546593445.392 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546593445.392 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593445.392 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593445.392 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593445.392 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593445.392 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.392 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.392 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.392 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.392 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.392 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.392 * [misc]taylor: Taking taylor expansion of k in k 1546593445.392 * [misc]backup-simplify: Simplify 0 into 0 1546593445.392 * [misc]backup-simplify: Simplify 1 into 1 1546593445.393 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.393 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593445.393 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593445.393 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.393 * [misc]backup-simplify: Simplify 2 into 2 1546593445.393 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.393 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.393 * [misc]backup-simplify: Simplify PI into PI 1546593445.393 * [misc]taylor: Taking taylor expansion of n in k 1546593445.393 * [misc]backup-simplify: Simplify n into n 1546593445.393 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.393 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593445.393 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593445.393 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.394 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.394 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.394 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593445.394 * [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)))) 1546593445.394 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.394 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.394 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.394 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.394 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.394 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.394 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.394 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.394 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.394 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.395 * [misc]taylor: Taking taylor expansion of k in n 1546593445.395 * [misc]backup-simplify: Simplify k into k 1546593445.395 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.395 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.395 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.395 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.395 * [misc]backup-simplify: Simplify 2 into 2 1546593445.395 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.395 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.395 * [misc]backup-simplify: Simplify PI into PI 1546593445.395 * [misc]taylor: Taking taylor expansion of n in n 1546593445.395 * [misc]backup-simplify: Simplify 0 into 0 1546593445.395 * [misc]backup-simplify: Simplify 1 into 1 1546593445.395 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.396 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.396 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.396 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.396 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.397 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.397 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.398 * [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))) 1546593445.399 * [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)))) 1546593445.399 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.399 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.399 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.399 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.399 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of k in n 1546593445.399 * [misc]backup-simplify: Simplify k into k 1546593445.399 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.399 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.399 * [misc]backup-simplify: Simplify 2 into 2 1546593445.399 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.399 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.399 * [misc]backup-simplify: Simplify PI into PI 1546593445.399 * [misc]taylor: Taking taylor expansion of n in n 1546593445.399 * [misc]backup-simplify: Simplify 0 into 0 1546593445.399 * [misc]backup-simplify: Simplify 1 into 1 1546593445.400 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.400 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.400 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.401 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.401 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.401 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.401 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.402 * [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))) 1546593445.403 * [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)))) 1546593445.403 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546593445.403 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546593445.403 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593445.403 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.403 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.403 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.403 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.403 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.403 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.403 * [misc]taylor: Taking taylor expansion of k in k 1546593445.403 * [misc]backup-simplify: Simplify 0 into 0 1546593445.403 * [misc]backup-simplify: Simplify 1 into 1 1546593445.403 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.403 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546593445.403 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593445.404 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593445.404 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.404 * [misc]backup-simplify: Simplify 2 into 2 1546593445.404 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.404 * [misc]backup-simplify: Simplify PI into PI 1546593445.404 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.404 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.404 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593445.404 * [misc]taylor: Taking taylor expansion of n in k 1546593445.404 * [misc]backup-simplify: Simplify n into n 1546593445.405 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593445.405 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.405 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.405 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.405 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593445.406 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546593445.406 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546593445.407 * [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)))) 1546593445.407 * [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)))) 1546593445.408 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593445.408 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593445.410 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593445.410 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593445.410 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593445.410 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.410 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.411 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.411 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593445.412 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593445.412 * [misc]taylor: Taking taylor expansion of 0 in k 1546593445.412 * [misc]backup-simplify: Simplify 0 into 0 1546593445.412 * [misc]backup-simplify: Simplify 0 into 0 1546593445.412 * [misc]backup-simplify: Simplify 0 into 0 1546593445.413 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.414 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593445.417 * [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 1546593445.417 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593445.417 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593445.417 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.417 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.418 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.418 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546593445.420 * [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 1546593445.420 * [misc]taylor: Taking taylor expansion of 0 in k 1546593445.420 * [misc]backup-simplify: Simplify 0 into 0 1546593445.420 * [misc]backup-simplify: Simplify 0 into 0 1546593445.420 * [misc]backup-simplify: Simplify 0 into 0 1546593445.420 * [misc]backup-simplify: Simplify 0 into 0 1546593445.421 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.422 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593445.426 * [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 1546593445.426 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593445.427 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593445.427 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.427 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.427 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.428 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546593445.430 * [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 1546593445.430 * [misc]taylor: Taking taylor expansion of 0 in k 1546593445.430 * [misc]backup-simplify: Simplify 0 into 0 1546593445.430 * [misc]backup-simplify: Simplify 0 into 0 1546593445.431 * [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))))) 1546593445.431 * [misc]backup-simplify: Simplify (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1546593445.431 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546593445.431 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.431 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.431 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of k in k 1546593445.431 * [misc]backup-simplify: Simplify 0 into 0 1546593445.431 * [misc]backup-simplify: Simplify 1 into 1 1546593445.431 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.431 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.431 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.431 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of -2 in k 1546593445.431 * [misc]backup-simplify: Simplify -2 into -2 1546593445.431 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.431 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.431 * [misc]backup-simplify: Simplify PI into PI 1546593445.431 * [misc]taylor: Taking taylor expansion of n in k 1546593445.431 * [misc]backup-simplify: Simplify n into n 1546593445.431 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.431 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593445.431 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593445.432 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.432 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.432 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593445.432 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1546593445.432 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.432 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.432 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of k in n 1546593445.432 * [misc]backup-simplify: Simplify k into k 1546593445.432 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.432 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.432 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.432 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.432 * [misc]backup-simplify: Simplify -2 into -2 1546593445.432 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.432 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.432 * [misc]backup-simplify: Simplify PI into PI 1546593445.432 * [misc]taylor: Taking taylor expansion of n in n 1546593445.432 * [misc]backup-simplify: Simplify 0 into 0 1546593445.432 * [misc]backup-simplify: Simplify 1 into 1 1546593445.433 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.433 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.433 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.433 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.433 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.434 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.434 * [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))) 1546593445.434 * [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)))) 1546593445.434 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.434 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593445.434 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593445.434 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.434 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.434 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.434 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.434 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.434 * [misc]taylor: Taking taylor expansion of k in n 1546593445.434 * [misc]backup-simplify: Simplify k into k 1546593445.435 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.435 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.435 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.435 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.435 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.435 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.435 * [misc]backup-simplify: Simplify -2 into -2 1546593445.435 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.435 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.435 * [misc]backup-simplify: Simplify PI into PI 1546593445.435 * [misc]taylor: Taking taylor expansion of n in n 1546593445.435 * [misc]backup-simplify: Simplify 0 into 0 1546593445.435 * [misc]backup-simplify: Simplify 1 into 1 1546593445.435 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.435 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.435 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.435 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.435 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.436 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.436 * [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))) 1546593445.437 * [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)))) 1546593445.437 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546593445.437 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546593445.437 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593445.437 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.437 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.437 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.437 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.437 * [misc]taylor: Taking taylor expansion of k in k 1546593445.437 * [misc]backup-simplify: Simplify 0 into 0 1546593445.437 * [misc]backup-simplify: Simplify 1 into 1 1546593445.437 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.437 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.437 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.437 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546593445.437 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546593445.437 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546593445.437 * [misc]taylor: Taking taylor expansion of -2 in k 1546593445.437 * [misc]backup-simplify: Simplify -2 into -2 1546593445.437 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.437 * [misc]backup-simplify: Simplify PI into PI 1546593445.437 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.438 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.438 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593445.438 * [misc]taylor: Taking taylor expansion of n in k 1546593445.438 * [misc]backup-simplify: Simplify n into n 1546593445.438 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593445.438 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.438 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.438 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593445.438 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546593445.439 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546593445.439 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593445.439 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593445.440 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593445.440 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593445.442 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593445.442 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593445.442 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593445.442 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.443 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.443 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546593445.444 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593445.444 * [misc]taylor: Taking taylor expansion of 0 in k 1546593445.444 * [misc]backup-simplify: Simplify 0 into 0 1546593445.444 * [misc]backup-simplify: Simplify 0 into 0 1546593445.444 * [misc]backup-simplify: Simplify 0 into 0 1546593445.445 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.446 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593445.449 * [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 1546593445.449 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593445.449 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593445.449 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.450 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.450 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546593445.452 * [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 1546593445.452 * [misc]taylor: Taking taylor expansion of 0 in k 1546593445.452 * [misc]backup-simplify: Simplify 0 into 0 1546593445.452 * [misc]backup-simplify: Simplify 0 into 0 1546593445.452 * [misc]backup-simplify: Simplify 0 into 0 1546593445.452 * [misc]backup-simplify: Simplify 0 into 0 1546593445.453 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.454 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593445.458 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1546593445.458 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593445.459 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593445.459 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.459 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.460 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546593445.462 * [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 1546593445.462 * [misc]taylor: Taking taylor expansion of 0 in k 1546593445.462 * [misc]backup-simplify: Simplify 0 into 0 1546593445.462 * [misc]backup-simplify: Simplify 0 into 0 1546593445.463 * [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))))) 1546593445.463 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1 2) 1546593445.463 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593445.463 * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 1546593445.463 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.463 * [misc]taylor: Taking taylor expansion of n in n 1546593445.463 * [misc]backup-simplify: Simplify 0 into 0 1546593445.463 * [misc]backup-simplify: Simplify 1 into 1 1546593445.463 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.463 * [misc]backup-simplify: Simplify PI into PI 1546593445.463 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.463 * [misc]taylor: Taking taylor expansion of n in n 1546593445.463 * [misc]backup-simplify: Simplify 0 into 0 1546593445.463 * [misc]backup-simplify: Simplify 1 into 1 1546593445.463 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.463 * [misc]backup-simplify: Simplify PI into PI 1546593445.463 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.463 * [misc]backup-simplify: Simplify 0 into 0 1546593445.464 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.464 * [misc]backup-simplify: Simplify PI into PI 1546593445.464 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593445.464 * [misc]backup-simplify: Simplify 0 into 0 1546593445.465 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593445.465 * [misc]backup-simplify: Simplify 0 into 0 1546593445.468 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593445.468 * [misc]backup-simplify: Simplify 0 into 0 1546593445.469 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593445.469 * [misc]backup-simplify: Simplify 0 into 0 1546593445.471 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593445.471 * [misc]backup-simplify: Simplify 0 into 0 1546593445.475 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546593445.475 * [misc]backup-simplify: Simplify 0 into 0 1546593445.475 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) 1546593445.475 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) 1546593445.475 * [misc]approximate: Taking taylor expansion of (/ PI n) in (n) around 0 1546593445.476 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.476 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.476 * [misc]backup-simplify: Simplify PI into PI 1546593445.476 * [misc]taylor: Taking taylor expansion of n in n 1546593445.476 * [misc]backup-simplify: Simplify 0 into 0 1546593445.476 * [misc]backup-simplify: Simplify 1 into 1 1546593445.476 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.476 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.476 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.476 * [misc]backup-simplify: Simplify PI into PI 1546593445.476 * [misc]taylor: Taking taylor expansion of n in n 1546593445.476 * [misc]backup-simplify: Simplify 0 into 0 1546593445.476 * [misc]backup-simplify: Simplify 1 into 1 1546593445.476 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.477 * [misc]backup-simplify: Simplify PI into PI 1546593445.478 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593445.478 * [misc]backup-simplify: Simplify 0 into 0 1546593445.479 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.479 * [misc]backup-simplify: Simplify 0 into 0 1546593445.481 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.481 * [misc]backup-simplify: Simplify 0 into 0 1546593445.483 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.483 * [misc]backup-simplify: Simplify 0 into 0 1546593445.485 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.485 * [misc]backup-simplify: Simplify 0 into 0 1546593445.487 * [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 1546593445.487 * [misc]backup-simplify: Simplify 0 into 0 1546593445.488 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 1546593445.488 * [misc]backup-simplify: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 1546593445.488 * [misc]approximate: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 1546593445.488 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1546593445.488 * [misc]taylor: Taking taylor expansion of -1 in n 1546593445.488 * [misc]backup-simplify: Simplify -1 into -1 1546593445.488 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.488 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.488 * [misc]backup-simplify: Simplify PI into PI 1546593445.488 * [misc]taylor: Taking taylor expansion of n in n 1546593445.488 * [misc]backup-simplify: Simplify 0 into 0 1546593445.488 * [misc]backup-simplify: Simplify 1 into 1 1546593445.488 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.488 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1546593445.488 * [misc]taylor: Taking taylor expansion of -1 in n 1546593445.488 * [misc]backup-simplify: Simplify -1 into -1 1546593445.488 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.488 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.488 * [misc]backup-simplify: Simplify PI into PI 1546593445.488 * [misc]taylor: Taking taylor expansion of n in n 1546593445.489 * [misc]backup-simplify: Simplify 0 into 0 1546593445.489 * [misc]backup-simplify: Simplify 1 into 1 1546593445.489 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.489 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1546593445.489 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1546593445.490 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593445.491 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1546593445.491 * [misc]backup-simplify: Simplify 0 into 0 1546593445.492 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.493 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1546593445.493 * [misc]backup-simplify: Simplify 0 into 0 1546593445.495 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.497 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593445.497 * [misc]backup-simplify: Simplify 0 into 0 1546593445.498 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.501 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593445.501 * [misc]backup-simplify: Simplify 0 into 0 1546593445.503 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.506 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593445.506 * [misc]backup-simplify: Simplify 0 into 0 1546593445.509 * [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 1546593445.512 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593445.512 * [misc]backup-simplify: Simplify 0 into 0 1546593445.512 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 1546593445.512 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1546593445.513 * [misc]backup-simplify: Simplify (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 1546593445.513 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 1546593445.513 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.513 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.513 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.513 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.513 * [misc]taylor: Taking taylor expansion of k in n 1546593445.513 * [misc]backup-simplify: Simplify k into k 1546593445.513 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.513 * [misc]backup-simplify: Simplify 2 into 2 1546593445.513 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.513 * [misc]taylor: Taking taylor expansion of n in n 1546593445.513 * [misc]backup-simplify: Simplify 0 into 0 1546593445.513 * [misc]backup-simplify: Simplify 1 into 1 1546593445.513 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.513 * [misc]backup-simplify: Simplify PI into PI 1546593445.514 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.514 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593445.515 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.515 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593445.516 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.516 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593445.516 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593445.516 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593445.517 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.517 * [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)))) 1546593445.518 * [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))))) 1546593445.519 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546593445.519 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546593445.519 * [misc]taylor: Taking taylor expansion of k in n 1546593445.519 * [misc]backup-simplify: Simplify k into k 1546593445.519 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546593445.519 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546593445.519 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.519 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.519 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.519 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.519 * [misc]taylor: Taking taylor expansion of k in k 1546593445.519 * [misc]backup-simplify: Simplify 0 into 0 1546593445.519 * [misc]backup-simplify: Simplify 1 into 1 1546593445.519 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.519 * [misc]backup-simplify: Simplify 2 into 2 1546593445.519 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593445.519 * [misc]taylor: Taking taylor expansion of n in k 1546593445.519 * [misc]backup-simplify: Simplify n into n 1546593445.519 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.520 * [misc]backup-simplify: Simplify PI into PI 1546593445.520 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593445.520 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593445.520 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593445.520 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593445.520 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.520 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.520 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593445.520 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593445.521 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546593445.521 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593445.521 * [misc]taylor: Taking taylor expansion of k in k 1546593445.521 * [misc]backup-simplify: Simplify 0 into 0 1546593445.521 * [misc]backup-simplify: Simplify 1 into 1 1546593445.521 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.521 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593445.521 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546593445.521 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593445.521 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593445.522 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593445.522 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593445.522 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593445.522 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.522 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.522 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593445.522 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.522 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.522 * [misc]taylor: Taking taylor expansion of k in k 1546593445.522 * [misc]backup-simplify: Simplify 0 into 0 1546593445.522 * [misc]backup-simplify: Simplify 1 into 1 1546593445.522 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593445.522 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593445.522 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.522 * [misc]backup-simplify: Simplify 2 into 2 1546593445.522 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593445.522 * [misc]taylor: Taking taylor expansion of n in k 1546593445.522 * [misc]backup-simplify: Simplify n into n 1546593445.522 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.522 * [misc]backup-simplify: Simplify PI into PI 1546593445.522 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593445.522 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593445.522 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593445.523 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593445.523 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.523 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.523 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593445.523 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593445.523 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546593445.523 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593445.523 * [misc]taylor: Taking taylor expansion of k in k 1546593445.523 * [misc]backup-simplify: Simplify 0 into 0 1546593445.523 * [misc]backup-simplify: Simplify 1 into 1 1546593445.524 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.524 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593445.524 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 1546593445.524 * [misc]taylor: Taking taylor expansion of 0 in n 1546593445.524 * [misc]backup-simplify: Simplify 0 into 0 1546593445.524 * [misc]backup-simplify: Simplify 0 into 0 1546593445.525 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546593445.525 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546593445.526 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546593445.526 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593445.526 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.526 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.527 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546593445.527 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546593445.528 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 1546593445.529 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 1546593445.529 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546593445.529 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546593445.529 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.529 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.529 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546593445.529 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546593445.529 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546593445.529 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.529 * [misc]taylor: Taking taylor expansion of n in n 1546593445.529 * [misc]backup-simplify: Simplify 0 into 0 1546593445.529 * [misc]backup-simplify: Simplify 1 into 1 1546593445.529 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.529 * [misc]backup-simplify: Simplify PI into PI 1546593445.530 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.530 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.531 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546593445.531 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.532 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546593445.532 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546593445.532 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.532 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.532 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546593445.532 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546593445.533 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593445.533 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546593445.535 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593445.537 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593445.537 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593445.538 * [misc]backup-simplify: Simplify 0 into 0 1546593445.539 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593445.539 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546593445.540 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546593445.541 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1546593445.542 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593445.542 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.542 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.542 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546593445.543 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546593445.546 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 1546593445.549 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 1546593445.550 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.550 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.550 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.550 * [misc]backup-simplify: Simplify 2 into 2 1546593445.550 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593445.550 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593445.550 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593445.550 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.551 * [misc]backup-simplify: Simplify 2 into 2 1546593445.551 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.551 * [misc]taylor: Taking taylor expansion of n in n 1546593445.551 * [misc]backup-simplify: Simplify 0 into 0 1546593445.551 * [misc]backup-simplify: Simplify 1 into 1 1546593445.551 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.551 * [misc]backup-simplify: Simplify PI into PI 1546593445.551 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.551 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593445.552 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.552 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593445.553 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.553 * [misc]taylor: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 1546593445.553 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546593445.553 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.553 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.553 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546593445.554 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546593445.554 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546593445.554 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546593445.554 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.554 * [misc]taylor: Taking taylor expansion of n in n 1546593445.554 * [misc]backup-simplify: Simplify 0 into 0 1546593445.554 * [misc]backup-simplify: Simplify 1 into 1 1546593445.554 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.554 * [misc]backup-simplify: Simplify PI into PI 1546593445.554 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.555 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.555 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546593445.555 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.556 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546593445.556 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546593445.556 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546593445.556 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.556 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.556 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546593445.556 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546593445.556 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546593445.556 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.556 * [misc]taylor: Taking taylor expansion of n in n 1546593445.556 * [misc]backup-simplify: Simplify 0 into 0 1546593445.556 * [misc]backup-simplify: Simplify 1 into 1 1546593445.556 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.556 * [misc]backup-simplify: Simplify PI into PI 1546593445.556 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.557 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.557 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546593445.557 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.558 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546593445.558 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546593445.558 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.558 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.558 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546593445.559 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546593445.559 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.560 * [misc]backup-simplify: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 1546593445.561 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 1546593445.562 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 1546593445.563 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.563 * [misc]backup-simplify: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 1546593445.564 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593445.565 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593445.568 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593445.569 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 1546593445.570 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 1546593445.572 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546593445.573 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 1546593445.578 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546593445.579 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593445.579 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546593445.581 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593445.582 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546593445.588 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546593445.594 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546593445.601 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546593445.602 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 1546593445.603 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593445.604 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1546593445.606 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1546593445.608 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546593445.612 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546593445.614 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546593445.615 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546593445.626 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546593445.626 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 k)) (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 1546593445.626 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 1546593445.626 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 1546593445.626 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593445.626 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.627 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.627 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.627 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.627 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of k in n 1546593445.627 * [misc]backup-simplify: Simplify k into k 1546593445.627 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.627 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.627 * [misc]backup-simplify: Simplify 2 into 2 1546593445.627 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.627 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.627 * [misc]backup-simplify: Simplify PI into PI 1546593445.627 * [misc]taylor: Taking taylor expansion of n in n 1546593445.627 * [misc]backup-simplify: Simplify 0 into 0 1546593445.627 * [misc]backup-simplify: Simplify 1 into 1 1546593445.628 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.628 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.628 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.628 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.628 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.628 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.629 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.629 * [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))) 1546593445.629 * [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)))) 1546593445.630 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593445.630 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546593445.630 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.630 * [misc]taylor: Taking taylor expansion of k in n 1546593445.630 * [misc]backup-simplify: Simplify k into k 1546593445.630 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.630 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546593445.630 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593445.630 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546593445.630 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.630 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.630 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of k in k 1546593445.630 * [misc]backup-simplify: Simplify 0 into 0 1546593445.630 * [misc]backup-simplify: Simplify 1 into 1 1546593445.630 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.630 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593445.630 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.631 * [misc]backup-simplify: Simplify 2 into 2 1546593445.631 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.631 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.631 * [misc]backup-simplify: Simplify PI into PI 1546593445.631 * [misc]taylor: Taking taylor expansion of n in k 1546593445.631 * [misc]backup-simplify: Simplify n into n 1546593445.631 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.631 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593445.631 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593445.631 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.631 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.631 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.631 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593445.631 * [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)))) 1546593445.631 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546593445.631 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593445.631 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.631 * [misc]taylor: Taking taylor expansion of k in k 1546593445.631 * [misc]backup-simplify: Simplify 0 into 0 1546593445.631 * [misc]backup-simplify: Simplify 1 into 1 1546593445.632 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.632 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.632 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593445.632 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.632 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.632 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.632 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.632 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of k in k 1546593445.632 * [misc]backup-simplify: Simplify 0 into 0 1546593445.632 * [misc]backup-simplify: Simplify 1 into 1 1546593445.632 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.632 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.632 * [misc]backup-simplify: Simplify 2 into 2 1546593445.632 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.632 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.632 * [misc]backup-simplify: Simplify PI into PI 1546593445.632 * [misc]taylor: Taking taylor expansion of n in k 1546593445.632 * [misc]backup-simplify: Simplify n into n 1546593445.633 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.633 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593445.633 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593445.633 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.633 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.633 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.633 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593445.633 * [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)))) 1546593445.633 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546593445.633 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593445.633 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.633 * [misc]taylor: Taking taylor expansion of k in k 1546593445.633 * [misc]backup-simplify: Simplify 0 into 0 1546593445.633 * [misc]backup-simplify: Simplify 1 into 1 1546593445.633 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.634 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.634 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593445.634 * [misc]backup-simplify: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1546593445.634 * [misc]taylor: Taking taylor expansion of 0 in n 1546593445.634 * [misc]backup-simplify: Simplify 0 into 0 1546593445.634 * [misc]backup-simplify: Simplify 0 into 0 1546593445.634 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546593445.634 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546593445.635 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.635 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.635 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.635 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.635 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.635 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.635 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of k in n 1546593445.635 * [misc]backup-simplify: Simplify k into k 1546593445.635 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.635 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.635 * [misc]backup-simplify: Simplify 2 into 2 1546593445.635 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.635 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.635 * [misc]backup-simplify: Simplify PI into PI 1546593445.635 * [misc]taylor: Taking taylor expansion of n in n 1546593445.635 * [misc]backup-simplify: Simplify 0 into 0 1546593445.635 * [misc]backup-simplify: Simplify 1 into 1 1546593445.635 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.636 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.636 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.636 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.636 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.636 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.636 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.637 * [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))) 1546593445.637 * [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)))) 1546593445.638 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593445.638 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593445.638 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593445.639 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593445.639 * [misc]backup-simplify: Simplify 0 into 0 1546593445.639 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546593445.640 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593445.640 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546593445.640 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546593445.640 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546593445.640 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593445.640 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.640 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.641 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.641 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.641 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.641 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.641 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of k in n 1546593445.641 * [misc]backup-simplify: Simplify k into k 1546593445.641 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.641 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.641 * [misc]backup-simplify: Simplify 2 into 2 1546593445.641 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.641 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.641 * [misc]backup-simplify: Simplify PI into PI 1546593445.641 * [misc]taylor: Taking taylor expansion of n in n 1546593445.641 * [misc]backup-simplify: Simplify 0 into 0 1546593445.641 * [misc]backup-simplify: Simplify 1 into 1 1546593445.641 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.641 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.642 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.642 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.642 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.642 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.642 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.643 * [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))) 1546593445.643 * [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)))) 1546593445.643 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593445.644 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593445.644 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593445.645 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593445.645 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593445.646 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593445.647 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593445.647 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593445.647 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593445.648 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.648 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.648 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.648 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593445.649 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593445.650 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546593445.651 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546593445.651 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.651 * [misc]backup-simplify: Simplify 0 into 0 1546593445.651 * [misc]backup-simplify: Simplify 0 into 0 1546593445.651 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.652 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593445.652 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546593445.652 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546593445.652 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.653 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.653 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.653 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.653 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.653 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.653 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of k in n 1546593445.653 * [misc]backup-simplify: Simplify k into k 1546593445.653 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.653 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.653 * [misc]backup-simplify: Simplify 2 into 2 1546593445.653 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.653 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.653 * [misc]backup-simplify: Simplify PI into PI 1546593445.653 * [misc]taylor: Taking taylor expansion of n in n 1546593445.653 * [misc]backup-simplify: Simplify 0 into 0 1546593445.653 * [misc]backup-simplify: Simplify 1 into 1 1546593445.653 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.653 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.654 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.654 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.654 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.654 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.654 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.655 * [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))) 1546593445.655 * [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)))) 1546593445.655 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593445.656 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546593445.656 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593445.657 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546593445.658 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546593445.658 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 (- k))) (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1546593445.658 * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 1546593445.658 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593445.658 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546593445.658 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546593445.658 * [misc]taylor: Taking taylor expansion of -1 in n 1546593445.658 * [misc]backup-simplify: Simplify -1 into -1 1546593445.658 * [misc]taylor: Taking taylor expansion of k in n 1546593445.659 * [misc]backup-simplify: Simplify k into k 1546593445.659 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546593445.659 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546593445.659 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546593445.659 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546593445.659 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.659 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.659 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of k in n 1546593445.659 * [misc]backup-simplify: Simplify k into k 1546593445.659 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.659 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.659 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.659 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.659 * [misc]backup-simplify: Simplify -2 into -2 1546593445.659 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.659 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.659 * [misc]backup-simplify: Simplify PI into PI 1546593445.659 * [misc]taylor: Taking taylor expansion of n in n 1546593445.659 * [misc]backup-simplify: Simplify 0 into 0 1546593445.659 * [misc]backup-simplify: Simplify 1 into 1 1546593445.660 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.660 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.660 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.660 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.660 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.661 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.662 * [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))) 1546593445.662 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593445.663 * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593445.663 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546593445.663 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593445.663 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593445.663 * [misc]taylor: Taking taylor expansion of -1 in k 1546593445.663 * [misc]backup-simplify: Simplify -1 into -1 1546593445.663 * [misc]taylor: Taking taylor expansion of k in k 1546593445.663 * [misc]backup-simplify: Simplify 0 into 0 1546593445.663 * [misc]backup-simplify: Simplify 1 into 1 1546593445.663 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593445.663 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.664 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593445.664 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593445.664 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593445.664 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593445.664 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593445.664 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.664 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.664 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.664 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.664 * [misc]taylor: Taking taylor expansion of k in k 1546593445.664 * [misc]backup-simplify: Simplify 0 into 0 1546593445.664 * [misc]backup-simplify: Simplify 1 into 1 1546593445.664 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.664 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.664 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.665 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593445.665 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593445.665 * [misc]taylor: Taking taylor expansion of -2 in k 1546593445.665 * [misc]backup-simplify: Simplify -2 into -2 1546593445.665 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.665 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.665 * [misc]backup-simplify: Simplify PI into PI 1546593445.665 * [misc]taylor: Taking taylor expansion of n in k 1546593445.665 * [misc]backup-simplify: Simplify n into n 1546593445.665 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.665 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593445.665 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593445.665 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.666 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.666 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593445.666 * [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))) 1546593445.667 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546593445.667 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546593445.667 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593445.667 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593445.667 * [misc]taylor: Taking taylor expansion of -1 in k 1546593445.667 * [misc]backup-simplify: Simplify -1 into -1 1546593445.667 * [misc]taylor: Taking taylor expansion of k in k 1546593445.667 * [misc]backup-simplify: Simplify 0 into 0 1546593445.667 * [misc]backup-simplify: Simplify 1 into 1 1546593445.667 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593445.667 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.668 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593445.668 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.668 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.668 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of k in k 1546593445.668 * [misc]backup-simplify: Simplify 0 into 0 1546593445.668 * [misc]backup-simplify: Simplify 1 into 1 1546593445.668 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.668 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.668 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.668 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of -2 in k 1546593445.668 * [misc]backup-simplify: Simplify -2 into -2 1546593445.668 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.668 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.668 * [misc]backup-simplify: Simplify PI into PI 1546593445.668 * [misc]taylor: Taking taylor expansion of n in k 1546593445.669 * [misc]backup-simplify: Simplify n into n 1546593445.669 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.669 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593445.669 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593445.669 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.669 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.669 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593445.669 * [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))) 1546593445.670 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546593445.670 * [misc]taylor: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593445.670 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.670 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.670 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593445.670 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.670 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.670 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.670 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.670 * [misc]backup-simplify: Simplify -2 into -2 1546593445.670 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.670 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.670 * [misc]backup-simplify: Simplify PI into PI 1546593445.670 * [misc]taylor: Taking taylor expansion of n in n 1546593445.670 * [misc]backup-simplify: Simplify 0 into 0 1546593445.670 * [misc]backup-simplify: Simplify 1 into 1 1546593445.670 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.671 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.671 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.671 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.671 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.671 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.671 * [misc]taylor: Taking taylor expansion of k in n 1546593445.671 * [misc]backup-simplify: Simplify k into k 1546593445.671 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.672 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.672 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.672 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.673 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593445.673 * [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)))) 1546593445.674 * [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))))) 1546593445.675 * [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))))) 1546593445.675 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593445.676 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593445.677 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546593445.677 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546593445.677 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546593445.677 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.677 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.677 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593445.677 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593445.677 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.677 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.677 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.677 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.677 * [misc]backup-simplify: Simplify -2 into -2 1546593445.677 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.677 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.677 * [misc]backup-simplify: Simplify PI into PI 1546593445.677 * [misc]taylor: Taking taylor expansion of n in n 1546593445.677 * [misc]backup-simplify: Simplify 0 into 0 1546593445.677 * [misc]backup-simplify: Simplify 1 into 1 1546593445.678 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.678 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.678 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.678 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.678 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.678 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.679 * [misc]taylor: Taking taylor expansion of k in n 1546593445.679 * [misc]backup-simplify: Simplify k into k 1546593445.679 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.679 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.679 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.679 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.679 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.679 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.680 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593445.681 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593445.681 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593445.682 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593445.683 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546593445.683 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546593445.684 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.684 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593445.684 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593445.685 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.686 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593445.686 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593445.689 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593445.689 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546593445.691 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593445.693 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546593445.693 * [misc]backup-simplify: Simplify 0 into 0 1546593445.693 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.694 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593445.696 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546593445.696 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546593445.696 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546593445.696 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.696 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.696 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593445.696 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593445.696 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.696 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.696 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.696 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.696 * [misc]backup-simplify: Simplify -2 into -2 1546593445.696 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.696 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.696 * [misc]backup-simplify: Simplify PI into PI 1546593445.696 * [misc]taylor: Taking taylor expansion of n in n 1546593445.696 * [misc]backup-simplify: Simplify 0 into 0 1546593445.696 * [misc]backup-simplify: Simplify 1 into 1 1546593445.697 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.697 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.697 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.697 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.697 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.697 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.697 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.697 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.697 * [misc]taylor: Taking taylor expansion of k in n 1546593445.697 * [misc]backup-simplify: Simplify k into k 1546593445.698 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.698 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.698 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.698 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.698 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.698 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.699 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593445.700 * [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)))) 1546593445.700 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593445.701 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546593445.702 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546593445.703 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546593445.705 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546593445.705 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1546593445.706 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1546593445.706 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 1546593445.706 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546593445.706 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546593445.706 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.706 * [misc]taylor: Taking taylor expansion of k in n 1546593445.706 * [misc]backup-simplify: Simplify k into k 1546593445.706 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.706 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546593445.706 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593445.706 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546593445.706 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593445.706 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593445.706 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593445.706 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593445.706 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.706 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.706 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593445.706 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.707 * [misc]taylor: Taking taylor expansion of k in n 1546593445.707 * [misc]backup-simplify: Simplify k into k 1546593445.707 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593445.707 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593445.707 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.707 * [misc]backup-simplify: Simplify 2 into 2 1546593445.707 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.707 * [misc]taylor: Taking taylor expansion of n in n 1546593445.707 * [misc]backup-simplify: Simplify 0 into 0 1546593445.707 * [misc]backup-simplify: Simplify 1 into 1 1546593445.707 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.707 * [misc]backup-simplify: Simplify PI into PI 1546593445.707 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.707 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593445.708 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.709 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593445.709 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.709 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593445.709 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593445.709 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593445.710 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.710 * [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)))) 1546593445.711 * [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))))) 1546593445.711 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593445.711 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593445.711 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.711 * [misc]taylor: Taking taylor expansion of k in k 1546593445.711 * [misc]backup-simplify: Simplify 0 into 0 1546593445.711 * [misc]backup-simplify: Simplify 1 into 1 1546593445.711 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.712 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.712 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593445.712 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593445.712 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593445.712 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593445.712 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593445.712 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.712 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593445.712 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.712 * [misc]taylor: Taking taylor expansion of k in k 1546593445.712 * [misc]backup-simplify: Simplify 0 into 0 1546593445.712 * [misc]backup-simplify: Simplify 1 into 1 1546593445.712 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593445.712 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593445.712 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.713 * [misc]backup-simplify: Simplify 2 into 2 1546593445.713 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593445.713 * [misc]taylor: Taking taylor expansion of n in k 1546593445.713 * [misc]backup-simplify: Simplify n into n 1546593445.713 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.713 * [misc]backup-simplify: Simplify PI into PI 1546593445.713 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593445.713 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593445.713 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593445.713 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593445.713 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.713 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.713 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593445.714 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593445.714 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593445.714 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546593445.714 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.714 * [misc]taylor: Taking taylor expansion of k in k 1546593445.714 * [misc]backup-simplify: Simplify 0 into 0 1546593445.714 * [misc]backup-simplify: Simplify 1 into 1 1546593445.714 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.714 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.715 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593445.715 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593445.715 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593445.715 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593445.715 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593445.715 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.715 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.715 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593445.715 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.715 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.715 * [misc]taylor: Taking taylor expansion of k in k 1546593445.715 * [misc]backup-simplify: Simplify 0 into 0 1546593445.715 * [misc]backup-simplify: Simplify 1 into 1 1546593445.715 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593445.715 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593445.715 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.715 * [misc]backup-simplify: Simplify 2 into 2 1546593445.715 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593445.715 * [misc]taylor: Taking taylor expansion of n in k 1546593445.715 * [misc]backup-simplify: Simplify n into n 1546593445.715 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.715 * [misc]backup-simplify: Simplify PI into PI 1546593445.715 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593445.715 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593445.715 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593445.716 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593445.716 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.716 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.716 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593445.716 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593445.716 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 1546593445.716 * [misc]taylor: Taking taylor expansion of 0 in n 1546593445.716 * [misc]backup-simplify: Simplify 0 into 0 1546593445.716 * [misc]backup-simplify: Simplify 0 into 0 1546593445.717 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546593445.717 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546593445.718 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546593445.718 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593445.718 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.718 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.719 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546593445.719 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546593445.719 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1546593445.719 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546593445.719 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546593445.720 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.720 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.720 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546593445.720 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593445.720 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.720 * [misc]backup-simplify: Simplify 2 into 2 1546593445.720 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593445.720 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593445.720 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593445.720 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.720 * [misc]taylor: Taking taylor expansion of n in n 1546593445.720 * [misc]backup-simplify: Simplify 0 into 0 1546593445.720 * [misc]backup-simplify: Simplify 1 into 1 1546593445.720 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.720 * [misc]backup-simplify: Simplify PI into PI 1546593445.721 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.721 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.722 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.722 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593445.723 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546593445.723 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593445.723 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.723 * [misc]backup-simplify: Simplify 0 into 0 1546593445.723 * [misc]backup-simplify: Simplify 0 into 0 1546593445.724 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546593445.724 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546593445.726 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1546593445.726 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593445.726 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.726 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.727 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546593445.728 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546593445.728 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546593445.729 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593445.730 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1546593445.730 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1546593445.730 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1546593445.730 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1546593445.730 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.730 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.730 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1546593445.730 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1546593445.730 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593445.730 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.731 * [misc]backup-simplify: Simplify 2 into 2 1546593445.731 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593445.731 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593445.731 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593445.731 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593445.731 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.731 * [misc]backup-simplify: Simplify 2 into 2 1546593445.731 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.731 * [misc]taylor: Taking taylor expansion of n in n 1546593445.731 * [misc]backup-simplify: Simplify 0 into 0 1546593445.731 * [misc]backup-simplify: Simplify 1 into 1 1546593445.731 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.731 * [misc]backup-simplify: Simplify PI into PI 1546593445.732 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.732 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593445.732 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.733 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593445.734 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.734 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593445.734 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.734 * [misc]taylor: Taking taylor expansion of n in n 1546593445.734 * [misc]backup-simplify: Simplify 0 into 0 1546593445.734 * [misc]backup-simplify: Simplify 1 into 1 1546593445.734 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.734 * [misc]backup-simplify: Simplify PI into PI 1546593445.734 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.735 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.735 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.735 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593445.735 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546593445.735 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546593445.735 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.735 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.735 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546593445.735 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593445.736 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.736 * [misc]backup-simplify: Simplify 2 into 2 1546593445.736 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593445.736 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593445.736 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593445.736 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.736 * [misc]taylor: Taking taylor expansion of n in n 1546593445.736 * [misc]backup-simplify: Simplify 0 into 0 1546593445.736 * [misc]backup-simplify: Simplify 1 into 1 1546593445.736 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.736 * [misc]backup-simplify: Simplify PI into PI 1546593445.736 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.737 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.737 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.738 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593445.738 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.739 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1546593445.740 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1546593445.740 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593445.740 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546593445.740 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593445.740 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.740 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.741 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.741 * [misc]backup-simplify: Simplify 0 into 0 1546593445.742 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593445.744 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593445.745 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593445.746 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593445.746 * [misc]backup-simplify: Simplify 0 into 0 1546593445.747 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593445.748 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1546593445.750 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 1546593445.751 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546593445.751 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.751 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.752 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1546593445.753 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 1546593445.754 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.755 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593445.756 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 1546593445.756 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 1546593445.756 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 1546593445.756 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1546593445.756 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.756 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.756 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1546593445.756 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1546593445.757 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593445.757 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.757 * [misc]backup-simplify: Simplify 2 into 2 1546593445.757 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593445.757 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593445.757 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593445.757 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593445.757 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.757 * [misc]backup-simplify: Simplify 2 into 2 1546593445.757 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.757 * [misc]taylor: Taking taylor expansion of n in n 1546593445.757 * [misc]backup-simplify: Simplify 0 into 0 1546593445.757 * [misc]backup-simplify: Simplify 1 into 1 1546593445.757 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.757 * [misc]backup-simplify: Simplify PI into PI 1546593445.758 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.758 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593445.758 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.759 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593445.759 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.759 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593445.760 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.760 * [misc]taylor: Taking taylor expansion of n in n 1546593445.760 * [misc]backup-simplify: Simplify 0 into 0 1546593445.760 * [misc]backup-simplify: Simplify 1 into 1 1546593445.760 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.760 * [misc]backup-simplify: Simplify PI into PI 1546593445.760 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.760 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.761 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.761 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593445.761 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1546593445.761 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1546593445.761 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1546593445.761 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.761 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.761 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1546593445.761 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1546593445.761 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593445.761 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.761 * [misc]backup-simplify: Simplify 2 into 2 1546593445.762 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593445.762 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593445.762 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1546593445.762 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593445.762 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593445.762 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.762 * [misc]backup-simplify: Simplify 2 into 2 1546593445.762 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.762 * [misc]taylor: Taking taylor expansion of n in n 1546593445.762 * [misc]backup-simplify: Simplify 0 into 0 1546593445.762 * [misc]backup-simplify: Simplify 1 into 1 1546593445.762 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.762 * [misc]backup-simplify: Simplify PI into PI 1546593445.762 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.763 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593445.763 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.764 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593445.764 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.765 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.765 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593445.765 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.765 * [misc]taylor: Taking taylor expansion of n in n 1546593445.765 * [misc]backup-simplify: Simplify 0 into 0 1546593445.765 * [misc]backup-simplify: Simplify 1 into 1 1546593445.765 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.765 * [misc]backup-simplify: Simplify PI into PI 1546593445.765 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.766 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.767 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.768 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593445.768 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546593445.768 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546593445.768 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.768 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.768 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546593445.768 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546593445.768 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.768 * [misc]backup-simplify: Simplify 2 into 2 1546593445.768 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546593445.768 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546593445.768 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546593445.768 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593445.768 * [misc]taylor: Taking taylor expansion of n in n 1546593445.768 * [misc]backup-simplify: Simplify 0 into 0 1546593445.768 * [misc]backup-simplify: Simplify 1 into 1 1546593445.768 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.769 * [misc]backup-simplify: Simplify PI into PI 1546593445.769 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593445.769 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593445.770 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.770 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546593445.771 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.771 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1546593445.772 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1546593445.773 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593445.773 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.774 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.775 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1546593445.776 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1546593445.776 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1546593445.777 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593445.777 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546593445.777 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546593445.777 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.777 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.777 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.777 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.778 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.778 * [misc]backup-simplify: Simplify 0 into 0 1546593445.779 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593445.780 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593445.782 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593445.783 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593445.784 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546593445.785 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1546593445.787 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1546593445.789 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593445.790 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593445.792 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546593445.795 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 1546593445.799 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546593445.801 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546593445.803 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593445.804 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1546593445.805 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1546593445.808 * [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)))) 1546593445.812 * [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)))) 1546593445.813 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546593445.815 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546593445.821 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1546593445.821 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546593445.821 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 1546593445.821 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of k in n 1546593445.822 * [misc]backup-simplify: Simplify k into k 1546593445.822 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546593445.822 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546593445.822 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.822 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.822 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of k in n 1546593445.822 * [misc]backup-simplify: Simplify k into k 1546593445.822 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.822 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.822 * [misc]backup-simplify: Simplify 2 into 2 1546593445.822 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.822 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.822 * [misc]backup-simplify: Simplify PI into PI 1546593445.822 * [misc]taylor: Taking taylor expansion of n in n 1546593445.822 * [misc]backup-simplify: Simplify 0 into 0 1546593445.822 * [misc]backup-simplify: Simplify 1 into 1 1546593445.823 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.823 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.824 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.824 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.824 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.824 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.825 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.826 * [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))) 1546593445.826 * [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)))) 1546593445.826 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593445.827 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593445.827 * [misc]taylor: Taking taylor expansion of k in k 1546593445.827 * [misc]backup-simplify: Simplify 0 into 0 1546593445.827 * [misc]backup-simplify: Simplify 1 into 1 1546593445.827 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.827 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593445.827 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593445.827 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593445.827 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593445.827 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593445.827 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.827 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.827 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.827 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.828 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.828 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.828 * [misc]taylor: Taking taylor expansion of k in k 1546593445.828 * [misc]backup-simplify: Simplify 0 into 0 1546593445.828 * [misc]backup-simplify: Simplify 1 into 1 1546593445.828 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.828 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593445.828 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593445.828 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.828 * [misc]backup-simplify: Simplify 2 into 2 1546593445.828 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.828 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.828 * [misc]backup-simplify: Simplify PI into PI 1546593445.828 * [misc]taylor: Taking taylor expansion of n in k 1546593445.828 * [misc]backup-simplify: Simplify n into n 1546593445.828 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.828 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593445.828 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593445.828 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.829 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.829 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.829 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593445.829 * [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)))) 1546593445.829 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593445.829 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546593445.829 * [misc]taylor: Taking taylor expansion of k in k 1546593445.829 * [misc]backup-simplify: Simplify 0 into 0 1546593445.829 * [misc]backup-simplify: Simplify 1 into 1 1546593445.829 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.830 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546593445.830 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593445.830 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593445.830 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593445.830 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593445.830 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.830 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.830 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.830 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.830 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.830 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.830 * [misc]taylor: Taking taylor expansion of k in k 1546593445.830 * [misc]backup-simplify: Simplify 0 into 0 1546593445.830 * [misc]backup-simplify: Simplify 1 into 1 1546593445.830 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.830 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593445.831 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593445.831 * [misc]taylor: Taking taylor expansion of 2 in k 1546593445.831 * [misc]backup-simplify: Simplify 2 into 2 1546593445.831 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.831 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.831 * [misc]backup-simplify: Simplify PI into PI 1546593445.831 * [misc]taylor: Taking taylor expansion of n in k 1546593445.831 * [misc]backup-simplify: Simplify n into n 1546593445.831 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.831 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593445.831 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593445.831 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.831 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593445.831 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593445.832 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593445.832 * [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)))) 1546593445.832 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 1546593445.832 * [misc]taylor: Taking taylor expansion of 0 in n 1546593445.832 * [misc]backup-simplify: Simplify 0 into 0 1546593445.832 * [misc]backup-simplify: Simplify 0 into 0 1546593445.832 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546593445.832 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.833 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.833 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.833 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.833 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.833 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.833 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of k in n 1546593445.833 * [misc]backup-simplify: Simplify k into k 1546593445.833 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.833 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.833 * [misc]backup-simplify: Simplify 2 into 2 1546593445.833 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.833 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.833 * [misc]backup-simplify: Simplify PI into PI 1546593445.833 * [misc]taylor: Taking taylor expansion of n in n 1546593445.833 * [misc]backup-simplify: Simplify 0 into 0 1546593445.833 * [misc]backup-simplify: Simplify 1 into 1 1546593445.833 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.834 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.834 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.834 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.834 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.835 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.835 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.836 * [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))) 1546593445.837 * [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)))) 1546593445.837 * [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))))) 1546593445.838 * [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)))))) 1546593445.839 * [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)))))) 1546593445.839 * [misc]backup-simplify: Simplify 0 into 0 1546593445.840 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593445.840 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546593445.840 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593445.840 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593445.840 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.840 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.840 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.840 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.840 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.841 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.841 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.841 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.841 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.841 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.841 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.841 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.841 * [misc]taylor: Taking taylor expansion of k in n 1546593445.841 * [misc]backup-simplify: Simplify k into k 1546593445.841 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.841 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.841 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.841 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.841 * [misc]backup-simplify: Simplify 2 into 2 1546593445.841 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.841 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.841 * [misc]backup-simplify: Simplify PI into PI 1546593445.841 * [misc]taylor: Taking taylor expansion of n in n 1546593445.841 * [misc]backup-simplify: Simplify 0 into 0 1546593445.841 * [misc]backup-simplify: Simplify 1 into 1 1546593445.841 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.842 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.842 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.842 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.842 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.842 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.843 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.844 * [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))) 1546593445.844 * [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)))) 1546593445.845 * [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))))) 1546593445.846 * [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)))))) 1546593445.846 * [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)))))) 1546593445.847 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593445.848 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593445.851 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593445.851 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593445.851 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593445.851 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.851 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.852 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.853 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593445.854 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593445.855 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546593445.855 * [misc]backup-simplify: Simplify (- 0) into 0 1546593445.855 * [misc]backup-simplify: Simplify 0 into 0 1546593445.855 * [misc]backup-simplify: Simplify 0 into 0 1546593445.857 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593445.857 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546593445.857 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546593445.857 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593445.857 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.857 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.857 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593445.857 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593445.857 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593445.857 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593445.857 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.857 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.857 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.857 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.858 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.858 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.858 * [misc]taylor: Taking taylor expansion of k in n 1546593445.858 * [misc]backup-simplify: Simplify k into k 1546593445.858 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.858 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593445.858 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593445.858 * [misc]taylor: Taking taylor expansion of 2 in n 1546593445.858 * [misc]backup-simplify: Simplify 2 into 2 1546593445.858 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.858 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.858 * [misc]backup-simplify: Simplify PI into PI 1546593445.858 * [misc]taylor: Taking taylor expansion of n in n 1546593445.858 * [misc]backup-simplify: Simplify 0 into 0 1546593445.858 * [misc]backup-simplify: Simplify 1 into 1 1546593445.858 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.858 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593445.859 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593445.859 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.859 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593445.859 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593445.860 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593445.860 * [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))) 1546593445.861 * [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)))) 1546593445.862 * [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))))) 1546593445.862 * [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)))))) 1546593445.863 * [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)))))) 1546593445.866 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1546593445.866 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1546593445.866 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 1546593445.866 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546593445.866 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.866 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593445.866 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593445.866 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.866 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.866 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.866 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.866 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.866 * [misc]taylor: Taking taylor expansion of k in n 1546593445.866 * [misc]backup-simplify: Simplify k into k 1546593445.866 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.867 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.867 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.867 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.867 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.867 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.867 * [misc]backup-simplify: Simplify -2 into -2 1546593445.867 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.867 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.867 * [misc]backup-simplify: Simplify PI into PI 1546593445.867 * [misc]taylor: Taking taylor expansion of n in n 1546593445.867 * [misc]backup-simplify: Simplify 0 into 0 1546593445.867 * [misc]backup-simplify: Simplify 1 into 1 1546593445.867 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.868 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.868 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.868 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.868 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.869 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.870 * [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))) 1546593445.870 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593445.870 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546593445.870 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546593445.870 * [misc]taylor: Taking taylor expansion of -1 in n 1546593445.870 * [misc]backup-simplify: Simplify -1 into -1 1546593445.870 * [misc]taylor: Taking taylor expansion of k in n 1546593445.870 * [misc]backup-simplify: Simplify k into k 1546593445.870 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546593445.870 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546593445.871 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546593445.871 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546593445.871 * [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))) 1546593445.871 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546593445.871 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593445.871 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593445.872 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593445.872 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593445.872 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.872 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.872 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.872 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.872 * [misc]taylor: Taking taylor expansion of k in k 1546593445.872 * [misc]backup-simplify: Simplify 0 into 0 1546593445.872 * [misc]backup-simplify: Simplify 1 into 1 1546593445.872 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.872 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.872 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.872 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593445.872 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593445.872 * [misc]taylor: Taking taylor expansion of -2 in k 1546593445.872 * [misc]backup-simplify: Simplify -2 into -2 1546593445.872 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.872 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.872 * [misc]backup-simplify: Simplify PI into PI 1546593445.872 * [misc]taylor: Taking taylor expansion of n in k 1546593445.872 * [misc]backup-simplify: Simplify n into n 1546593445.872 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.872 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593445.873 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593445.873 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.873 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.873 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593445.873 * [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))) 1546593445.873 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593445.873 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593445.873 * [misc]taylor: Taking taylor expansion of -1 in k 1546593445.873 * [misc]backup-simplify: Simplify -1 into -1 1546593445.873 * [misc]taylor: Taking taylor expansion of k in k 1546593445.873 * [misc]backup-simplify: Simplify 0 into 0 1546593445.873 * [misc]backup-simplify: Simplify 1 into 1 1546593445.874 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593445.874 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.874 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593445.874 * [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)))) 1546593445.874 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546593445.874 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.875 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.875 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of k in k 1546593445.875 * [misc]backup-simplify: Simplify 0 into 0 1546593445.875 * [misc]backup-simplify: Simplify 1 into 1 1546593445.875 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593445.875 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593445.875 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.875 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of -2 in k 1546593445.875 * [misc]backup-simplify: Simplify -2 into -2 1546593445.875 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593445.875 * [misc]taylor: Taking taylor expansion of PI in k 1546593445.875 * [misc]backup-simplify: Simplify PI into PI 1546593445.875 * [misc]taylor: Taking taylor expansion of n in k 1546593445.875 * [misc]backup-simplify: Simplify n into n 1546593445.875 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593445.875 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593445.876 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593445.876 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593445.876 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593445.876 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593445.876 * [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))) 1546593445.876 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593445.876 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593445.876 * [misc]taylor: Taking taylor expansion of -1 in k 1546593445.876 * [misc]backup-simplify: Simplify -1 into -1 1546593445.876 * [misc]taylor: Taking taylor expansion of k in k 1546593445.876 * [misc]backup-simplify: Simplify 0 into 0 1546593445.876 * [misc]backup-simplify: Simplify 1 into 1 1546593445.877 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593445.877 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593445.877 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593445.878 * [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)))) 1546593445.878 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593445.878 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.878 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.878 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593445.878 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.878 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.878 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.878 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.878 * [misc]backup-simplify: Simplify -2 into -2 1546593445.878 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.878 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.878 * [misc]backup-simplify: Simplify PI into PI 1546593445.878 * [misc]taylor: Taking taylor expansion of n in n 1546593445.878 * [misc]backup-simplify: Simplify 0 into 0 1546593445.878 * [misc]backup-simplify: Simplify 1 into 1 1546593445.879 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.879 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.879 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.879 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.880 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.880 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.880 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.880 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.880 * [misc]taylor: Taking taylor expansion of k in n 1546593445.880 * [misc]backup-simplify: Simplify k into k 1546593445.880 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.880 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.880 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.880 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.881 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.881 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.881 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593445.882 * [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)))) 1546593445.882 * [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))))) 1546593445.883 * [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))))) 1546593445.883 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593445.884 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593445.885 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1546593445.885 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546593445.885 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593445.885 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.885 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.885 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593445.885 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.885 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.885 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.885 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.885 * [misc]backup-simplify: Simplify -2 into -2 1546593445.885 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.885 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.885 * [misc]backup-simplify: Simplify PI into PI 1546593445.885 * [misc]taylor: Taking taylor expansion of n in n 1546593445.885 * [misc]backup-simplify: Simplify 0 into 0 1546593445.886 * [misc]backup-simplify: Simplify 1 into 1 1546593445.886 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.886 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.886 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.887 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.887 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.887 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.887 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.887 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.887 * [misc]taylor: Taking taylor expansion of k in n 1546593445.887 * [misc]backup-simplify: Simplify k into k 1546593445.887 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.887 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.887 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.887 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.888 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.888 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.888 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593445.889 * [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)))) 1546593445.889 * [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))))) 1546593445.890 * [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)))))) 1546593445.891 * [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)))))) 1546593445.892 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.892 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593445.892 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593445.892 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593445.893 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593445.894 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593445.896 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593445.897 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546593445.899 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593445.900 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 1546593445.900 * [misc]backup-simplify: Simplify 0 into 0 1546593445.900 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593445.901 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593445.902 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1546593445.902 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546593445.902 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546593445.902 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546593445.902 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546593445.902 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593445.902 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593445.902 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593445.902 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593445.902 * [misc]taylor: Taking taylor expansion of -2 in n 1546593445.903 * [misc]backup-simplify: Simplify -2 into -2 1546593445.903 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593445.903 * [misc]taylor: Taking taylor expansion of PI in n 1546593445.903 * [misc]backup-simplify: Simplify PI into PI 1546593445.903 * [misc]taylor: Taking taylor expansion of n in n 1546593445.903 * [misc]backup-simplify: Simplify 0 into 0 1546593445.903 * [misc]backup-simplify: Simplify 1 into 1 1546593445.903 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593445.903 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593445.904 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593445.904 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593445.904 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593445.904 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.904 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.904 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593445.904 * [misc]taylor: Taking taylor expansion of k in n 1546593445.904 * [misc]backup-simplify: Simplify k into k 1546593445.904 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593445.904 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593445.904 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593445.905 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593445.905 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593445.905 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593445.905 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546593445.906 * [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)))) 1546593445.907 * [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))))) 1546593445.907 * [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)))))) 1546593445.908 * [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)))))) 1546593445.911 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1546593445.911 * * * [misc]progress: simplifying candidates 1546593445.911 * * * * [misc]progress: [ 1 / 119 ] simplifiying candidate # 1546593445.911 * [enter]simplify: Simplifying (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) 1546593445.911 * * [misc]simplify: iters left: 6 (11 enodes) 1546593445.916 * * [misc]simplify: iters left: 5 (21 enodes) 1546593445.922 * * [misc]simplify: iters left: 4 (47 enodes) 1546593445.940 * * [misc]simplify: iters left: 3 (109 enodes) 1546593445.987 * * [misc]simplify: iters left: 2 (300 enodes) 1546593446.206 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) 1546593446.206 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))))))) 1546593446.206 * * * * [misc]progress: [ 2 / 119 ] simplifiying candidate # 1546593446.206 * * * * [misc]progress: [ 3 / 119 ] simplifiying candidate # 1546593446.207 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593446.207 * * [misc]simplify: iters left: 4 (5 enodes) 1546593446.207 * * [misc]simplify: iters left: 3 (9 enodes) 1546593446.209 * * [misc]simplify: iters left: 2 (15 enodes) 1546593446.211 * * [misc]simplify: iters left: 1 (17 enodes) 1546593446.213 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593446.213 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (* 1 (- 1/2 (/ k 2))))))) 1546593446.213 * * * * [misc]progress: [ 4 / 119 ] simplifiying candidate # 1546593446.213 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (/ k 2)) 1546593446.213 * * [misc]simplify: iters left: 5 (8 enodes) 1546593446.214 * * [misc]simplify: iters left: 4 (12 enodes) 1546593446.216 * * [misc]simplify: iters left: 3 (18 enodes) 1546593446.218 * * [misc]simplify: iters left: 2 (20 enodes) 1546593446.221 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) 1546593446.221 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* 2 (* n PI)) 1/2) (pow (* (* PI n) 2) (/ k 2)))))) 1546593446.221 * * * * [misc]progress: [ 5 / 119 ] simplifiying candidate # 1546593446.221 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546593446.221 * * [misc]simplify: iters left: 5 (6 enodes) 1546593446.224 * * [misc]simplify: iters left: 4 (8 enodes) 1546593446.225 * * [misc]simplify: iters left: 3 (11 enodes) 1546593446.226 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546593446.226 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* 2 (* n PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))))) 1546593446.226 * * * * [misc]progress: [ 6 / 119 ] simplifiying candidate # 1546593446.226 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546593446.226 * * [misc]simplify: iters left: 5 (6 enodes) 1546593446.227 * * [misc]simplify: iters left: 4 (8 enodes) 1546593446.228 * * [misc]simplify: iters left: 3 (11 enodes) 1546593446.230 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546593446.230 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* 2 (* n PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))))) 1546593446.230 * * * * [misc]progress: [ 7 / 119 ] simplifiying candidate # 1546593446.230 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546593446.230 * * [misc]simplify: iters left: 4 (5 enodes) 1546593446.231 * * [misc]simplify: iters left: 3 (7 enodes) 1546593446.232 * * [misc]simplify: iters left: 2 (10 enodes) 1546593446.235 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546593446.235 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* 2 (* n PI)) 1) (- 1/2 (/ k 2)))))) 1546593446.235 * * * * [misc]progress: [ 8 / 119 ] simplifiying candidate # 1546593446.235 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- (/ k 2))) 1546593446.235 * * [misc]simplify: iters left: 5 (9 enodes) 1546593446.238 * * [misc]simplify: iters left: 4 (15 enodes) 1546593446.243 * * [misc]simplify: iters left: 3 (21 enodes) 1546593446.248 * * [misc]simplify: iters left: 2 (22 enodes) 1546593446.253 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1546593446.253 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* 2 (* n PI)) 1/2) (pow (* (* 2 n) PI) (- (/ k 2))))))) 1546593446.254 * * * * [misc]progress: [ 9 / 119 ] simplifiying candidate # 1546593446.254 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- (/ k 2))) 1546593446.254 * * [misc]simplify: iters left: 5 (9 enodes) 1546593446.257 * * [misc]simplify: iters left: 4 (15 enodes) 1546593446.260 * * [misc]simplify: iters left: 3 (21 enodes) 1546593446.263 * * [misc]simplify: iters left: 2 (22 enodes) 1546593446.265 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1546593446.265 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* 2 (* n PI)) 1/2) (pow (* (* 2 n) PI) (- (/ k 2))))))) 1546593446.266 * * * * [misc]progress: [ 10 / 119 ] simplifiying candidate # 1546593446.266 * [enter]simplify: Simplifying (pow 2 (- 1/2 (/ k 2))) 1546593446.266 * * [misc]simplify: iters left: 5 (6 enodes) 1546593446.267 * * [misc]simplify: iters left: 4 (8 enodes) 1546593446.268 * * [misc]simplify: iters left: 3 (11 enodes) 1546593446.269 * [exit]simplify: Simplified to (pow 2 (- 1/2 (/ k 2))) 1546593446.269 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2))))))) 1546593446.269 * * * * [misc]progress: [ 11 / 119 ] simplifiying candidate # 1546593446.269 * * * * [misc]progress: [ 12 / 119 ] simplifiying candidate # 1546593446.269 * * * * [misc]progress: [ 13 / 119 ] simplifiying candidate # 1546593446.269 * * * * [misc]progress: [ 14 / 119 ] simplifiying candidate # 1546593446.269 * * * * [misc]progress: [ 15 / 119 ] simplifiying candidate # 1546593446.269 * * * * [misc]progress: [ 16 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 17 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 18 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 19 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 20 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 21 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 22 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 23 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 24 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 25 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 26 / 119 ] simplifiying candidate # 1546593446.270 * * * * [misc]progress: [ 27 / 119 ] simplifiying candidate # 1546593446.270 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))) 1546593446.270 * * [misc]simplify: iters left: 6 (14 enodes) 1546593446.273 * * [misc]simplify: iters left: 5 (26 enodes) 1546593446.277 * * [misc]simplify: iters left: 4 (59 enodes) 1546593446.288 * * [misc]simplify: iters left: 3 (164 enodes) 1546593446.337 * * [misc]simplify: iters left: 2 (488 enodes) 1546593446.579 * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* 2 PI) n)))) 1546593446.579 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* 2 PI) n))))))) 1546593446.579 * * * * [misc]progress: [ 28 / 119 ] simplifiying candidate # 1546593446.580 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))) 1546593446.580 * * [misc]simplify: iters left: 6 (14 enodes) 1546593446.582 * * [misc]simplify: iters left: 5 (26 enodes) 1546593446.587 * * [misc]simplify: iters left: 4 (59 enodes) 1546593446.598 * * [misc]simplify: iters left: 3 (164 enodes) 1546593446.674 * * [misc]simplify: iters left: 2 (488 enodes) 1546593446.970 * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* 2 PI) n)))) 1546593446.970 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* 2 PI) n))))))) 1546593446.970 * * * * [misc]progress: [ 29 / 119 ] simplifiying candidate # 1546593446.970 * [enter]simplify: Simplifying (- (log (sqrt k)) (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593446.970 * * [misc]simplify: iters left: 6 (14 enodes) 1546593446.975 * * [misc]simplify: iters left: 5 (24 enodes) 1546593446.983 * * [misc]simplify: iters left: 4 (46 enodes) 1546593446.997 * * [misc]simplify: iters left: 3 (103 enodes) 1546593447.046 * * [misc]simplify: iters left: 2 (336 enodes) 1546593447.240 * [exit]simplify: Simplified to (+ (* (log (* n (* 2 PI))) (+ (/ k 2) -1/2)) (log (sqrt k))) 1546593447.240 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (* (log (* n (* 2 PI))) (+ (/ k 2) -1/2)) (log (sqrt k)))))) 1546593447.240 * * * * [misc]progress: [ 30 / 119 ] simplifiying candidate # 1546593447.240 * * * * [misc]progress: [ 31 / 119 ] simplifiying candidate # 1546593447.241 * * * * [misc]progress: [ 32 / 119 ] simplifiying candidate # 1546593447.241 * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.241 * * [misc]simplify: iters left: 6 (16 enodes) 1546593447.244 * * [misc]simplify: iters left: 5 (31 enodes) 1546593447.248 * * [misc]simplify: iters left: 4 (70 enodes) 1546593447.265 * * [misc]simplify: iters left: 3 (130 enodes) 1546593447.291 * * [misc]simplify: iters left: 2 (206 enodes) 1546593447.344 * * [misc]simplify: iters left: 1 (288 enodes) 1546593447.483 * [exit]simplify: Simplified to (/ (/ (* k (sqrt k)) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1546593447.483 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* k (sqrt k)) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))))) 1546593447.483 * * * * [misc]progress: [ 33 / 119 ] simplifiying candidate # 1546593447.483 * * * * [misc]progress: [ 34 / 119 ] simplifiying candidate # 1546593447.483 * * * * [misc]progress: [ 35 / 119 ] simplifiying candidate # 1546593447.483 * * * * [misc]progress: [ 36 / 119 ] simplifiying candidate # 1546593447.483 * * * * [misc]progress: [ 37 / 119 ] simplifiying candidate # 1546593447.483 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2 (* n PI)) 1/2)) 1546593447.483 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.485 * * [misc]simplify: iters left: 5 (19 enodes) 1546593447.488 * * [misc]simplify: iters left: 4 (27 enodes) 1546593447.491 * * [misc]simplify: iters left: 3 (29 enodes) 1546593447.495 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n PI) 2))) 1546593447.495 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n PI) 2))) (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2))))))) 1546593447.495 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593447.496 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.498 * * [misc]simplify: iters left: 5 (18 enodes) 1546593447.500 * * [misc]simplify: iters left: 4 (24 enodes) 1546593447.503 * * [misc]simplify: iters left: 3 (25 enodes) 1546593447.507 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))) 1546593447.507 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n PI) 2))) (/ (cbrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2)))))) 1546593447.507 * * * * [misc]progress: [ 38 / 119 ] simplifiying candidate # 1546593447.507 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2 (* n PI)) 1/2)) 1546593447.507 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.511 * * [misc]simplify: iters left: 5 (19 enodes) 1546593447.516 * * [misc]simplify: iters left: 4 (27 enodes) 1546593447.523 * * [misc]simplify: iters left: 3 (29 enodes) 1546593447.532 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n PI) 2))) 1546593447.532 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n PI) 2))) (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2))))))) 1546593447.532 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593447.533 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.536 * * [misc]simplify: iters left: 5 (18 enodes) 1546593447.541 * * [misc]simplify: iters left: 4 (24 enodes) 1546593447.545 * * [misc]simplify: iters left: 3 (25 enodes) 1546593447.549 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))) 1546593447.549 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n PI) 2))) (/ (cbrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2)))))) 1546593447.549 * * * * [misc]progress: [ 39 / 119 ] simplifiying candidate # 1546593447.549 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow 2 (- 1/2 (/ k 2)))) 1546593447.549 * * [misc]simplify: iters left: 6 (10 enodes) 1546593447.551 * * [misc]simplify: iters left: 5 (14 enodes) 1546593447.553 * * [misc]simplify: iters left: 4 (19 enodes) 1546593447.555 * * [misc]simplify: iters left: 3 (20 enodes) 1546593447.558 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow 2 (- 1/2 (/ k 2)))) 1546593447.558 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow 2 (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))))) 1546593447.558 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593447.558 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.560 * * [misc]simplify: iters left: 5 (15 enodes) 1546593447.562 * * [misc]simplify: iters left: 4 (18 enodes) 1546593447.564 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593447.564 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow 2 (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))))) 1546593447.564 * * * * [misc]progress: [ 40 / 119 ] simplifiying candidate # 1546593447.564 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) 1546593447.565 * * [misc]simplify: iters left: 6 (16 enodes) 1546593447.567 * * [misc]simplify: iters left: 5 (28 enodes) 1546593447.571 * * [misc]simplify: iters left: 4 (46 enodes) 1546593447.584 * * [misc]simplify: iters left: 3 (50 enodes) 1546593447.596 * * [misc]simplify: iters left: 2 (53 enodes) 1546593447.606 * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546593447.606 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (/ (cbrt (sqrt k)) (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 (* 2 (* n PI)) (- 1/2 (/ k 2)))))))) 1546593447.607 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.607 * * [misc]simplify: iters left: 6 (14 enodes) 1546593447.609 * * [misc]simplify: iters left: 5 (20 enodes) 1546593447.612 * * [misc]simplify: iters left: 4 (29 enodes) 1546593447.615 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.619 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593447.619 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))))) 1546593447.619 * * * * [misc]progress: [ 41 / 119 ] simplifiying candidate # 1546593447.619 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.619 * * [misc]simplify: iters left: 6 (15 enodes) 1546593447.622 * * [misc]simplify: iters left: 5 (23 enodes) 1546593447.625 * * [misc]simplify: iters left: 4 (34 enodes) 1546593447.630 * * [misc]simplify: iters left: 3 (36 enodes) 1546593447.638 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593447.638 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))) 1546593447.639 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.639 * * [misc]simplify: iters left: 6 (14 enodes) 1546593447.643 * * [misc]simplify: iters left: 5 (20 enodes) 1546593447.648 * * [misc]simplify: iters left: 4 (29 enodes) 1546593447.652 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.656 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593447.656 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))))) 1546593447.656 * * * * [misc]progress: [ 42 / 119 ] simplifiying candidate # 1546593447.656 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) 1546593447.656 * * [misc]simplify: iters left: 6 (6 enodes) 1546593447.657 * * [misc]simplify: iters left: 5 (10 enodes) 1546593447.659 * * [misc]simplify: iters left: 4 (16 enodes) 1546593447.661 * * [misc]simplify: iters left: 3 (18 enodes) 1546593447.663 * * [misc]simplify: iters left: 2 (23 enodes) 1546593447.665 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546593447.665 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) 1546593447.666 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593447.666 * * [misc]simplify: iters left: 6 (13 enodes) 1546593447.667 * * [misc]simplify: iters left: 5 (19 enodes) 1546593447.670 * * [misc]simplify: iters left: 4 (28 enodes) 1546593447.674 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.678 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* PI (* 2 n)) (- 1/2 (/ k 2)))) 1546593447.678 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))))) 1546593447.678 * * * * [misc]progress: [ 43 / 119 ] simplifiying candidate # 1546593447.678 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) 1/2)) 1546593447.678 * * [misc]simplify: iters left: 6 (11 enodes) 1546593447.680 * * [misc]simplify: iters left: 5 (16 enodes) 1546593447.682 * * [misc]simplify: iters left: 4 (22 enodes) 1546593447.684 * * [misc]simplify: iters left: 3 (23 enodes) 1546593447.687 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* 2 n) PI))) 1546593447.687 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* 2 n) PI))) (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2))))))) 1546593447.687 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593447.688 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.689 * * [misc]simplify: iters left: 5 (18 enodes) 1546593447.692 * * [misc]simplify: iters left: 4 (24 enodes) 1546593447.695 * * [misc]simplify: iters left: 3 (25 enodes) 1546593447.698 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))) 1546593447.698 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* 2 n) PI))) (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2)))))) 1546593447.698 * * * * [misc]progress: [ 44 / 119 ] simplifiying candidate # 1546593447.698 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) 1/2)) 1546593447.698 * * [misc]simplify: iters left: 6 (11 enodes) 1546593447.700 * * [misc]simplify: iters left: 5 (16 enodes) 1546593447.702 * * [misc]simplify: iters left: 4 (22 enodes) 1546593447.707 * * [misc]simplify: iters left: 3 (23 enodes) 1546593447.710 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* 2 n) PI))) 1546593447.710 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* 2 n) PI))) (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2))))))) 1546593447.710 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593447.710 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.712 * * [misc]simplify: iters left: 5 (18 enodes) 1546593447.715 * * [misc]simplify: iters left: 4 (24 enodes) 1546593447.718 * * [misc]simplify: iters left: 3 (25 enodes) 1546593447.721 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))) 1546593447.721 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* 2 n) PI))) (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2)))))) 1546593447.721 * * * * [misc]progress: [ 45 / 119 ] simplifiying candidate # 1546593447.722 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow 2 (- 1/2 (/ k 2)))) 1546593447.722 * * [misc]simplify: iters left: 6 (9 enodes) 1546593447.723 * * [misc]simplify: iters left: 5 (11 enodes) 1546593447.725 * * [misc]simplify: iters left: 4 (14 enodes) 1546593447.727 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow 2 (- 1/2 (/ k 2)))) 1546593447.727 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))))) 1546593447.727 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593447.727 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.729 * * [misc]simplify: iters left: 5 (15 enodes) 1546593447.731 * * [misc]simplify: iters left: 4 (18 enodes) 1546593447.733 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593447.733 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))))) 1546593447.733 * * * * [misc]progress: [ 46 / 119 ] simplifiying candidate # 1546593447.733 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) 1546593447.733 * * [misc]simplify: iters left: 6 (15 enodes) 1546593447.736 * * [misc]simplify: iters left: 5 (23 enodes) 1546593447.739 * * [misc]simplify: iters left: 4 (32 enodes) 1546593447.744 * * [misc]simplify: iters left: 3 (34 enodes) 1546593447.749 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546593447.749 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))) 1546593447.750 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.750 * * [misc]simplify: iters left: 6 (14 enodes) 1546593447.754 * * [misc]simplify: iters left: 5 (20 enodes) 1546593447.760 * * [misc]simplify: iters left: 4 (29 enodes) 1546593447.768 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.775 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593447.775 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))))) 1546593447.775 * * * * [misc]progress: [ 47 / 119 ] simplifiying candidate # 1546593447.776 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.776 * * [misc]simplify: iters left: 6 (14 enodes) 1546593447.778 * * [misc]simplify: iters left: 5 (20 enodes) 1546593447.780 * * [misc]simplify: iters left: 4 (29 enodes) 1546593447.784 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.788 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593447.788 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))) 1546593447.788 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.788 * * [misc]simplify: iters left: 6 (14 enodes) 1546593447.790 * * [misc]simplify: iters left: 5 (20 enodes) 1546593447.793 * * [misc]simplify: iters left: 4 (29 enodes) 1546593447.796 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.800 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593447.800 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))))) 1546593447.800 * * * * [misc]progress: [ 48 / 119 ] simplifiying candidate # 1546593447.800 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) 1) 1546593447.800 * * [misc]simplify: iters left: 4 (5 enodes) 1546593447.801 * * [misc]simplify: iters left: 3 (7 enodes) 1546593447.803 * * [misc]simplify: iters left: 2 (9 enodes) 1546593447.804 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546593447.804 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) 1546593447.804 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593447.804 * * [misc]simplify: iters left: 6 (13 enodes) 1546593447.806 * * [misc]simplify: iters left: 5 (19 enodes) 1546593447.809 * * [misc]simplify: iters left: 4 (28 enodes) 1546593447.813 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.817 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* PI (* 2 n)) (- 1/2 (/ k 2)))) 1546593447.818 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))))) 1546593447.818 * * * * [misc]progress: [ 49 / 119 ] simplifiying candidate # 1546593447.818 * [enter]simplify: Simplifying (/ 1 (pow (* 2 (* n PI)) 1/2)) 1546593447.818 * * [misc]simplify: iters left: 6 (9 enodes) 1546593447.821 * * [misc]simplify: iters left: 5 (16 enodes) 1546593447.825 * * [misc]simplify: iters left: 4 (22 enodes) 1546593447.831 * * [misc]simplify: iters left: 3 (23 enodes) 1546593447.836 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* PI 2)))) 1546593447.836 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* PI 2)))) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))))) 1546593447.836 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593447.836 * * [misc]simplify: iters left: 6 (11 enodes) 1546593447.839 * * [misc]simplify: iters left: 5 (17 enodes) 1546593447.844 * * [misc]simplify: iters left: 4 (23 enodes) 1546593447.850 * * [misc]simplify: iters left: 3 (24 enodes) 1546593447.856 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* 2 n)) (- (/ k 2)))) 1546593447.856 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* PI 2)))) (/ (sqrt k) (pow (* PI (* 2 n)) (- (/ k 2))))))) 1546593447.856 * * * * [misc]progress: [ 50 / 119 ] simplifiying candidate # 1546593447.856 * [enter]simplify: Simplifying (/ 1 (pow (* 2 (* n PI)) 1/2)) 1546593447.856 * * [misc]simplify: iters left: 6 (9 enodes) 1546593447.859 * * [misc]simplify: iters left: 5 (16 enodes) 1546593447.863 * * [misc]simplify: iters left: 4 (22 enodes) 1546593447.869 * * [misc]simplify: iters left: 3 (23 enodes) 1546593447.874 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* PI 2)))) 1546593447.874 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* PI 2)))) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))))) 1546593447.874 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593447.874 * * [misc]simplify: iters left: 6 (11 enodes) 1546593447.876 * * [misc]simplify: iters left: 5 (17 enodes) 1546593447.878 * * [misc]simplify: iters left: 4 (23 enodes) 1546593447.881 * * [misc]simplify: iters left: 3 (24 enodes) 1546593447.884 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* 2 n)) (- (/ k 2)))) 1546593447.884 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* PI 2)))) (/ (sqrt k) (pow (* PI (* 2 n)) (- (/ k 2))))))) 1546593447.884 * * * * [misc]progress: [ 51 / 119 ] simplifiying candidate # 1546593447.885 * [enter]simplify: Simplifying (/ 1 (pow 2 (- 1/2 (/ k 2)))) 1546593447.885 * * [misc]simplify: iters left: 6 (8 enodes) 1546593447.886 * * [misc]simplify: iters left: 5 (12 enodes) 1546593447.887 * * [misc]simplify: iters left: 4 (15 enodes) 1546593447.889 * [exit]simplify: Simplified to (/ 1 (pow 2 (- 1/2 (/ k 2)))) 1546593447.889 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))))) 1546593447.889 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593447.889 * * [misc]simplify: iters left: 6 (11 enodes) 1546593447.891 * * [misc]simplify: iters left: 5 (14 enodes) 1546593447.893 * * [misc]simplify: iters left: 4 (17 enodes) 1546593447.895 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593447.895 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))))) 1546593447.895 * * * * [misc]progress: [ 52 / 119 ] simplifiying candidate # 1546593447.895 * [enter]simplify: Simplifying (/ 1 (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) 1546593447.895 * * [misc]simplify: iters left: 6 (14 enodes) 1546593447.897 * * [misc]simplify: iters left: 5 (24 enodes) 1546593447.902 * * [misc]simplify: iters left: 4 (33 enodes) 1546593447.911 * * [misc]simplify: iters left: 3 (34 enodes) 1546593447.921 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593447.921 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (/ 1 (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))) 1546593447.921 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.921 * * [misc]simplify: iters left: 6 (13 enodes) 1546593447.925 * * [misc]simplify: iters left: 5 (19 enodes) 1546593447.931 * * [misc]simplify: iters left: 4 (28 enodes) 1546593447.935 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.938 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))) 1546593447.939 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2)))))))) 1546593447.939 * * * * [misc]progress: [ 53 / 119 ] simplifiying candidate # 1546593447.939 * [enter]simplify: Simplifying (/ 1 (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.939 * * [misc]simplify: iters left: 6 (13 enodes) 1546593447.941 * * [misc]simplify: iters left: 5 (21 enodes) 1546593447.944 * * [misc]simplify: iters left: 4 (30 enodes) 1546593447.948 * * [misc]simplify: iters left: 3 (31 enodes) 1546593447.951 * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1546593447.951 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))) 1546593447.951 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593447.952 * * [misc]simplify: iters left: 6 (13 enodes) 1546593447.953 * * [misc]simplify: iters left: 5 (19 enodes) 1546593447.957 * * [misc]simplify: iters left: 4 (28 enodes) 1546593447.961 * * [misc]simplify: iters left: 3 (30 enodes) 1546593447.969 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))) 1546593447.969 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2)))))))) 1546593447.969 * * * * [misc]progress: [ 54 / 119 ] simplifiying candidate # 1546593447.970 * [enter]simplify: Simplifying (/ 1 1) 1546593447.970 * * [misc]simplify: iters left: 2 (2 enodes) 1546593447.970 * * [misc]simplify: iters left: 1 (4 enodes) 1546593447.971 * [exit]simplify: Simplified to 1 1546593447.971 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) 1546593447.971 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593447.972 * * [misc]simplify: iters left: 6 (12 enodes) 1546593447.975 * * [misc]simplify: iters left: 5 (18 enodes) 1546593447.980 * * [misc]simplify: iters left: 4 (27 enodes) 1546593447.987 * * [misc]simplify: iters left: 3 (29 enodes) 1546593447.995 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593447.995 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) 1546593447.995 * * * * [misc]progress: [ 55 / 119 ] simplifiying candidate # 1546593447.995 * * * * [misc]progress: [ 56 / 119 ] simplifiying candidate # 1546593447.995 * * * * [misc]progress: [ 57 / 119 ] simplifiying candidate # 1546593447.995 * * * * [misc]progress: [ 58 / 119 ] simplifiying candidate # 1546593447.995 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- (/ k 2))) 1546593447.995 * * [misc]simplify: iters left: 5 (9 enodes) 1546593447.998 * * [misc]simplify: iters left: 4 (15 enodes) 1546593448.002 * * [misc]simplify: iters left: 3 (21 enodes) 1546593448.008 * * [misc]simplify: iters left: 2 (22 enodes) 1546593448.014 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1546593448.014 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* 2 (* n PI)) 1/2)) (pow (* (* 2 n) PI) (- (/ k 2)))))) 1546593448.014 * * * * [misc]progress: [ 59 / 119 ] simplifiying candidate # 1546593448.014 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- (/ k 2))) 1546593448.014 * * [misc]simplify: iters left: 5 (9 enodes) 1546593448.017 * * [misc]simplify: iters left: 4 (15 enodes) 1546593448.021 * * [misc]simplify: iters left: 3 (21 enodes) 1546593448.027 * * [misc]simplify: iters left: 2 (22 enodes) 1546593448.032 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1546593448.032 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* 2 (* n PI)) 1/2)) (pow (* (* 2 n) PI) (- (/ k 2)))))) 1546593448.032 * * * * [misc]progress: [ 60 / 119 ] simplifiying candidate # 1546593448.033 * [enter]simplify: Simplifying (pow (* n PI) (- 1/2 (/ k 2))) 1546593448.033 * * [misc]simplify: iters left: 5 (9 enodes) 1546593448.036 * * [misc]simplify: iters left: 4 (12 enodes) 1546593448.039 * * [misc]simplify: iters left: 3 (15 enodes) 1546593448.044 * [exit]simplify: Simplified to (pow (* n PI) (- 1/2 (/ k 2))) 1546593448.044 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow 2 (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))))) 1546593448.044 * * * * [misc]progress: [ 61 / 119 ] simplifiying candidate # 1546593448.044 * [enter]simplify: Simplifying (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.044 * * [misc]simplify: iters left: 6 (11 enodes) 1546593448.048 * * [misc]simplify: iters left: 5 (17 enodes) 1546593448.053 * * [misc]simplify: iters left: 4 (26 enodes) 1546593448.060 * * [misc]simplify: iters left: 3 (27 enodes) 1546593448.067 * [exit]simplify: Simplified to (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1546593448.067 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (* (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))))))) 1546593448.067 * * * * [misc]progress: [ 62 / 119 ] simplifiying candidate # 1546593448.067 * [enter]simplify: Simplifying (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.067 * * [misc]simplify: iters left: 6 (11 enodes) 1546593448.071 * * [misc]simplify: iters left: 5 (17 enodes) 1546593448.075 * * [misc]simplify: iters left: 4 (26 enodes) 1546593448.079 * * [misc]simplify: iters left: 3 (27 enodes) 1546593448.082 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1546593448.082 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) 1546593448.082 * * * * [misc]progress: [ 63 / 119 ] simplifiying candidate # 1546593448.082 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1546593448.082 * * [misc]simplify: iters left: 5 (10 enodes) 1546593448.084 * * [misc]simplify: iters left: 4 (16 enodes) 1546593448.086 * * [misc]simplify: iters left: 3 (25 enodes) 1546593448.089 * * [misc]simplify: iters left: 2 (26 enodes) 1546593448.092 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- 1/2 (/ k 2))) 1546593448.092 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546593448.092 * * * * [misc]progress: [ 64 / 119 ] simplifiying candidate # 1546593448.092 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546593448.093 * * [misc]simplify: iters left: 4 (4 enodes) 1546593448.093 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546593448.093 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546593448.093 * * * * [misc]progress: [ 65 / 119 ] simplifiying candidate # 1546593448.093 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546593448.093 * * [misc]simplify: iters left: 2 (3 enodes) 1546593448.094 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546593448.094 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546593448.094 * * * * [misc]progress: [ 66 / 119 ] simplifiying candidate # 1546593448.094 * * * * [misc]progress: [ 67 / 119 ] simplifiying candidate # 1546593448.094 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (/ k 2)) 1546593448.094 * * [misc]simplify: iters left: 5 (8 enodes) 1546593448.095 * * [misc]simplify: iters left: 4 (12 enodes) 1546593448.097 * * [misc]simplify: iters left: 3 (18 enodes) 1546593448.100 * * [misc]simplify: iters left: 2 (20 enodes) 1546593448.102 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) 1546593448.102 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* 2 (* n PI)) 1/2)) (pow (* (* PI n) 2) (/ k 2))))) 1546593448.102 * * * * [misc]progress: [ 68 / 119 ] simplifiying candidate # 1546593448.102 * * * * [misc]progress: [ 69 / 119 ] simplifiying candidate # 1546593448.102 * [enter]simplify: Simplifying (- 1) 1546593448.102 * * [misc]simplify: iters left: 2 (2 enodes) 1546593448.103 * * [misc]simplify: iters left: 1 (5 enodes) 1546593448.104 * [exit]simplify: Simplified to -1 1546593448.104 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) -1)) 1546593448.104 * * * * [misc]progress: [ 70 / 119 ] simplifiying candidate # 1546593448.104 * * * * [misc]progress: [ 71 / 119 ] simplifiying candidate # 1546593448.104 * * * * [misc]progress: [ 72 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 73 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 74 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 75 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 76 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 77 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 78 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 79 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 80 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 81 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 82 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 83 / 119 ] simplifiying candidate # 1546593448.105 * * * * [misc]progress: [ 84 / 119 ] simplifiying candidate # 1546593448.106 * [enter]simplify: Simplifying (cbrt (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593448.106 * * [misc]simplify: iters left: 6 (13 enodes) 1546593448.109 * * [misc]simplify: iters left: 5 (19 enodes) 1546593448.115 * * [misc]simplify: iters left: 4 (28 enodes) 1546593448.122 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.130 * [exit]simplify: Simplified to (cbrt (/ (sqrt k) (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))) 1546593448.130 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) (cbrt (/ (sqrt k) (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))))) 1546593448.130 * * * * [misc]progress: [ 85 / 119 ] simplifiying candidate # 1546593448.130 * [enter]simplify: Simplifying (sqrt (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593448.131 * * [misc]simplify: iters left: 6 (13 enodes) 1546593448.134 * * [misc]simplify: iters left: 5 (19 enodes) 1546593448.140 * * [misc]simplify: iters left: 4 (28 enodes) 1546593448.147 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.155 * [exit]simplify: Simplified to (sqrt (/ (sqrt k) (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))) 1546593448.155 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) (sqrt (/ (sqrt k) (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))))) 1546593448.155 * * * * [misc]progress: [ 86 / 119 ] simplifiying candidate # 1546593448.155 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593448.155 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.159 * * [misc]simplify: iters left: 5 (18 enodes) 1546593448.165 * * [misc]simplify: iters left: 4 (24 enodes) 1546593448.168 * * [misc]simplify: iters left: 3 (25 enodes) 1546593448.171 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))) 1546593448.171 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2 (* n PI)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))))) 1546593448.171 * * * * [misc]progress: [ 87 / 119 ] simplifiying candidate # 1546593448.172 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593448.172 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.173 * * [misc]simplify: iters left: 5 (18 enodes) 1546593448.176 * * [misc]simplify: iters left: 4 (24 enodes) 1546593448.179 * * [misc]simplify: iters left: 3 (25 enodes) 1546593448.182 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))) 1546593448.182 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2 (* n PI)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))))) 1546593448.182 * * * * [misc]progress: [ 88 / 119 ] simplifiying candidate # 1546593448.182 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593448.182 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.184 * * [misc]simplify: iters left: 5 (15 enodes) 1546593448.186 * * [misc]simplify: iters left: 4 (18 enodes) 1546593448.188 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593448.189 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow 2 (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))))) 1546593448.189 * * * * [misc]progress: [ 89 / 119 ] simplifiying candidate # 1546593448.189 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593448.189 * * [misc]simplify: iters left: 6 (14 enodes) 1546593448.191 * * [misc]simplify: iters left: 5 (20 enodes) 1546593448.194 * * [misc]simplify: iters left: 4 (29 enodes) 1546593448.197 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.201 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593448.201 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) 1546593448.201 * * * * [misc]progress: [ 90 / 119 ] simplifiying candidate # 1546593448.201 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593448.201 * * [misc]simplify: iters left: 6 (14 enodes) 1546593448.203 * * [misc]simplify: iters left: 5 (20 enodes) 1546593448.206 * * [misc]simplify: iters left: 4 (29 enodes) 1546593448.210 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.214 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593448.214 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) 1546593448.214 * * * * [misc]progress: [ 91 / 119 ] simplifiying candidate # 1546593448.214 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.214 * * [misc]simplify: iters left: 6 (13 enodes) 1546593448.216 * * [misc]simplify: iters left: 5 (19 enodes) 1546593448.218 * * [misc]simplify: iters left: 4 (28 enodes) 1546593448.222 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.228 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* PI (* 2 n)) (- 1/2 (/ k 2)))) 1546593448.228 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* PI (* 2 n)) (- 1/2 (/ k 2)))))) 1546593448.228 * * * * [misc]progress: [ 92 / 119 ] simplifiying candidate # 1546593448.229 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593448.229 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.233 * * [misc]simplify: iters left: 5 (18 enodes) 1546593448.238 * * [misc]simplify: iters left: 4 (24 enodes) 1546593448.244 * * [misc]simplify: iters left: 3 (25 enodes) 1546593448.251 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))) 1546593448.251 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))))) 1546593448.251 * * * * [misc]progress: [ 93 / 119 ] simplifiying candidate # 1546593448.251 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593448.251 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.256 * * [misc]simplify: iters left: 5 (18 enodes) 1546593448.261 * * [misc]simplify: iters left: 4 (24 enodes) 1546593448.268 * * [misc]simplify: iters left: 3 (25 enodes) 1546593448.274 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))) 1546593448.274 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (/ (- k) 2))))) 1546593448.274 * * * * [misc]progress: [ 94 / 119 ] simplifiying candidate # 1546593448.274 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593448.274 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.278 * * [misc]simplify: iters left: 5 (15 enodes) 1546593448.282 * * [misc]simplify: iters left: 4 (18 enodes) 1546593448.287 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593448.287 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow 2 (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))))) 1546593448.288 * * * * [misc]progress: [ 95 / 119 ] simplifiying candidate # 1546593448.288 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593448.288 * * [misc]simplify: iters left: 6 (14 enodes) 1546593448.292 * * [misc]simplify: iters left: 5 (20 enodes) 1546593448.298 * * [misc]simplify: iters left: 4 (29 enodes) 1546593448.307 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.315 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593448.315 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) 1546593448.315 * * * * [misc]progress: [ 96 / 119 ] simplifiying candidate # 1546593448.315 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593448.315 * * [misc]simplify: iters left: 6 (14 enodes) 1546593448.320 * * [misc]simplify: iters left: 5 (20 enodes) 1546593448.326 * * [misc]simplify: iters left: 4 (29 enodes) 1546593448.333 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.341 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593448.341 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) 1546593448.341 * * * * [misc]progress: [ 97 / 119 ] simplifiying candidate # 1546593448.342 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.342 * * [misc]simplify: iters left: 6 (13 enodes) 1546593448.346 * * [misc]simplify: iters left: 5 (19 enodes) 1546593448.351 * * [misc]simplify: iters left: 4 (28 enodes) 1546593448.359 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.366 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* PI (* 2 n)) (- 1/2 (/ k 2)))) 1546593448.366 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* PI (* 2 n)) (- 1/2 (/ k 2)))))) 1546593448.366 * * * * [misc]progress: [ 98 / 119 ] simplifiying candidate # 1546593448.367 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593448.367 * * [misc]simplify: iters left: 6 (11 enodes) 1546593448.370 * * [misc]simplify: iters left: 5 (17 enodes) 1546593448.375 * * [misc]simplify: iters left: 4 (23 enodes) 1546593448.382 * * [misc]simplify: iters left: 3 (24 enodes) 1546593448.388 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* 2 n)) (- (/ k 2)))) 1546593448.388 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* 2 (* n PI)) 1/2))) (/ (sqrt k) (pow (* PI (* 2 n)) (- (/ k 2)))))) 1546593448.388 * * * * [misc]progress: [ 99 / 119 ] simplifiying candidate # 1546593448.389 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2)))) 1546593448.389 * * [misc]simplify: iters left: 6 (11 enodes) 1546593448.392 * * [misc]simplify: iters left: 5 (17 enodes) 1546593448.397 * * [misc]simplify: iters left: 4 (23 enodes) 1546593448.401 * * [misc]simplify: iters left: 3 (24 enodes) 1546593448.405 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* 2 n)) (- (/ k 2)))) 1546593448.405 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* 2 (* n PI)) 1/2))) (/ (sqrt k) (pow (* PI (* 2 n)) (- (/ k 2)))))) 1546593448.405 * * * * [misc]progress: [ 100 / 119 ] simplifiying candidate # 1546593448.405 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593448.405 * * [misc]simplify: iters left: 6 (11 enodes) 1546593448.407 * * [misc]simplify: iters left: 5 (14 enodes) 1546593448.408 * * [misc]simplify: iters left: 4 (17 enodes) 1546593448.411 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))) 1546593448.411 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow 2 (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))))) 1546593448.411 * * * * [misc]progress: [ 101 / 119 ] simplifiying candidate # 1546593448.411 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593448.411 * * [misc]simplify: iters left: 6 (13 enodes) 1546593448.413 * * [misc]simplify: iters left: 5 (19 enodes) 1546593448.415 * * [misc]simplify: iters left: 4 (28 enodes) 1546593448.419 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.423 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))) 1546593448.423 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))))) 1546593448.423 * * * * [misc]progress: [ 102 / 119 ] simplifiying candidate # 1546593448.423 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546593448.423 * * [misc]simplify: iters left: 6 (13 enodes) 1546593448.425 * * [misc]simplify: iters left: 5 (19 enodes) 1546593448.428 * * [misc]simplify: iters left: 4 (28 enodes) 1546593448.431 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.435 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))) 1546593448.435 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (- 1/2 (/ k 2))))))) 1546593448.435 * * * * [misc]progress: [ 103 / 119 ] simplifiying candidate # 1546593448.435 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.435 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.437 * * [misc]simplify: iters left: 5 (18 enodes) 1546593448.440 * * [misc]simplify: iters left: 4 (27 enodes) 1546593448.443 * * [misc]simplify: iters left: 3 (29 enodes) 1546593448.447 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.447 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) 1546593448.447 * * * * [misc]progress: [ 104 / 119 ] simplifiying candidate # 1546593448.447 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.447 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.449 * * [misc]simplify: iters left: 5 (18 enodes) 1546593448.452 * * [misc]simplify: iters left: 4 (27 enodes) 1546593448.455 * * [misc]simplify: iters left: 3 (29 enodes) 1546593448.459 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.459 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) 1546593448.459 * * * * [misc]progress: [ 105 / 119 ] simplifiying candidate # 1546593448.459 * [enter]simplify: Simplifying (/ 1 (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1546593448.459 * * [misc]simplify: iters left: 6 (12 enodes) 1546593448.461 * * [misc]simplify: iters left: 5 (20 enodes) 1546593448.464 * * [misc]simplify: iters left: 4 (29 enodes) 1546593448.467 * * [misc]simplify: iters left: 3 (30 enodes) 1546593448.471 * [exit]simplify: Simplified to (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1546593448.471 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))) 1546593448.471 * * * * [misc]progress: [ 106 / 119 ] simplifiying candidate # 1546593448.471 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (/ k 2)) 1546593448.471 * * [misc]simplify: iters left: 5 (8 enodes) 1546593448.472 * * [misc]simplify: iters left: 4 (12 enodes) 1546593448.474 * * [misc]simplify: iters left: 3 (18 enodes) 1546593448.477 * * [misc]simplify: iters left: 2 (20 enodes) 1546593448.480 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) 1546593448.480 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) 1/2))) (pow (* (* PI n) 2) (/ k 2)))) 1546593448.480 * * * * [misc]progress: [ 107 / 119 ] simplifiying candidate # 1546593448.480 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1546593448.480 * * [misc]simplify: iters left: 5 (10 enodes) 1546593448.483 * * [misc]simplify: iters left: 4 (16 enodes) 1546593448.488 * * [misc]simplify: iters left: 3 (25 enodes) 1546593448.495 * * [misc]simplify: iters left: 2 (26 enodes) 1546593448.501 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- 1/2 (/ k 2))) 1546593448.502 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546593448.502 * * * * [misc]progress: [ 108 / 119 ] simplifiying candidate # 1546593448.502 * [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))))) 1546593448.502 * * [misc]simplify: iters left: 6 (37 enodes) 1546593448.517 * * [misc]simplify: iters left: 5 (105 enodes) 1546593448.559 * * [misc]simplify: iters left: 4 (339 enodes) 1546593448.753 * [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))))) 1546593448.753 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)))))))) 1546593448.753 * * * * [misc]progress: [ 109 / 119 ] simplifiying candidate # 1546593448.754 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546593448.754 * * [misc]simplify: iters left: 6 (15 enodes) 1546593448.757 * * [misc]simplify: iters left: 5 (33 enodes) 1546593448.762 * * [misc]simplify: iters left: 4 (64 enodes) 1546593448.774 * * [misc]simplify: iters left: 3 (171 enodes) 1546593448.883 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546593448.883 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))))))) 1546593448.883 * * * * [misc]progress: [ 110 / 119 ] simplifiying candidate # 1546593448.883 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546593448.884 * * [misc]simplify: iters left: 6 (15 enodes) 1546593448.890 * * [misc]simplify: iters left: 5 (30 enodes) 1546593448.900 * * [misc]simplify: iters left: 4 (65 enodes) 1546593448.928 * * [misc]simplify: iters left: 3 (200 enodes) 1546593449.022 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546593449.023 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))))) 1546593449.023 * * * * [misc]progress: [ 111 / 119 ] simplifiying candidate # 1546593449.023 * [enter]simplify: Simplifying (* n PI) 1546593449.023 * * [misc]simplify: iters left: 2 (3 enodes) 1546593449.023 * * [misc]simplify: iters left: 1 (4 enodes) 1546593449.024 * [exit]simplify: Simplified to (* n PI) 1546593449.024 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) 1546593449.024 * * * * [misc]progress: [ 112 / 119 ] simplifiying candidate # 1546593449.024 * [enter]simplify: Simplifying (* n PI) 1546593449.024 * * [misc]simplify: iters left: 2 (3 enodes) 1546593449.025 * * [misc]simplify: iters left: 1 (4 enodes) 1546593449.025 * [exit]simplify: Simplified to (* n PI) 1546593449.025 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) 1546593449.025 * * * * [misc]progress: [ 113 / 119 ] simplifiying candidate # 1546593449.025 * [enter]simplify: Simplifying (* n PI) 1546593449.025 * * [misc]simplify: iters left: 2 (3 enodes) 1546593449.026 * * [misc]simplify: iters left: 1 (4 enodes) 1546593449.026 * [exit]simplify: Simplified to (* n PI) 1546593449.026 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))) 1546593449.026 * * * * [misc]progress: [ 114 / 119 ] simplifiying candidate # 1546593449.026 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546593449.027 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546593449.027 * * * * [misc]progress: [ 115 / 119 ] simplifiying candidate # 1546593449.027 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546593449.027 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546593449.027 * * * * [misc]progress: [ 116 / 119 ] simplifiying candidate # 1546593449.027 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546593449.027 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546593449.027 * * * * [misc]progress: [ 117 / 119 ] simplifiying candidate # 1546593449.027 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1546593449.027 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593449.027 * * * * [misc]progress: [ 118 / 119 ] simplifiying candidate # 1546593449.027 * [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)))))))) 1546593449.027 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593449.027 * * * * [misc]progress: [ 119 / 119 ] simplifiying candidate # 1546593449.028 * [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))))))))))) 1546593449.028 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546593449.028 * * * [misc]progress: adding candidates to table 1546593450.395 * * [misc]progress: iteration 4 / 4 1546593450.395 * * * [misc]progress: picking best candidate 1546593450.416 * * * * [misc]pick: Picked # 1546593450.416 * * * [misc]progress: localizing error 1546593450.425 * * * [misc]progress: generating rewritten candidates 1546593450.425 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 1) 1546593450.426 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) 1546593450.427 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1) 1546593450.433 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) 1546593450.435 * * * [misc]progress: generating series expansions 1546593450.435 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) 1546593450.435 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546593450.435 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546593450.435 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593450.435 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593450.435 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593450.435 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593450.435 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.435 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.435 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593450.435 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.435 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.435 * [misc]taylor: Taking taylor expansion of k in k 1546593450.435 * [misc]backup-simplify: Simplify 0 into 0 1546593450.435 * [misc]backup-simplify: Simplify 1 into 1 1546593450.435 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593450.435 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593450.435 * [misc]taylor: Taking taylor expansion of 2 in k 1546593450.435 * [misc]backup-simplify: Simplify 2 into 2 1546593450.435 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593450.435 * [misc]taylor: Taking taylor expansion of n in k 1546593450.435 * [misc]backup-simplify: Simplify n into n 1546593450.435 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.435 * [misc]backup-simplify: Simplify PI into PI 1546593450.435 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593450.435 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593450.435 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593450.436 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593450.436 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.436 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593450.436 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593450.436 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593450.436 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593450.436 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593450.436 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593450.436 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593450.436 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.436 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.436 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593450.436 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.436 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.436 * [misc]taylor: Taking taylor expansion of k in n 1546593450.436 * [misc]backup-simplify: Simplify k into k 1546593450.436 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593450.436 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593450.436 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.436 * [misc]backup-simplify: Simplify 2 into 2 1546593450.436 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593450.436 * [misc]taylor: Taking taylor expansion of n in n 1546593450.436 * [misc]backup-simplify: Simplify 0 into 0 1546593450.436 * [misc]backup-simplify: Simplify 1 into 1 1546593450.436 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.436 * [misc]backup-simplify: Simplify PI into PI 1546593450.437 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593450.437 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593450.437 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593450.438 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593450.438 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.438 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593450.438 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593450.438 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593450.438 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.439 * [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)))) 1546593450.439 * [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))))) 1546593450.439 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593450.439 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593450.439 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593450.439 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593450.439 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.439 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.439 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593450.439 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.439 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.439 * [misc]taylor: Taking taylor expansion of k in n 1546593450.439 * [misc]backup-simplify: Simplify k into k 1546593450.439 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593450.439 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593450.439 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.439 * [misc]backup-simplify: Simplify 2 into 2 1546593450.439 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593450.439 * [misc]taylor: Taking taylor expansion of n in n 1546593450.439 * [misc]backup-simplify: Simplify 0 into 0 1546593450.439 * [misc]backup-simplify: Simplify 1 into 1 1546593450.439 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.439 * [misc]backup-simplify: Simplify PI into PI 1546593450.440 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593450.440 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593450.440 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593450.441 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593450.441 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.441 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593450.441 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593450.441 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593450.441 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.442 * [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)))) 1546593450.442 * [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))))) 1546593450.442 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546593450.442 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546593450.442 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593450.442 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.442 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.442 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593450.442 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.442 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.442 * [misc]taylor: Taking taylor expansion of k in k 1546593450.442 * [misc]backup-simplify: Simplify 0 into 0 1546593450.442 * [misc]backup-simplify: Simplify 1 into 1 1546593450.442 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546593450.442 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593450.442 * [misc]taylor: Taking taylor expansion of n in k 1546593450.442 * [misc]backup-simplify: Simplify n into n 1546593450.442 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593450.443 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593450.443 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593450.443 * [misc]taylor: Taking taylor expansion of 2 in k 1546593450.443 * [misc]backup-simplify: Simplify 2 into 2 1546593450.443 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.443 * [misc]backup-simplify: Simplify PI into PI 1546593450.443 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.443 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.443 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593450.443 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.443 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593450.444 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.444 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546593450.444 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593450.445 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593450.445 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593450.446 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593450.448 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593450.448 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546593450.448 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.448 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.448 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.449 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546593450.450 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.450 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.450 * [misc]backup-simplify: Simplify 0 into 0 1546593450.450 * [misc]backup-simplify: Simplify 0 into 0 1546593450.450 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546593450.451 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593450.452 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593450.452 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.452 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593450.452 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593450.453 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593450.453 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546593450.454 * [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))))))) 1546593450.455 * [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))))))) 1546593450.456 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593450.457 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593450.460 * [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 1546593450.460 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546593450.461 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.461 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.461 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.461 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593450.463 * [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 1546593450.463 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.463 * [misc]backup-simplify: Simplify 0 into 0 1546593450.463 * [misc]backup-simplify: Simplify 0 into 0 1546593450.463 * [misc]backup-simplify: Simplify 0 into 0 1546593450.464 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546593450.465 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593450.468 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1546593450.468 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.468 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593450.468 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.468 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.469 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593450.470 * [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))))) 1546593450.471 * [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))))) 1546593450.474 * [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))))) 1546593450.474 * [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)))) 1546593450.474 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546593450.474 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.475 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.475 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.475 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.475 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of k in k 1546593450.475 * [misc]backup-simplify: Simplify 0 into 0 1546593450.475 * [misc]backup-simplify: Simplify 1 into 1 1546593450.475 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.475 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of 2 in k 1546593450.475 * [misc]backup-simplify: Simplify 2 into 2 1546593450.475 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593450.475 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.475 * [misc]backup-simplify: Simplify PI into PI 1546593450.475 * [misc]taylor: Taking taylor expansion of n in k 1546593450.475 * [misc]backup-simplify: Simplify n into n 1546593450.475 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593450.475 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593450.475 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593450.475 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593450.475 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593450.475 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593450.476 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593450.476 * [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)))) 1546593450.476 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.476 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.476 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.476 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.476 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of k in n 1546593450.476 * [misc]backup-simplify: Simplify k into k 1546593450.476 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.476 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.476 * [misc]backup-simplify: Simplify 2 into 2 1546593450.476 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.476 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.476 * [misc]backup-simplify: Simplify PI into PI 1546593450.476 * [misc]taylor: Taking taylor expansion of n in n 1546593450.476 * [misc]backup-simplify: Simplify 0 into 0 1546593450.476 * [misc]backup-simplify: Simplify 1 into 1 1546593450.476 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.477 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.477 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.477 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593450.477 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593450.477 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593450.477 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.478 * [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))) 1546593450.478 * [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)))) 1546593450.478 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593450.478 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593450.478 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593450.478 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593450.478 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.478 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.478 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593450.478 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.478 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.478 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.478 * [misc]taylor: Taking taylor expansion of k in n 1546593450.478 * [misc]backup-simplify: Simplify k into k 1546593450.479 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.479 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593450.479 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593450.479 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.479 * [misc]backup-simplify: Simplify 2 into 2 1546593450.479 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.479 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.479 * [misc]backup-simplify: Simplify PI into PI 1546593450.479 * [misc]taylor: Taking taylor expansion of n in n 1546593450.479 * [misc]backup-simplify: Simplify 0 into 0 1546593450.479 * [misc]backup-simplify: Simplify 1 into 1 1546593450.479 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.479 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.479 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.479 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593450.479 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593450.479 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593450.480 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.480 * [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))) 1546593450.481 * [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)))) 1546593450.481 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546593450.481 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546593450.481 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593450.481 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.481 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.481 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593450.481 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.481 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.481 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.481 * [misc]taylor: Taking taylor expansion of k in k 1546593450.481 * [misc]backup-simplify: Simplify 0 into 0 1546593450.481 * [misc]backup-simplify: Simplify 1 into 1 1546593450.481 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.481 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546593450.481 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593450.481 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593450.481 * [misc]taylor: Taking taylor expansion of 2 in k 1546593450.481 * [misc]backup-simplify: Simplify 2 into 2 1546593450.481 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.481 * [misc]backup-simplify: Simplify PI into PI 1546593450.481 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.482 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.482 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593450.482 * [misc]taylor: Taking taylor expansion of n in k 1546593450.482 * [misc]backup-simplify: Simplify n into n 1546593450.482 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593450.482 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593450.482 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593450.482 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593450.482 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593450.483 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546593450.483 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546593450.483 * [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)))) 1546593450.484 * [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)))) 1546593450.484 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593450.485 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593450.486 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593450.486 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593450.487 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593450.487 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.487 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.487 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.488 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593450.488 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.489 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.489 * [misc]backup-simplify: Simplify 0 into 0 1546593450.489 * [misc]backup-simplify: Simplify 0 into 0 1546593450.489 * [misc]backup-simplify: Simplify 0 into 0 1546593450.489 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.490 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593450.493 * [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 1546593450.493 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.493 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593450.493 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.493 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.494 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.494 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546593450.496 * [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 1546593450.496 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.496 * [misc]backup-simplify: Simplify 0 into 0 1546593450.496 * [misc]backup-simplify: Simplify 0 into 0 1546593450.496 * [misc]backup-simplify: Simplify 0 into 0 1546593450.496 * [misc]backup-simplify: Simplify 0 into 0 1546593450.497 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.500 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593450.505 * [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 1546593450.505 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.505 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593450.505 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.505 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.506 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.506 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546593450.508 * [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 1546593450.508 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.508 * [misc]backup-simplify: Simplify 0 into 0 1546593450.509 * [misc]backup-simplify: Simplify 0 into 0 1546593450.509 * [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))))) 1546593450.509 * [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)) 1546593450.509 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546593450.509 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593450.509 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593450.509 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593450.509 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593450.509 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593450.509 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.509 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.509 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.509 * [misc]taylor: Taking taylor expansion of k in k 1546593450.509 * [misc]backup-simplify: Simplify 0 into 0 1546593450.509 * [misc]backup-simplify: Simplify 1 into 1 1546593450.509 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.509 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.509 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.510 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593450.510 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593450.510 * [misc]taylor: Taking taylor expansion of -2 in k 1546593450.510 * [misc]backup-simplify: Simplify -2 into -2 1546593450.510 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593450.510 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.510 * [misc]backup-simplify: Simplify PI into PI 1546593450.510 * [misc]taylor: Taking taylor expansion of n in k 1546593450.510 * [misc]backup-simplify: Simplify n into n 1546593450.510 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593450.510 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593450.510 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593450.510 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593450.510 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593450.510 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593450.510 * [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))) 1546593450.510 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593450.510 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593450.510 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593450.510 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593450.510 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593450.510 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.510 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.510 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.510 * [misc]taylor: Taking taylor expansion of k in n 1546593450.510 * [misc]backup-simplify: Simplify k into k 1546593450.510 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.510 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.510 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.510 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593450.510 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593450.511 * [misc]taylor: Taking taylor expansion of -2 in n 1546593450.511 * [misc]backup-simplify: Simplify -2 into -2 1546593450.511 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.511 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.511 * [misc]backup-simplify: Simplify PI into PI 1546593450.511 * [misc]taylor: Taking taylor expansion of n in n 1546593450.511 * [misc]backup-simplify: Simplify 0 into 0 1546593450.511 * [misc]backup-simplify: Simplify 1 into 1 1546593450.511 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.511 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593450.511 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593450.511 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593450.511 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593450.512 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.512 * [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))) 1546593450.513 * [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)))) 1546593450.513 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.513 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.513 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of k in n 1546593450.513 * [misc]backup-simplify: Simplify k into k 1546593450.513 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.513 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.513 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.513 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of -2 in n 1546593450.513 * [misc]backup-simplify: Simplify -2 into -2 1546593450.513 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.513 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.513 * [misc]backup-simplify: Simplify PI into PI 1546593450.513 * [misc]taylor: Taking taylor expansion of n in n 1546593450.513 * [misc]backup-simplify: Simplify 0 into 0 1546593450.513 * [misc]backup-simplify: Simplify 1 into 1 1546593450.513 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.513 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593450.514 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593450.514 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593450.514 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593450.515 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.515 * [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))) 1546593450.515 * [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)))) 1546593450.515 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546593450.515 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546593450.515 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593450.515 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593450.515 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.515 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.516 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.516 * [misc]taylor: Taking taylor expansion of k in k 1546593450.516 * [misc]backup-simplify: Simplify 0 into 0 1546593450.516 * [misc]backup-simplify: Simplify 1 into 1 1546593450.516 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.516 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.516 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.516 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546593450.516 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546593450.516 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546593450.516 * [misc]taylor: Taking taylor expansion of -2 in k 1546593450.516 * [misc]backup-simplify: Simplify -2 into -2 1546593450.516 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.516 * [misc]backup-simplify: Simplify PI into PI 1546593450.516 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593450.516 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593450.516 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593450.516 * [misc]taylor: Taking taylor expansion of n in k 1546593450.516 * [misc]backup-simplify: Simplify n into n 1546593450.516 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593450.516 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593450.517 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593450.517 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593450.517 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546593450.517 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546593450.518 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593450.518 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593450.519 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593450.519 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593450.522 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593450.522 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593450.522 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593450.522 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.523 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.523 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546593450.525 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.525 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.525 * [misc]backup-simplify: Simplify 0 into 0 1546593450.525 * [misc]backup-simplify: Simplify 0 into 0 1546593450.525 * [misc]backup-simplify: Simplify 0 into 0 1546593450.527 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.528 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593450.532 * [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 1546593450.533 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.533 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593450.533 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.534 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.535 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546593450.537 * [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 1546593450.537 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.537 * [misc]backup-simplify: Simplify 0 into 0 1546593450.537 * [misc]backup-simplify: Simplify 0 into 0 1546593450.537 * [misc]backup-simplify: Simplify 0 into 0 1546593450.537 * [misc]backup-simplify: Simplify 0 into 0 1546593450.539 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.540 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593450.548 * [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 1546593450.548 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.549 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593450.549 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.550 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.551 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546593450.553 * [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 1546593450.553 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.553 * [misc]backup-simplify: Simplify 0 into 0 1546593450.553 * [misc]backup-simplify: Simplify 0 into 0 1546593450.554 * [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))))) 1546593450.554 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1) 1546593450.554 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546593450.554 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546593450.554 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593450.554 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.554 * [misc]backup-simplify: Simplify 2 into 2 1546593450.554 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593450.554 * [misc]taylor: Taking taylor expansion of n in n 1546593450.554 * [misc]backup-simplify: Simplify 0 into 0 1546593450.554 * [misc]backup-simplify: Simplify 1 into 1 1546593450.554 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.554 * [misc]backup-simplify: Simplify PI into PI 1546593450.554 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593450.554 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.554 * [misc]backup-simplify: Simplify 2 into 2 1546593450.554 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593450.554 * [misc]taylor: Taking taylor expansion of n in n 1546593450.554 * [misc]backup-simplify: Simplify 0 into 0 1546593450.554 * [misc]backup-simplify: Simplify 1 into 1 1546593450.554 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.554 * [misc]backup-simplify: Simplify PI into PI 1546593450.554 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593450.554 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593450.554 * [misc]backup-simplify: Simplify 0 into 0 1546593450.555 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593450.555 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593450.555 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.556 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593450.557 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593450.557 * [misc]backup-simplify: Simplify 0 into 0 1546593450.558 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593450.558 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593450.558 * [misc]backup-simplify: Simplify 0 into 0 1546593450.560 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593450.561 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546593450.561 * [misc]backup-simplify: Simplify 0 into 0 1546593450.562 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593450.564 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546593450.564 * [misc]backup-simplify: Simplify 0 into 0 1546593450.566 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593450.568 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546593450.568 * [misc]backup-simplify: Simplify 0 into 0 1546593450.570 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546593450.573 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546593450.573 * [misc]backup-simplify: Simplify 0 into 0 1546593450.573 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546593450.573 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546593450.573 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546593450.573 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593450.573 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.573 * [misc]backup-simplify: Simplify 2 into 2 1546593450.573 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.573 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.573 * [misc]backup-simplify: Simplify PI into PI 1546593450.573 * [misc]taylor: Taking taylor expansion of n in n 1546593450.573 * [misc]backup-simplify: Simplify 0 into 0 1546593450.573 * [misc]backup-simplify: Simplify 1 into 1 1546593450.573 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.573 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593450.573 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.573 * [misc]backup-simplify: Simplify 2 into 2 1546593450.573 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.573 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.573 * [misc]backup-simplify: Simplify PI into PI 1546593450.573 * [misc]taylor: Taking taylor expansion of n in n 1546593450.573 * [misc]backup-simplify: Simplify 0 into 0 1546593450.573 * [misc]backup-simplify: Simplify 1 into 1 1546593450.574 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.574 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.574 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.575 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593450.575 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593450.575 * [misc]backup-simplify: Simplify 0 into 0 1546593450.576 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.577 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593450.577 * [misc]backup-simplify: Simplify 0 into 0 1546593450.579 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.580 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593450.581 * [misc]backup-simplify: Simplify 0 into 0 1546593450.582 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.584 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593450.584 * [misc]backup-simplify: Simplify 0 into 0 1546593450.587 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.589 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593450.589 * [misc]backup-simplify: Simplify 0 into 0 1546593450.592 * [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 1546593450.595 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593450.595 * [misc]backup-simplify: Simplify 0 into 0 1546593450.595 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546593450.596 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546593450.596 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546593450.596 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593450.596 * [misc]taylor: Taking taylor expansion of -2 in n 1546593450.596 * [misc]backup-simplify: Simplify -2 into -2 1546593450.596 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.596 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.596 * [misc]backup-simplify: Simplify PI into PI 1546593450.596 * [misc]taylor: Taking taylor expansion of n in n 1546593450.596 * [misc]backup-simplify: Simplify 0 into 0 1546593450.596 * [misc]backup-simplify: Simplify 1 into 1 1546593450.596 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.596 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593450.596 * [misc]taylor: Taking taylor expansion of -2 in n 1546593450.596 * [misc]backup-simplify: Simplify -2 into -2 1546593450.596 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.596 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.596 * [misc]backup-simplify: Simplify PI into PI 1546593450.596 * [misc]taylor: Taking taylor expansion of n in n 1546593450.596 * [misc]backup-simplify: Simplify 0 into 0 1546593450.596 * [misc]backup-simplify: Simplify 1 into 1 1546593450.597 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.597 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593450.597 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593450.598 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593450.599 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593450.599 * [misc]backup-simplify: Simplify 0 into 0 1546593450.600 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.601 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593450.601 * [misc]backup-simplify: Simplify 0 into 0 1546593450.603 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.605 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593450.605 * [misc]backup-simplify: Simplify 0 into 0 1546593450.607 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.609 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546593450.609 * [misc]backup-simplify: Simplify 0 into 0 1546593450.611 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.614 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546593450.614 * [misc]backup-simplify: Simplify 0 into 0 1546593450.617 * [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 1546593450.620 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546593450.620 * [misc]backup-simplify: Simplify 0 into 0 1546593450.621 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546593450.621 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1) 1546593450.621 * [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)))) 1546593450.621 * [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 1546593450.621 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546593450.621 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1546593450.621 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1546593450.621 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1546593450.621 * [misc]taylor: Taking taylor expansion of 1/4 in k 1546593450.621 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.621 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k 1546593450.621 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.621 * [misc]taylor: Taking taylor expansion of k in k 1546593450.621 * [misc]backup-simplify: Simplify 0 into 0 1546593450.621 * [misc]backup-simplify: Simplify 1 into 1 1546593450.622 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.622 * [misc]backup-simplify: Simplify (log 1) into 0 1546593450.622 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.622 * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 1546593450.622 * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 1546593450.622 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546593450.622 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546593450.622 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546593450.622 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593450.622 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.622 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.622 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593450.622 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.622 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.622 * [misc]taylor: Taking taylor expansion of k in k 1546593450.622 * [misc]backup-simplify: Simplify 0 into 0 1546593450.622 * [misc]backup-simplify: Simplify 1 into 1 1546593450.622 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546593450.622 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546593450.623 * [misc]taylor: Taking taylor expansion of 2 in k 1546593450.623 * [misc]backup-simplify: Simplify 2 into 2 1546593450.623 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546593450.623 * [misc]taylor: Taking taylor expansion of n in k 1546593450.623 * [misc]backup-simplify: Simplify n into n 1546593450.623 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.623 * [misc]backup-simplify: Simplify PI into PI 1546593450.623 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546593450.623 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546593450.623 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546593450.623 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593450.623 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.623 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593450.624 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546593450.624 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546593450.624 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of 1/4 in n 1546593450.624 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.624 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of k in n 1546593450.624 * [misc]backup-simplify: Simplify k into k 1546593450.624 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.624 * [misc]backup-simplify: Simplify (log (/ 1 k)) into (log (/ 1 k)) 1546593450.624 * [misc]backup-simplify: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 1546593450.624 * [misc]backup-simplify: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 1546593450.624 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593450.624 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593450.625 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.625 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.625 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593450.625 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.625 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.625 * [misc]taylor: Taking taylor expansion of k in n 1546593450.625 * [misc]backup-simplify: Simplify k into k 1546593450.625 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593450.625 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593450.625 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.625 * [misc]backup-simplify: Simplify 2 into 2 1546593450.625 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593450.625 * [misc]taylor: Taking taylor expansion of n in n 1546593450.625 * [misc]backup-simplify: Simplify 0 into 0 1546593450.625 * [misc]backup-simplify: Simplify 1 into 1 1546593450.625 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.625 * [misc]backup-simplify: Simplify PI into PI 1546593450.625 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593450.626 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593450.626 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593450.627 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593450.628 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.628 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593450.628 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593450.628 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593450.629 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.630 * [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)))) 1546593450.630 * [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))))) 1546593450.630 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546593450.630 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 1546593450.630 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 1546593450.630 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 1546593450.630 * [misc]taylor: Taking taylor expansion of 1/4 in n 1546593450.630 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.630 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of k in n 1546593450.631 * [misc]backup-simplify: Simplify k into k 1546593450.631 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.631 * [misc]backup-simplify: Simplify (log (/ 1 k)) into (log (/ 1 k)) 1546593450.631 * [misc]backup-simplify: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 1546593450.631 * [misc]backup-simplify: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 1546593450.631 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.631 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.631 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.631 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.631 * [misc]taylor: Taking taylor expansion of k in n 1546593450.631 * [misc]backup-simplify: Simplify k into k 1546593450.631 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.631 * [misc]backup-simplify: Simplify 2 into 2 1546593450.631 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546593450.631 * [misc]taylor: Taking taylor expansion of n in n 1546593450.631 * [misc]backup-simplify: Simplify 0 into 0 1546593450.631 * [misc]backup-simplify: Simplify 1 into 1 1546593450.631 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.631 * [misc]backup-simplify: Simplify PI into PI 1546593450.632 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546593450.632 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546593450.632 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546593450.633 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546593450.633 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.634 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546593450.634 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546593450.634 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546593450.634 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.635 * [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)))) 1546593450.635 * [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))))) 1546593450.636 * [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)) 1546593450.636 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) in k 1546593450.636 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546593450.636 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546593450.636 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546593450.636 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.636 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.636 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546593450.636 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.636 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.636 * [misc]taylor: Taking taylor expansion of k in k 1546593450.636 * [misc]backup-simplify: Simplify 0 into 0 1546593450.636 * [misc]backup-simplify: Simplify 1 into 1 1546593450.637 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546593450.637 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593450.637 * [misc]taylor: Taking taylor expansion of n in k 1546593450.637 * [misc]backup-simplify: Simplify n into n 1546593450.637 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593450.637 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593450.637 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593450.637 * [misc]taylor: Taking taylor expansion of 2 in k 1546593450.637 * [misc]backup-simplify: Simplify 2 into 2 1546593450.637 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.637 * [misc]backup-simplify: Simplify PI into PI 1546593450.637 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.638 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.638 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546593450.638 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.638 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593450.639 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.639 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546593450.640 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546593450.640 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1546593450.640 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1546593450.640 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1546593450.640 * [misc]taylor: Taking taylor expansion of 1/4 in k 1546593450.640 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.640 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k 1546593450.640 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.640 * [misc]taylor: Taking taylor expansion of k in k 1546593450.640 * [misc]backup-simplify: Simplify 0 into 0 1546593450.640 * [misc]backup-simplify: Simplify 1 into 1 1546593450.640 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.640 * [misc]backup-simplify: Simplify (log 1) into 0 1546593450.640 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.641 * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 1546593450.641 * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 1546593450.641 * [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)) 1546593450.642 * [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)) 1546593450.643 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546593450.644 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546593450.647 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593450.647 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546593450.647 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.647 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.648 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.649 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546593450.650 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.650 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593450.651 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 k) 1)))) 1) into 0 1546593450.652 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log (/ 1 k)))) into 0 1546593450.653 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.653 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1546593450.653 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.653 * [misc]backup-simplify: Simplify 0 into 0 1546593450.653 * [misc]backup-simplify: Simplify 0 into 0 1546593450.654 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546593450.656 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1546593450.656 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.656 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 1546593450.658 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.658 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546593450.659 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593450.662 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593450.662 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.662 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546593450.662 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593450.662 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593450.663 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546593450.664 * [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))))))) 1546593450.667 * [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))))) 1546593450.669 * [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))))) 1546593450.670 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593450.672 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546593450.677 * [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 1546593450.678 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546593450.678 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.678 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.679 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546593450.679 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593450.682 * [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 1546593450.682 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.683 * [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 1546593450.684 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log (/ 1 k))))) into 0 1546593450.685 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546593450.685 * [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 1546593450.685 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.685 * [misc]backup-simplify: Simplify 0 into 0 1546593450.685 * [misc]backup-simplify: Simplify 0 into 0 1546593450.685 * [misc]backup-simplify: Simplify 0 into 0 1546593450.686 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.688 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1546593450.688 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.688 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 1546593450.690 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546593450.690 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546593450.691 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593450.694 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1546593450.694 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.694 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546593450.694 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.694 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.695 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546593450.696 * [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))))) 1546593450.699 * [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)))))))) 1546593450.702 * [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)))))))) 1546593450.706 * [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))))) 1546593450.707 * [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))))) 1546593450.707 * [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 1546593450.707 * [misc]taylor: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of 1/4 in k 1546593450.707 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.707 * [misc]taylor: Taking taylor expansion of (log k) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of k in k 1546593450.707 * [misc]backup-simplify: Simplify 0 into 0 1546593450.707 * [misc]backup-simplify: Simplify 1 into 1 1546593450.707 * [misc]backup-simplify: Simplify (log 1) into 0 1546593450.707 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.707 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1546593450.707 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1546593450.707 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.707 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.707 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.707 * [misc]taylor: Taking taylor expansion of k in k 1546593450.707 * [misc]backup-simplify: Simplify 0 into 0 1546593450.707 * [misc]backup-simplify: Simplify 1 into 1 1546593450.707 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.708 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546593450.708 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546593450.708 * [misc]taylor: Taking taylor expansion of 2 in k 1546593450.708 * [misc]backup-simplify: Simplify 2 into 2 1546593450.708 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593450.708 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.708 * [misc]backup-simplify: Simplify PI into PI 1546593450.708 * [misc]taylor: Taking taylor expansion of n in k 1546593450.708 * [misc]backup-simplify: Simplify n into n 1546593450.708 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593450.708 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546593450.708 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546593450.708 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593450.708 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593450.708 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593450.708 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546593450.708 * [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)))) 1546593450.708 * [misc]taylor: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593450.708 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in n 1546593450.708 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in n 1546593450.708 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in n 1546593450.708 * [misc]taylor: Taking taylor expansion of 1/4 in n 1546593450.708 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.708 * [misc]taylor: Taking taylor expansion of (log k) in n 1546593450.708 * [misc]taylor: Taking taylor expansion of k in n 1546593450.708 * [misc]backup-simplify: Simplify k into k 1546593450.708 * [misc]backup-simplify: Simplify (log k) into (log k) 1546593450.709 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1546593450.709 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1546593450.709 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.709 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.709 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.709 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.709 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of k in n 1546593450.709 * [misc]backup-simplify: Simplify k into k 1546593450.709 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.709 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.709 * [misc]backup-simplify: Simplify 2 into 2 1546593450.709 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.709 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.709 * [misc]backup-simplify: Simplify PI into PI 1546593450.709 * [misc]taylor: Taking taylor expansion of n in n 1546593450.709 * [misc]backup-simplify: Simplify 0 into 0 1546593450.709 * [misc]backup-simplify: Simplify 1 into 1 1546593450.709 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.709 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.710 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.710 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593450.710 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593450.710 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593450.710 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.711 * [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))) 1546593450.711 * [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)))) 1546593450.711 * [misc]taylor: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546593450.711 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in n 1546593450.711 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in n 1546593450.711 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in n 1546593450.711 * [misc]taylor: Taking taylor expansion of 1/4 in n 1546593450.711 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.711 * [misc]taylor: Taking taylor expansion of (log k) in n 1546593450.711 * [misc]taylor: Taking taylor expansion of k in n 1546593450.711 * [misc]backup-simplify: Simplify k into k 1546593450.711 * [misc]backup-simplify: Simplify (log k) into (log k) 1546593450.711 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1546593450.712 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1546593450.712 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.712 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.712 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of k in n 1546593450.712 * [misc]backup-simplify: Simplify k into k 1546593450.712 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.712 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of 2 in n 1546593450.712 * [misc]backup-simplify: Simplify 2 into 2 1546593450.712 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.712 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.712 * [misc]backup-simplify: Simplify PI into PI 1546593450.712 * [misc]taylor: Taking taylor expansion of n in n 1546593450.712 * [misc]backup-simplify: Simplify 0 into 0 1546593450.712 * [misc]backup-simplify: Simplify 1 into 1 1546593450.712 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.712 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.713 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.713 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593450.713 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546593450.713 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546593450.713 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.714 * [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))) 1546593450.714 * [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)))) 1546593450.714 * [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)) 1546593450.715 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.715 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.715 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.715 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.715 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of k in k 1546593450.715 * [misc]backup-simplify: Simplify 0 into 0 1546593450.715 * [misc]backup-simplify: Simplify 1 into 1 1546593450.715 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.715 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of 2 in k 1546593450.715 * [misc]backup-simplify: Simplify 2 into 2 1546593450.715 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.715 * [misc]backup-simplify: Simplify PI into PI 1546593450.715 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546593450.715 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546593450.715 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593450.715 * [misc]taylor: Taking taylor expansion of n in k 1546593450.715 * [misc]backup-simplify: Simplify n into n 1546593450.716 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593450.716 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593450.716 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546593450.716 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546593450.716 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593450.716 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546593450.717 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546593450.717 * [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)))) 1546593450.717 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k 1546593450.717 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1546593450.717 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k 1546593450.717 * [misc]taylor: Taking taylor expansion of 1/4 in k 1546593450.717 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.717 * [misc]taylor: Taking taylor expansion of (log k) in k 1546593450.717 * [misc]taylor: Taking taylor expansion of k in k 1546593450.717 * [misc]backup-simplify: Simplify 0 into 0 1546593450.717 * [misc]backup-simplify: Simplify 1 into 1 1546593450.717 * [misc]backup-simplify: Simplify (log 1) into 0 1546593450.717 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.717 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1546593450.717 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1546593450.718 * [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)) 1546593450.718 * [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)) 1546593450.719 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593450.720 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546593450.722 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546593450.722 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593450.723 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593450.723 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.723 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.724 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.724 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546593450.726 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.727 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow k 1)))) 1) into 0 1546593450.727 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 1546593450.728 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.728 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546593450.729 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.729 * [misc]backup-simplify: Simplify 0 into 0 1546593450.729 * [misc]backup-simplify: Simplify 0 into 0 1546593450.731 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1546593450.731 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.731 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 1546593450.732 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.733 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (* 0 (pow k 1/4))) into 0 1546593450.733 * [misc]backup-simplify: Simplify 0 into 0 1546593450.735 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.736 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593450.740 * [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 1546593450.741 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.741 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593450.741 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.741 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.742 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.743 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546593450.745 * [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 1546593450.746 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow k 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow k 1)))) 2) into 0 1546593450.747 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 1546593450.748 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546593450.749 * [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 1546593450.749 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.749 * [misc]backup-simplify: Simplify 0 into 0 1546593450.749 * [misc]backup-simplify: Simplify 0 into 0 1546593450.749 * [misc]backup-simplify: Simplify 0 into 0 1546593450.753 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1546593450.754 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.754 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 1546593450.756 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546593450.757 * [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 1546593450.757 * [misc]backup-simplify: Simplify 0 into 0 1546593450.759 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.760 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546593450.769 * [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 1546593450.769 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.770 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546593450.770 * [misc]backup-simplify: Simplify (- 0) into 0 1546593450.770 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.770 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546593450.771 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546593450.775 * [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 1546593450.778 * [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 1546593450.778 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 1546593450.781 * [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 1546593450.782 * [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 1546593450.782 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.782 * [misc]backup-simplify: Simplify 0 into 0 1546593450.782 * [misc]backup-simplify: Simplify 0 into 0 1546593450.783 * [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)) 1546593450.783 * [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))) 1546593450.783 * [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 1546593450.784 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546593450.784 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 1546593450.784 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1546593450.784 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593450.784 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593450.784 * [misc]taylor: Taking taylor expansion of -1 in k 1546593450.784 * [misc]backup-simplify: Simplify -1 into -1 1546593450.784 * [misc]taylor: Taking taylor expansion of k in k 1546593450.784 * [misc]backup-simplify: Simplify 0 into 0 1546593450.784 * [misc]backup-simplify: Simplify 1 into 1 1546593450.784 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593450.784 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593450.785 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593450.785 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1546593450.785 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1546593450.785 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593450.786 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593450.787 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1546593450.788 * [misc]backup-simplify: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 1546593450.788 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.788 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.788 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of k in k 1546593450.788 * [misc]backup-simplify: Simplify 0 into 0 1546593450.788 * [misc]backup-simplify: Simplify 1 into 1 1546593450.788 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.788 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.788 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.788 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of -2 in k 1546593450.788 * [misc]backup-simplify: Simplify -2 into -2 1546593450.788 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546593450.788 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.789 * [misc]backup-simplify: Simplify PI into PI 1546593450.789 * [misc]taylor: Taking taylor expansion of n in k 1546593450.789 * [misc]backup-simplify: Simplify n into n 1546593450.789 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546593450.789 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546593450.789 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546593450.789 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593450.789 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593450.789 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546593450.789 * [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))) 1546593450.789 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593450.790 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 1546593450.790 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 1546593450.790 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546593450.790 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546593450.790 * [misc]taylor: Taking taylor expansion of -1 in n 1546593450.790 * [misc]backup-simplify: Simplify -1 into -1 1546593450.790 * [misc]taylor: Taking taylor expansion of k in n 1546593450.790 * [misc]backup-simplify: Simplify k into k 1546593450.790 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546593450.790 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546593450.790 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546593450.790 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546593450.790 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 1546593450.790 * [misc]backup-simplify: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 1546593450.790 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1546593450.791 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 1546593450.791 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.791 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.791 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of k in n 1546593450.791 * [misc]backup-simplify: Simplify k into k 1546593450.791 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.791 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.791 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.791 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of -2 in n 1546593450.791 * [misc]backup-simplify: Simplify -2 into -2 1546593450.791 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.791 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.791 * [misc]backup-simplify: Simplify PI into PI 1546593450.791 * [misc]taylor: Taking taylor expansion of n in n 1546593450.791 * [misc]backup-simplify: Simplify 0 into 0 1546593450.791 * [misc]backup-simplify: Simplify 1 into 1 1546593450.792 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.792 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593450.792 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593450.792 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593450.793 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593450.793 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.794 * [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))) 1546593450.794 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1546593450.794 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546593450.794 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 1546593450.794 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 1546593450.794 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546593450.795 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546593450.795 * [misc]taylor: Taking taylor expansion of -1 in n 1546593450.795 * [misc]backup-simplify: Simplify -1 into -1 1546593450.795 * [misc]taylor: Taking taylor expansion of k in n 1546593450.795 * [misc]backup-simplify: Simplify k into k 1546593450.795 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546593450.795 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546593450.795 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546593450.795 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546593450.795 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 1546593450.795 * [misc]backup-simplify: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 1546593450.795 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1546593450.796 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 1546593450.796 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.796 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.796 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of k in n 1546593450.796 * [misc]backup-simplify: Simplify k into k 1546593450.796 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546593450.796 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546593450.796 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.796 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of -2 in n 1546593450.796 * [misc]backup-simplify: Simplify -2 into -2 1546593450.796 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546593450.796 * [misc]taylor: Taking taylor expansion of PI in n 1546593450.796 * [misc]backup-simplify: Simplify PI into PI 1546593450.796 * [misc]taylor: Taking taylor expansion of n in n 1546593450.796 * [misc]backup-simplify: Simplify 0 into 0 1546593450.796 * [misc]backup-simplify: Simplify 1 into 1 1546593450.797 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546593450.797 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593450.797 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593450.797 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546593450.797 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546593450.798 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.799 * [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))) 1546593450.799 * [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)))) 1546593450.800 * [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))))) 1546593450.800 * [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 1546593450.800 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 1546593450.800 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 1546593450.800 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593450.800 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593450.800 * [misc]taylor: Taking taylor expansion of -1 in k 1546593450.800 * [misc]backup-simplify: Simplify -1 into -1 1546593450.800 * [misc]taylor: Taking taylor expansion of k in k 1546593450.800 * [misc]backup-simplify: Simplify 0 into 0 1546593450.800 * [misc]backup-simplify: Simplify 1 into 1 1546593450.801 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593450.801 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593450.801 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593450.801 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 1546593450.801 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1546593450.802 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593450.803 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593450.803 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1546593450.804 * [misc]backup-simplify: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 1546593450.804 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546593450.804 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546593450.804 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546593450.804 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546593450.804 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.804 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.804 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.804 * [misc]taylor: Taking taylor expansion of k in k 1546593450.804 * [misc]backup-simplify: Simplify 0 into 0 1546593450.804 * [misc]backup-simplify: Simplify 1 into 1 1546593450.804 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.805 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546593450.805 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546593450.805 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546593450.805 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546593450.805 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546593450.805 * [misc]taylor: Taking taylor expansion of -2 in k 1546593450.805 * [misc]backup-simplify: Simplify -2 into -2 1546593450.805 * [misc]taylor: Taking taylor expansion of PI in k 1546593450.805 * [misc]backup-simplify: Simplify PI into PI 1546593450.805 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546593450.806 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546593450.806 * [misc]taylor: Taking taylor expansion of (log n) in k 1546593450.806 * [misc]taylor: Taking taylor expansion of n in k 1546593450.806 * [misc]backup-simplify: Simplify n into n 1546593450.806 * [misc]backup-simplify: Simplify (log n) into (log n) 1546593450.806 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546593450.806 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546593450.806 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546593450.807 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546593450.807 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546593450.808 * [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)))) 1546593450.808 * [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)) 1546593450.809 * [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)) 1546593450.809 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546593450.810 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546593450.811 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546593450.811 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546593450.811 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546593450.811 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.812 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.812 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546593450.813 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.814 * [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 1546593450.814 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.814 * [misc]backup-simplify: Simplify 0 into 0 1546593450.814 * [misc]backup-simplify: Simplify 0 into 0 1546593450.814 * [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)))) 1546593450.815 * [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)))) 1546593450.816 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.816 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546593450.819 * [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 1546593450.819 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.820 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546593450.820 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546593450.820 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546593450.820 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546593450.822 * [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 1546593450.822 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546593450.822 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1546593450.823 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1546593450.823 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 1546593450.824 * [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 1546593450.824 * [misc]taylor: Taking taylor expansion of 0 in k 1546593450.824 * [misc]backup-simplify: Simplify 0 into 0 1546593450.824 * [misc]backup-simplify: Simplify 0 into 0 1546593450.824 * [misc]backup-simplify: Simplify 0 into 0 1546593450.824 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.825 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593450.825 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1546593450.827 * [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))) 1546593450.829 * [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)))))) 1546593450.830 * [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)))))) 1546593450.833 * [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))))))))) 1546593450.833 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) 1546593450.833 * [misc]backup-simplify: Simplify (sqrt (sqrt k)) into (pow k 1/4) 1546593450.833 * [misc]approximate: Taking taylor expansion of (pow k 1/4) in (k) around 0 1546593450.833 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k 1546593450.833 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1546593450.833 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k 1546593450.833 * [misc]taylor: Taking taylor expansion of 1/4 in k 1546593450.833 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.833 * [misc]taylor: Taking taylor expansion of (log k) in k 1546593450.833 * [misc]taylor: Taking taylor expansion of k in k 1546593450.833 * [misc]backup-simplify: Simplify 0 into 0 1546593450.833 * [misc]backup-simplify: Simplify 1 into 1 1546593450.833 * [misc]backup-simplify: Simplify (log 1) into 0 1546593450.833 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.833 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1546593450.833 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1546593450.833 * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k 1546593450.833 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k 1546593450.833 * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k 1546593450.833 * [misc]taylor: Taking taylor expansion of 1/4 in k 1546593450.833 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.833 * [misc]taylor: Taking taylor expansion of (log k) in k 1546593450.833 * [misc]taylor: Taking taylor expansion of k in k 1546593450.833 * [misc]backup-simplify: Simplify 0 into 0 1546593450.833 * [misc]backup-simplify: Simplify 1 into 1 1546593450.833 * [misc]backup-simplify: Simplify (log 1) into 0 1546593450.834 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.834 * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 1546593450.834 * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 1546593450.834 * [misc]backup-simplify: Simplify (pow k 1/4) into (pow k 1/4) 1546593450.835 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1546593450.835 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.836 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 1546593450.836 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.836 * [misc]backup-simplify: Simplify 0 into 0 1546593450.839 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1546593450.839 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.839 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 1546593450.841 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546593450.841 * [misc]backup-simplify: Simplify 0 into 0 1546593450.847 * [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 1546593450.848 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.848 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 1546593450.851 * [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 1546593450.851 * [misc]backup-simplify: Simplify 0 into 0 1546593450.863 * [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 1546593450.863 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.864 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 1546593450.869 * [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 1546593450.869 * [misc]backup-simplify: Simplify 0 into 0 1546593450.886 * [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 1546593450.886 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.887 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 1546593450.895 * [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 1546593450.895 * [misc]backup-simplify: Simplify 0 into 0 1546593450.923 * [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 1546593450.924 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) 1546593450.925 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 1546593450.938 * [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 1546593450.938 * [misc]backup-simplify: Simplify 0 into 0 1546593450.938 * [misc]backup-simplify: Simplify (pow k 1/4) into (pow k 1/4) 1546593450.938 * [misc]backup-simplify: Simplify (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) 1546593450.938 * [misc]approximate: Taking taylor expansion of (pow (/ 1 k) 1/4) in (k) around 0 1546593450.938 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1546593450.938 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1546593450.939 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1546593450.939 * [misc]taylor: Taking taylor expansion of 1/4 in k 1546593450.939 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.939 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k 1546593450.939 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.939 * [misc]taylor: Taking taylor expansion of k in k 1546593450.939 * [misc]backup-simplify: Simplify 0 into 0 1546593450.939 * [misc]backup-simplify: Simplify 1 into 1 1546593450.939 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.939 * [misc]backup-simplify: Simplify (log 1) into 0 1546593450.939 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.939 * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 1546593450.940 * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 1546593450.940 * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 1546593450.940 * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 1546593450.940 * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 1546593450.940 * [misc]taylor: Taking taylor expansion of 1/4 in k 1546593450.940 * [misc]backup-simplify: Simplify 1/4 into 1/4 1546593450.940 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k 1546593450.940 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546593450.940 * [misc]taylor: Taking taylor expansion of k in k 1546593450.940 * [misc]backup-simplify: Simplify 0 into 0 1546593450.940 * [misc]backup-simplify: Simplify 1 into 1 1546593450.940 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546593450.940 * [misc]backup-simplify: Simplify (log 1) into 0 1546593450.940 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.940 * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 1546593450.941 * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 1546593450.941 * [misc]backup-simplify: Simplify (pow k -1/4) into (pow k -1/4) 1546593450.941 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546593450.943 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1546593450.944 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.944 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 1546593450.945 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 1546593450.945 * [misc]backup-simplify: Simplify 0 into 0 1546593450.945 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.950 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1546593450.950 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.950 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 1546593450.952 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1546593450.952 * [misc]backup-simplify: Simplify 0 into 0 1546593450.953 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.959 * [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 1546593450.960 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.960 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 1546593450.963 * [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 1546593450.963 * [misc]backup-simplify: Simplify 0 into 0 1546593450.964 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.975 * [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 1546593450.975 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593450.976 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 1546593450.981 * [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 1546593450.982 * [misc]backup-simplify: Simplify 0 into 0 1546593450.982 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593450.999 * [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 1546593450.999 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593451.000 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 1546593451.008 * [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 1546593451.008 * [misc]backup-simplify: Simplify 0 into 0 1546593451.009 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593451.036 * [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 1546593451.036 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 1546593451.037 * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 1546593451.050 * [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 1546593451.050 * [misc]backup-simplify: Simplify 0 into 0 1546593451.050 * [misc]backup-simplify: Simplify (pow (/ 1 k) -1/4) into (pow (/ 1 k) -1/4) 1546593451.050 * [misc]backup-simplify: Simplify (sqrt (sqrt (/ 1 (- k)))) into (sqrt (sqrt (/ -1 k))) 1546593451.050 * [misc]approximate: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in (k) around 0 1546593451.050 * [misc]taylor: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k 1546593451.050 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593451.050 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593451.050 * [misc]taylor: Taking taylor expansion of -1 in k 1546593451.050 * [misc]backup-simplify: Simplify -1 into -1 1546593451.050 * [misc]taylor: Taking taylor expansion of k in k 1546593451.050 * [misc]backup-simplify: Simplify 0 into 0 1546593451.050 * [misc]backup-simplify: Simplify 1 into 1 1546593451.050 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593451.051 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593451.051 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593451.051 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1546593451.052 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593451.053 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593451.054 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 1546593451.054 * [misc]taylor: Taking taylor expansion of (sqrt (sqrt (/ -1 k))) in k 1546593451.054 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546593451.054 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546593451.054 * [misc]taylor: Taking taylor expansion of -1 in k 1546593451.054 * [misc]backup-simplify: Simplify -1 into -1 1546593451.054 * [misc]taylor: Taking taylor expansion of k in k 1546593451.054 * [misc]backup-simplify: Simplify 0 into 0 1546593451.054 * [misc]backup-simplify: Simplify 1 into 1 1546593451.054 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546593451.054 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546593451.055 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546593451.055 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1546593451.055 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546593451.056 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546593451.057 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 1546593451.057 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) 1546593451.057 * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt +nan.0)) into (/ +nan.0 (sqrt +nan.0)) 1546593451.058 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546593451.059 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546593451.060 * [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))) 1546593451.063 * [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))) 1546593451.066 * [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))))))))) 1546593451.066 * * * [misc]progress: simplifying candidates 1546593451.066 * * * * [misc]progress: [ 1 / 113 ] simplifiying candidate # 1546593451.066 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546593451.066 * * [misc]simplify: iters left: 6 (11 enodes) 1546593451.069 * * [misc]simplify: iters left: 5 (21 enodes) 1546593451.076 * * [misc]simplify: iters left: 4 (47 enodes) 1546593451.087 * * [misc]simplify: iters left: 3 (109 enodes) 1546593451.118 * * [misc]simplify: iters left: 2 (300 enodes) 1546593451.279 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546593451.280 * [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)))) 1546593451.280 * * * * [misc]progress: [ 2 / 113 ] simplifiying candidate # 1546593451.280 * * * * [misc]progress: [ 3 / 113 ] simplifiying candidate # 1546593451.282 * [enter]simplify: Simplifying (* PI (* n 2)) 1546593451.282 * * [misc]simplify: iters left: 4 (5 enodes) 1546593451.283 * * [misc]simplify: iters left: 3 (9 enodes) 1546593451.284 * * [misc]simplify: iters left: 2 (15 enodes) 1546593451.286 * * [misc]simplify: iters left: 1 (17 enodes) 1546593451.288 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546593451.288 * [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)))) 1546593451.288 * * * * [misc]progress: [ 4 / 113 ] simplifiying candidate # 1546593451.289 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546593451.289 * * [misc]simplify: iters left: 5 (8 enodes) 1546593451.290 * * [misc]simplify: iters left: 4 (12 enodes) 1546593451.292 * * [misc]simplify: iters left: 3 (18 enodes) 1546593451.294 * * [misc]simplify: iters left: 2 (20 enodes) 1546593451.296 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546593451.297 * [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)))) 1546593451.297 * * * * [misc]progress: [ 5 / 113 ] simplifiying candidate # 1546593451.297 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546593451.297 * * [misc]simplify: iters left: 5 (6 enodes) 1546593451.298 * * [misc]simplify: iters left: 4 (8 enodes) 1546593451.299 * * [misc]simplify: iters left: 3 (11 enodes) 1546593451.300 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546593451.300 * [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)))) 1546593451.300 * * * * [misc]progress: [ 6 / 113 ] simplifiying candidate # 1546593451.300 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546593451.301 * * [misc]simplify: iters left: 5 (6 enodes) 1546593451.301 * * [misc]simplify: iters left: 4 (8 enodes) 1546593451.302 * * [misc]simplify: iters left: 3 (11 enodes) 1546593451.304 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546593451.304 * [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)))) 1546593451.304 * * * * [misc]progress: [ 7 / 113 ] simplifiying candidate # 1546593451.304 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546593451.304 * * [misc]simplify: iters left: 4 (5 enodes) 1546593451.305 * * [misc]simplify: iters left: 3 (7 enodes) 1546593451.306 * * [misc]simplify: iters left: 2 (10 enodes) 1546593451.307 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546593451.307 * [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)))) 1546593451.307 * * * * [misc]progress: [ 8 / 113 ] simplifiying candidate # 1546593451.307 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546593451.307 * * [misc]simplify: iters left: 5 (9 enodes) 1546593451.309 * * [misc]simplify: iters left: 4 (15 enodes) 1546593451.311 * * [misc]simplify: iters left: 3 (21 enodes) 1546593451.314 * * [misc]simplify: iters left: 2 (22 enodes) 1546593451.317 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546593451.317 * [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)))) 1546593451.317 * * * * [misc]progress: [ 9 / 113 ] simplifiying candidate # 1546593451.317 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546593451.317 * * [misc]simplify: iters left: 5 (9 enodes) 1546593451.319 * * [misc]simplify: iters left: 4 (15 enodes) 1546593451.321 * * [misc]simplify: iters left: 3 (21 enodes) 1546593451.323 * * [misc]simplify: iters left: 2 (22 enodes) 1546593451.326 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546593451.326 * [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)))) 1546593451.326 * * * * [misc]progress: [ 10 / 113 ] simplifiying candidate # 1546593451.326 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546593451.326 * * [misc]simplify: iters left: 5 (7 enodes) 1546593451.327 * * [misc]simplify: iters left: 4 (9 enodes) 1546593451.329 * * [misc]simplify: iters left: 3 (12 enodes) 1546593451.330 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546593451.330 * [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)))) 1546593451.330 * * * * [misc]progress: [ 11 / 113 ] simplifiying candidate # 1546593451.330 * * * * [misc]progress: [ 12 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 13 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 14 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 15 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 16 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 17 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 18 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 19 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 20 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 21 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 22 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 23 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 24 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 25 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 26 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 27 / 113 ] simplifiying candidate # 1546593451.331 * * * * [misc]progress: [ 28 / 113 ] simplifiying candidate # 1546593451.331 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt (sqrt k)))) 1546593451.331 * * [misc]simplify: iters left: 6 (15 enodes) 1546593451.334 * * [misc]simplify: iters left: 5 (27 enodes) 1546593451.341 * * [misc]simplify: iters left: 4 (54 enodes) 1546593451.361 * * [misc]simplify: iters left: 3 (138 enodes) 1546593451.409 * * [misc]simplify: iters left: 2 (489 enodes) 1546593451.923 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt (sqrt k)))) 1546593451.924 * [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)))) 1546593451.924 * * * * [misc]progress: [ 29 / 113 ] simplifiying candidate # 1546593451.924 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt (sqrt k)))) 1546593451.924 * * [misc]simplify: iters left: 6 (15 enodes) 1546593451.926 * * [misc]simplify: iters left: 5 (27 enodes) 1546593451.930 * * [misc]simplify: iters left: 4 (54 enodes) 1546593451.941 * * [misc]simplify: iters left: 3 (138 enodes) 1546593451.993 * * [misc]simplify: iters left: 2 (489 enodes) 1546593452.532 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt (sqrt k)))) 1546593452.532 * [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)))) 1546593452.533 * * * * [misc]progress: [ 30 / 113 ] simplifiying candidate # 1546593452.533 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt (sqrt k)))) 1546593452.533 * * [misc]simplify: iters left: 6 (15 enodes) 1546593452.538 * * [misc]simplify: iters left: 5 (25 enodes) 1546593452.545 * * [misc]simplify: iters left: 4 (43 enodes) 1546593452.558 * * [misc]simplify: iters left: 3 (72 enodes) 1546593452.573 * * [misc]simplify: iters left: 2 (209 enodes) 1546593452.730 * [exit]simplify: Simplified to (- (* (log (* (* PI 2) n)) (- 1/2 (/ k 2))) (log (sqrt (sqrt k)))) 1546593452.730 * [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)))) 1546593452.730 * * * * [misc]progress: [ 31 / 113 ] simplifiying candidate # 1546593452.730 * * * * [misc]progress: [ 32 / 113 ] simplifiying candidate # 1546593452.730 * * * * [misc]progress: [ 33 / 113 ] simplifiying candidate # 1546593452.731 * [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)))) 1546593452.731 * * [misc]simplify: iters left: 6 (17 enodes) 1546593452.734 * * [misc]simplify: iters left: 5 (32 enodes) 1546593452.739 * * [misc]simplify: iters left: 4 (70 enodes) 1546593452.750 * * [misc]simplify: iters left: 3 (122 enodes) 1546593452.771 * * [misc]simplify: iters left: 2 (175 enodes) 1546593452.804 * * [misc]simplify: iters left: 1 (192 enodes) 1546593452.827 * [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))))) 1546593452.827 * [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)))) 1546593452.827 * * * * [misc]progress: [ 34 / 113 ] simplifiying candidate # 1546593452.827 * * * * [misc]progress: [ 35 / 113 ] simplifiying candidate # 1546593452.827 * * * * [misc]progress: [ 36 / 113 ] simplifiying candidate # 1546593452.828 * * * * [misc]progress: [ 37 / 113 ] simplifiying candidate # 1546593452.828 * * * * [misc]progress: [ 38 / 113 ] simplifiying candidate # 1546593452.828 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1546593452.828 * * [misc]simplify: iters left: 6 (13 enodes) 1546593452.832 * * [misc]simplify: iters left: 5 (20 enodes) 1546593452.838 * * [misc]simplify: iters left: 4 (26 enodes) 1546593452.845 * * [misc]simplify: iters left: 3 (28 enodes) 1546593452.852 * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) 1546593452.852 * [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)))) 1546593452.852 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt (sqrt k)))) 1546593452.853 * * [misc]simplify: iters left: 6 (13 enodes) 1546593452.857 * * [misc]simplify: iters left: 5 (19 enodes) 1546593452.864 * * [misc]simplify: iters left: 4 (25 enodes) 1546593452.870 * * [misc]simplify: iters left: 3 (26 enodes) 1546593452.877 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt (sqrt k)))) 1546593452.877 * [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)))) 1546593452.877 * * * * [misc]progress: [ 39 / 113 ] simplifiying candidate # 1546593452.878 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546593452.878 * * [misc]simplify: iters left: 6 (13 enodes) 1546593452.882 * * [misc]simplify: iters left: 5 (19 enodes) 1546593452.885 * * [misc]simplify: iters left: 4 (25 enodes) 1546593452.888 * * [misc]simplify: iters left: 3 (26 enodes) 1546593452.892 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (fabs (cbrt (sqrt k)))) 1546593452.892 * [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)))) 1546593452.892 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (cbrt (sqrt k)))) 1546593452.892 * * [misc]simplify: iters left: 6 (13 enodes) 1546593452.894 * * [misc]simplify: iters left: 5 (19 enodes) 1546593452.897 * * [misc]simplify: iters left: 4 (25 enodes) 1546593452.900 * * [misc]simplify: iters left: 3 (26 enodes) 1546593452.903 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (cbrt (sqrt k)))) 1546593452.903 * [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)))) 1546593452.903 * * * * [misc]progress: [ 40 / 113 ] simplifiying candidate # 1546593452.903 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt (sqrt k)))) 1546593452.903 * * [misc]simplify: iters left: 6 (12 enodes) 1546593452.905 * * [misc]simplify: iters left: 5 (17 enodes) 1546593452.907 * * [misc]simplify: iters left: 4 (23 enodes) 1546593452.910 * * [misc]simplify: iters left: 3 (24 enodes) 1546593452.913 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) 1546593452.913 * [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)))) 1546593452.913 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593452.913 * * [misc]simplify: iters left: 6 (13 enodes) 1546593452.915 * * [misc]simplify: iters left: 5 (19 enodes) 1546593452.918 * * [misc]simplify: iters left: 4 (25 enodes) 1546593452.921 * * [misc]simplify: iters left: 3 (26 enodes) 1546593452.925 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593452.925 * [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)))) 1546593452.925 * * * * [misc]progress: [ 41 / 113 ] simplifiying candidate # 1546593452.926 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt 1)) 1546593452.926 * * [misc]simplify: iters left: 6 (10 enodes) 1546593452.930 * * [misc]simplify: iters left: 5 (17 enodes) 1546593452.934 * * [misc]simplify: iters left: 4 (23 enodes) 1546593452.939 * * [misc]simplify: iters left: 3 (24 enodes) 1546593452.945 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546593452.945 * [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)))) 1546593452.945 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546593452.945 * * [misc]simplify: iters left: 6 (12 enodes) 1546593452.949 * * [misc]simplify: iters left: 5 (18 enodes) 1546593452.954 * * [misc]simplify: iters left: 4 (24 enodes) 1546593452.961 * * [misc]simplify: iters left: 3 (25 enodes) 1546593452.967 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546593452.967 * [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)))) 1546593452.967 * * * * [misc]progress: [ 42 / 113 ] simplifiying candidate # 1546593452.967 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt (sqrt k)))) 1546593452.968 * * [misc]simplify: iters left: 6 (12 enodes) 1546593452.972 * * [misc]simplify: iters left: 5 (17 enodes) 1546593452.978 * * [misc]simplify: iters left: 4 (23 enodes) 1546593452.981 * * [misc]simplify: iters left: 3 (24 enodes) 1546593452.984 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) 1546593452.984 * [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)))) 1546593452.985 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593452.985 * * [misc]simplify: iters left: 6 (13 enodes) 1546593452.987 * * [misc]simplify: iters left: 5 (19 enodes) 1546593452.989 * * [misc]simplify: iters left: 4 (25 enodes) 1546593452.993 * * [misc]simplify: iters left: 3 (26 enodes) 1546593452.996 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593452.996 * [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)))) 1546593452.996 * * * * [misc]progress: [ 43 / 113 ] simplifiying candidate # 1546593452.996 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546593452.996 * * [misc]simplify: iters left: 6 (9 enodes) 1546593452.998 * * [misc]simplify: iters left: 5 (16 enodes) 1546593453.000 * * [misc]simplify: iters left: 4 (24 enodes) 1546593453.004 * * [misc]simplify: iters left: 3 (26 enodes) 1546593453.006 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546593453.006 * [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)))) 1546593453.007 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546593453.007 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.008 * * [misc]simplify: iters left: 5 (18 enodes) 1546593453.011 * * [misc]simplify: iters left: 4 (24 enodes) 1546593453.014 * * [misc]simplify: iters left: 3 (25 enodes) 1546593453.017 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546593453.017 * [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)))) 1546593453.018 * * * * [misc]progress: [ 44 / 113 ] simplifiying candidate # 1546593453.018 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1546593453.018 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.020 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.023 * * [misc]simplify: iters left: 4 (26 enodes) 1546593453.026 * * [misc]simplify: iters left: 3 (28 enodes) 1546593453.032 * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) 1546593453.032 * [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)))) 1546593453.032 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt (sqrt k)))) 1546593453.033 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.037 * * [misc]simplify: iters left: 5 (19 enodes) 1546593453.042 * * [misc]simplify: iters left: 4 (25 enodes) 1546593453.049 * * [misc]simplify: iters left: 3 (26 enodes) 1546593453.056 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt (sqrt k)))) 1546593453.056 * [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)))) 1546593453.056 * * * * [misc]progress: [ 45 / 113 ] simplifiying candidate # 1546593453.056 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546593453.057 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.061 * * [misc]simplify: iters left: 5 (19 enodes) 1546593453.066 * * [misc]simplify: iters left: 4 (25 enodes) 1546593453.073 * * [misc]simplify: iters left: 3 (26 enodes) 1546593453.080 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (fabs (cbrt (sqrt k)))) 1546593453.081 * [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)))) 1546593453.081 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (cbrt (sqrt k)))) 1546593453.081 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.085 * * [misc]simplify: iters left: 5 (19 enodes) 1546593453.090 * * [misc]simplify: iters left: 4 (25 enodes) 1546593453.094 * * [misc]simplify: iters left: 3 (26 enodes) 1546593453.097 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (cbrt (sqrt k)))) 1546593453.097 * [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)))) 1546593453.097 * * * * [misc]progress: [ 46 / 113 ] simplifiying candidate # 1546593453.097 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt (sqrt k)))) 1546593453.097 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.099 * * [misc]simplify: iters left: 5 (17 enodes) 1546593453.101 * * [misc]simplify: iters left: 4 (23 enodes) 1546593453.104 * * [misc]simplify: iters left: 3 (24 enodes) 1546593453.107 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) 1546593453.107 * [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)))) 1546593453.107 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.107 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.109 * * [misc]simplify: iters left: 5 (19 enodes) 1546593453.112 * * [misc]simplify: iters left: 4 (25 enodes) 1546593453.115 * * [misc]simplify: iters left: 3 (26 enodes) 1546593453.118 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.118 * [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)))) 1546593453.118 * * * * [misc]progress: [ 47 / 113 ] simplifiying candidate # 1546593453.119 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt 1)) 1546593453.119 * * [misc]simplify: iters left: 6 (10 enodes) 1546593453.121 * * [misc]simplify: iters left: 5 (17 enodes) 1546593453.123 * * [misc]simplify: iters left: 4 (23 enodes) 1546593453.126 * * [misc]simplify: iters left: 3 (24 enodes) 1546593453.128 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546593453.128 * [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)))) 1546593453.129 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546593453.129 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.130 * * [misc]simplify: iters left: 5 (18 enodes) 1546593453.133 * * [misc]simplify: iters left: 4 (24 enodes) 1546593453.136 * * [misc]simplify: iters left: 3 (25 enodes) 1546593453.139 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546593453.139 * [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)))) 1546593453.139 * * * * [misc]progress: [ 48 / 113 ] simplifiying candidate # 1546593453.139 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt (sqrt k)))) 1546593453.139 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.141 * * [misc]simplify: iters left: 5 (17 enodes) 1546593453.143 * * [misc]simplify: iters left: 4 (23 enodes) 1546593453.146 * * [misc]simplify: iters left: 3 (24 enodes) 1546593453.149 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt (sqrt k)))) 1546593453.149 * [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)))) 1546593453.149 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.149 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.151 * * [misc]simplify: iters left: 5 (19 enodes) 1546593453.154 * * [misc]simplify: iters left: 4 (25 enodes) 1546593453.157 * * [misc]simplify: iters left: 3 (26 enodes) 1546593453.161 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.161 * [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)))) 1546593453.161 * * * * [misc]progress: [ 49 / 113 ] simplifiying candidate # 1546593453.161 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546593453.161 * * [misc]simplify: iters left: 6 (9 enodes) 1546593453.162 * * [misc]simplify: iters left: 5 (16 enodes) 1546593453.165 * * [misc]simplify: iters left: 4 (24 enodes) 1546593453.168 * * [misc]simplify: iters left: 3 (26 enodes) 1546593453.170 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546593453.170 * [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)))) 1546593453.170 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546593453.170 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.172 * * [misc]simplify: iters left: 5 (18 enodes) 1546593453.175 * * [misc]simplify: iters left: 4 (24 enodes) 1546593453.178 * * [misc]simplify: iters left: 3 (25 enodes) 1546593453.183 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546593453.183 * [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)))) 1546593453.184 * * * * [misc]progress: [ 50 / 113 ] simplifiying candidate # 1546593453.184 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1546593453.184 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.187 * * [misc]simplify: iters left: 5 (16 enodes) 1546593453.192 * * [misc]simplify: iters left: 4 (19 enodes) 1546593453.197 * [exit]simplify: Simplified to (/ (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) 1546593453.197 * [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)))) 1546593453.198 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) 1546593453.198 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.201 * * [misc]simplify: iters left: 5 (15 enodes) 1546593453.206 * * [misc]simplify: iters left: 4 (18 enodes) 1546593453.211 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) 1546593453.211 * [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)))) 1546593453.211 * * * * [misc]progress: [ 51 / 113 ] simplifiying candidate # 1546593453.211 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546593453.211 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.215 * * [misc]simplify: iters left: 5 (15 enodes) 1546593453.219 * * [misc]simplify: iters left: 4 (18 enodes) 1546593453.224 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (fabs (cbrt (sqrt k)))) 1546593453.224 * [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)))) 1546593453.224 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k)))) 1546593453.224 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.228 * * [misc]simplify: iters left: 5 (15 enodes) 1546593453.232 * * [misc]simplify: iters left: 4 (18 enodes) 1546593453.238 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k)))) 1546593453.238 * [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)))) 1546593453.238 * * * * [misc]progress: [ 52 / 113 ] simplifiying candidate # 1546593453.239 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.239 * * [misc]simplify: iters left: 6 (11 enodes) 1546593453.242 * * [misc]simplify: iters left: 5 (13 enodes) 1546593453.246 * * [misc]simplify: iters left: 4 (16 enodes) 1546593453.250 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.250 * [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)))) 1546593453.251 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.251 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.254 * * [misc]simplify: iters left: 5 (15 enodes) 1546593453.259 * * [misc]simplify: iters left: 4 (18 enodes) 1546593453.264 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.264 * [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)))) 1546593453.264 * * * * [misc]progress: [ 53 / 113 ] simplifiying candidate # 1546593453.264 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt 1)) 1546593453.264 * * [misc]simplify: iters left: 6 (10 enodes) 1546593453.268 * * [misc]simplify: iters left: 5 (14 enodes) 1546593453.271 * * [misc]simplify: iters left: 4 (17 enodes) 1546593453.274 * * [misc]simplify: iters left: 3 (19 enodes) 1546593453.276 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546593453.276 * [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)))) 1546593453.276 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593453.276 * * [misc]simplify: iters left: 6 (11 enodes) 1546593453.278 * * [misc]simplify: iters left: 5 (14 enodes) 1546593453.280 * * [misc]simplify: iters left: 4 (17 enodes) 1546593453.283 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593453.283 * [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)))) 1546593453.283 * * * * [misc]progress: [ 54 / 113 ] simplifiying candidate # 1546593453.283 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.283 * * [misc]simplify: iters left: 6 (11 enodes) 1546593453.285 * * [misc]simplify: iters left: 5 (13 enodes) 1546593453.286 * * [misc]simplify: iters left: 4 (16 enodes) 1546593453.289 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.289 * [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)))) 1546593453.289 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.289 * * [misc]simplify: iters left: 6 (12 enodes) 1546593453.291 * * [misc]simplify: iters left: 5 (15 enodes) 1546593453.293 * * [misc]simplify: iters left: 4 (18 enodes) 1546593453.296 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.296 * [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)))) 1546593453.296 * * * * [misc]progress: [ 55 / 113 ] simplifiying candidate # 1546593453.296 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1546593453.296 * * [misc]simplify: iters left: 6 (9 enodes) 1546593453.297 * * [misc]simplify: iters left: 5 (13 enodes) 1546593453.300 * * [misc]simplify: iters left: 4 (18 enodes) 1546593453.304 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546593453.304 * [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)))) 1546593453.304 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593453.304 * * [misc]simplify: iters left: 6 (11 enodes) 1546593453.307 * * [misc]simplify: iters left: 5 (14 enodes) 1546593453.311 * * [misc]simplify: iters left: 4 (17 enodes) 1546593453.316 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593453.316 * [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)))) 1546593453.316 * * * * [misc]progress: [ 56 / 113 ] simplifiying candidate # 1546593453.316 * [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))))) 1546593453.317 * * [misc]simplify: iters left: 6 (17 enodes) 1546593453.322 * * [misc]simplify: iters left: 5 (29 enodes) 1546593453.330 * * [misc]simplify: iters left: 4 (47 enodes) 1546593453.343 * * [misc]simplify: iters left: 3 (51 enodes) 1546593453.356 * * [misc]simplify: iters left: 2 (54 enodes) 1546593453.370 * [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))))) 1546593453.370 * [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)))) 1546593453.371 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) 1546593453.371 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.373 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.376 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.380 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.384 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) 1546593453.385 * [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)))) 1546593453.385 * * * * [misc]progress: [ 57 / 113 ] simplifiying candidate # 1546593453.385 * [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))))) 1546593453.385 * * [misc]simplify: iters left: 6 (17 enodes) 1546593453.387 * * [misc]simplify: iters left: 5 (26 enodes) 1546593453.391 * * [misc]simplify: iters left: 4 (37 enodes) 1546593453.397 * * [misc]simplify: iters left: 3 (40 enodes) 1546593453.405 * [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))))) 1546593453.406 * [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)))) 1546593453.406 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k)))) 1546593453.406 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.409 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.412 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.416 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.419 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k)))) 1546593453.420 * [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)))) 1546593453.420 * * * * [misc]progress: [ 58 / 113 ] simplifiying candidate # 1546593453.420 * [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)))) 1546593453.420 * * [misc]simplify: iters left: 6 (16 enodes) 1546593453.422 * * [misc]simplify: iters left: 5 (24 enodes) 1546593453.426 * * [misc]simplify: iters left: 4 (35 enodes) 1546593453.430 * * [misc]simplify: iters left: 3 (37 enodes) 1546593453.435 * [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)))))) 1546593453.435 * [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)))) 1546593453.435 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.435 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.437 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.441 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.449 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.457 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.457 * [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)))) 1546593453.457 * * * * [misc]progress: [ 59 / 113 ] simplifiying candidate # 1546593453.458 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt 1)) 1546593453.458 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.463 * * [misc]simplify: iters left: 5 (25 enodes) 1546593453.467 * * [misc]simplify: iters left: 4 (36 enodes) 1546593453.471 * * [misc]simplify: iters left: 3 (41 enodes) 1546593453.476 * * [misc]simplify: iters left: 2 (56 enodes) 1546593453.482 * * [misc]simplify: iters left: 1 (57 enodes) 1546593453.488 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593453.488 * [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)))) 1546593453.488 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593453.489 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.491 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.493 * * [misc]simplify: iters left: 4 (29 enodes) 1546593453.497 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.502 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593453.502 * [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)))) 1546593453.502 * * * * [misc]progress: [ 60 / 113 ] simplifiying candidate # 1546593453.503 * [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)))) 1546593453.503 * * [misc]simplify: iters left: 6 (16 enodes) 1546593453.509 * * [misc]simplify: iters left: 5 (24 enodes) 1546593453.515 * * [misc]simplify: iters left: 4 (35 enodes) 1546593453.525 * * [misc]simplify: iters left: 3 (37 enodes) 1546593453.535 * [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)))))) 1546593453.535 * [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)))) 1546593453.535 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.535 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.539 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.546 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.553 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.562 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.562 * [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)))) 1546593453.562 * * * * [misc]progress: [ 61 / 113 ] simplifiying candidate # 1546593453.562 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1546593453.562 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.567 * * [misc]simplify: iters left: 5 (24 enodes) 1546593453.574 * * [misc]simplify: iters left: 4 (39 enodes) 1546593453.584 * * [misc]simplify: iters left: 3 (54 enodes) 1546593453.592 * * [misc]simplify: iters left: 2 (80 enodes) 1546593453.602 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1546593453.602 * [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)))) 1546593453.603 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593453.603 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.605 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.608 * * [misc]simplify: iters left: 4 (29 enodes) 1546593453.612 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.616 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593453.616 * [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)))) 1546593453.616 * * * * [misc]progress: [ 62 / 113 ] simplifiying candidate # 1546593453.617 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1546593453.617 * * [misc]simplify: iters left: 6 (16 enodes) 1546593453.622 * * [misc]simplify: iters left: 5 (24 enodes) 1546593453.629 * * [misc]simplify: iters left: 4 (33 enodes) 1546593453.638 * * [misc]simplify: iters left: 3 (34 enodes) 1546593453.647 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1546593453.647 * [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)))) 1546593453.647 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) 1546593453.647 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.652 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.658 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.666 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.674 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt (sqrt k)))) 1546593453.674 * [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)))) 1546593453.674 * * * * [misc]progress: [ 63 / 113 ] simplifiying candidate # 1546593453.675 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546593453.675 * * [misc]simplify: iters left: 6 (16 enodes) 1546593453.680 * * [misc]simplify: iters left: 5 (23 enodes) 1546593453.686 * * [misc]simplify: iters left: 4 (32 enodes) 1546593453.694 * * [misc]simplify: iters left: 3 (34 enodes) 1546593453.703 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (fabs (cbrt (sqrt k)))) 1546593453.703 * [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)))) 1546593453.703 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k)))) 1546593453.704 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.708 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.711 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.714 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.718 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt (sqrt k)))) 1546593453.718 * [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)))) 1546593453.718 * * * * [misc]progress: [ 64 / 113 ] simplifiying candidate # 1546593453.718 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.719 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.721 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.724 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.729 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.737 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.738 * [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)))) 1546593453.738 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.738 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.742 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.748 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.756 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.764 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.764 * [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)))) 1546593453.764 * * * * [misc]progress: [ 65 / 113 ] simplifiying candidate # 1546593453.764 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt 1)) 1546593453.764 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.769 * * [misc]simplify: iters left: 5 (22 enodes) 1546593453.775 * * [misc]simplify: iters left: 4 (31 enodes) 1546593453.783 * * [misc]simplify: iters left: 3 (35 enodes) 1546593453.792 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1546593453.792 * [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)))) 1546593453.792 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593453.792 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.796 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.799 * * [misc]simplify: iters left: 4 (29 enodes) 1546593453.802 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.806 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593453.806 * [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)))) 1546593453.806 * * * * [misc]progress: [ 66 / 113 ] simplifiying candidate # 1546593453.806 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.807 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.809 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.812 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.816 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.820 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.820 * [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)))) 1546593453.820 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.820 * * [misc]simplify: iters left: 6 (15 enodes) 1546593453.822 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.826 * * [misc]simplify: iters left: 4 (30 enodes) 1546593453.829 * * [misc]simplify: iters left: 3 (31 enodes) 1546593453.833 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt (sqrt k)))) 1546593453.833 * [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)))) 1546593453.833 * * * * [misc]progress: [ 67 / 113 ] simplifiying candidate # 1546593453.834 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1546593453.834 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.836 * * [misc]simplify: iters left: 5 (21 enodes) 1546593453.840 * * [misc]simplify: iters left: 4 (32 enodes) 1546593453.848 * * [misc]simplify: iters left: 3 (33 enodes) 1546593453.855 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1546593453.855 * [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)))) 1546593453.856 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593453.856 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.860 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.866 * * [misc]simplify: iters left: 4 (29 enodes) 1546593453.874 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.878 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546593453.878 * [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)))) 1546593453.878 * * * * [misc]progress: [ 68 / 113 ] simplifiying candidate # 1546593453.879 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1546593453.879 * * [misc]simplify: iters left: 6 (7 enodes) 1546593453.880 * * [misc]simplify: iters left: 5 (11 enodes) 1546593453.881 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) 1546593453.881 * [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)))) 1546593453.881 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) 1546593453.881 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.884 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.886 * * [misc]simplify: iters left: 4 (29 enodes) 1546593453.890 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.894 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt (sqrt k)))) 1546593453.894 * [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)))) 1546593453.894 * * * * [misc]progress: [ 69 / 113 ] simplifiying candidate # 1546593453.895 * [enter]simplify: Simplifying (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1546593453.895 * * [misc]simplify: iters left: 6 (7 enodes) 1546593453.896 * * [misc]simplify: iters left: 5 (10 enodes) 1546593453.897 * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (sqrt k)))) 1546593453.897 * [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)))) 1546593453.897 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k)))) 1546593453.897 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.899 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.902 * * [misc]simplify: iters left: 4 (29 enodes) 1546593453.909 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.917 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (cbrt (sqrt k)))) 1546593453.917 * [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)))) 1546593453.917 * * * * [misc]progress: [ 70 / 113 ] simplifiying candidate # 1546593453.917 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) 1546593453.917 * * [misc]simplify: iters left: 5 (6 enodes) 1546593453.919 * * [misc]simplify: iters left: 4 (8 enodes) 1546593453.921 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) 1546593453.921 * [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)))) 1546593453.921 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.921 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.926 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.932 * * [misc]simplify: iters left: 4 (29 enodes) 1546593453.939 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.946 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.947 * [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)))) 1546593453.947 * * * * [misc]progress: [ 71 / 113 ] simplifiying candidate # 1546593453.947 * [enter]simplify: Simplifying (/ 1 (sqrt 1)) 1546593453.947 * * [misc]simplify: iters left: 3 (3 enodes) 1546593453.950 * * [misc]simplify: iters left: 2 (5 enodes) 1546593453.950 * [exit]simplify: Simplified to 1 1546593453.950 * [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)))) 1546593453.951 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593453.951 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.955 * * [misc]simplify: iters left: 5 (19 enodes) 1546593453.960 * * [misc]simplify: iters left: 4 (28 enodes) 1546593453.967 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.971 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593453.971 * [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)))) 1546593453.971 * * * * [misc]progress: [ 72 / 113 ] simplifiying candidate # 1546593453.971 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) 1546593453.971 * * [misc]simplify: iters left: 5 (6 enodes) 1546593453.972 * * [misc]simplify: iters left: 4 (8 enodes) 1546593453.973 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) 1546593453.973 * [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)))) 1546593453.973 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.973 * * [misc]simplify: iters left: 6 (14 enodes) 1546593453.975 * * [misc]simplify: iters left: 5 (20 enodes) 1546593453.978 * * [misc]simplify: iters left: 4 (29 enodes) 1546593453.982 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.985 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt (sqrt k)))) 1546593453.985 * [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)))) 1546593453.986 * * * * [misc]progress: [ 73 / 113 ] simplifiying candidate # 1546593453.986 * [enter]simplify: Simplifying (/ 1 1) 1546593453.986 * * [misc]simplify: iters left: 2 (2 enodes) 1546593453.986 * * [misc]simplify: iters left: 1 (4 enodes) 1546593453.986 * [exit]simplify: Simplified to 1 1546593453.986 * [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)))) 1546593453.987 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593453.987 * * [misc]simplify: iters left: 6 (13 enodes) 1546593453.989 * * [misc]simplify: iters left: 5 (19 enodes) 1546593453.991 * * [misc]simplify: iters left: 4 (28 enodes) 1546593453.995 * * [misc]simplify: iters left: 3 (30 enodes) 1546593453.999 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546593453.999 * [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)))) 1546593453.999 * * * * [misc]progress: [ 74 / 113 ] simplifiying candidate # 1546593453.999 * * * * [misc]progress: [ 75 / 113 ] simplifiying candidate # 1546593453.999 * * * * [misc]progress: [ 76 / 113 ] simplifiying candidate # 1546593453.999 * * * * [misc]progress: [ 77 / 113 ] simplifiying candidate # 1546593453.999 * [enter]simplify: Simplifying (cbrt (sqrt (sqrt k))) 1546593453.999 * * [misc]simplify: iters left: 3 (4 enodes) 1546593454.000 * [exit]simplify: Simplified to (cbrt (sqrt (sqrt k))) 1546593454.000 * [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)))) 1546593454.000 * * * * [misc]progress: [ 78 / 113 ] simplifiying candidate # 1546593454.000 * [enter]simplify: Simplifying (sqrt (cbrt (sqrt k))) 1546593454.000 * * [misc]simplify: iters left: 3 (4 enodes) 1546593454.001 * [exit]simplify: Simplified to (sqrt (cbrt (sqrt k))) 1546593454.001 * [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)))) 1546593454.001 * * * * [misc]progress: [ 79 / 113 ] simplifiying candidate # 1546593454.001 * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) 1546593454.001 * * [misc]simplify: iters left: 3 (4 enodes) 1546593454.002 * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) 1546593454.002 * [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)))) 1546593454.002 * * * * [misc]progress: [ 80 / 113 ] simplifiying candidate # 1546593454.002 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546593454.002 * * [misc]simplify: iters left: 2 (3 enodes) 1546593454.002 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546593454.002 * [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)))) 1546593454.002 * * * * [misc]progress: [ 81 / 113 ] simplifiying candidate # 1546593454.002 * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) 1546593454.002 * * [misc]simplify: iters left: 3 (4 enodes) 1546593454.003 * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) 1546593454.003 * [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)))) 1546593454.003 * * * * [misc]progress: [ 82 / 113 ] simplifiying candidate # 1546593454.003 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546593454.003 * * [misc]simplify: iters left: 2 (3 enodes) 1546593454.004 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546593454.004 * [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)))) 1546593454.004 * * * * [misc]progress: [ 83 / 113 ] simplifiying candidate # 1546593454.004 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546593454.004 * * [misc]simplify: iters left: 5 (7 enodes) 1546593454.005 * * [misc]simplify: iters left: 4 (12 enodes) 1546593454.007 * * [misc]simplify: iters left: 3 (18 enodes) 1546593454.010 * * [misc]simplify: iters left: 2 (20 enodes) 1546593454.014 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546593454.014 * [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)))) 1546593454.015 * * * * [misc]progress: [ 84 / 113 ] simplifiying candidate # 1546593454.015 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546593454.015 * * [misc]simplify: iters left: 5 (7 enodes) 1546593454.017 * * [misc]simplify: iters left: 4 (12 enodes) 1546593454.020 * * [misc]simplify: iters left: 3 (18 enodes) 1546593454.025 * * [misc]simplify: iters left: 2 (20 enodes) 1546593454.030 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546593454.030 * [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)))) 1546593454.030 * * * * [misc]progress: [ 85 / 113 ] simplifiying candidate # 1546593454.030 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546593454.030 * * [misc]simplify: iters left: 5 (7 enodes) 1546593454.032 * * [misc]simplify: iters left: 4 (9 enodes) 1546593454.035 * * [misc]simplify: iters left: 3 (12 enodes) 1546593454.038 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546593454.038 * [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)))) 1546593454.039 * * * * [misc]progress: [ 86 / 113 ] simplifiying candidate # 1546593454.039 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546593454.039 * * [misc]simplify: iters left: 6 (12 enodes) 1546593454.043 * * [misc]simplify: iters left: 5 (18 enodes) 1546593454.048 * * [misc]simplify: iters left: 4 (27 enodes) 1546593454.055 * * [misc]simplify: iters left: 3 (29 enodes) 1546593454.061 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546593454.061 * [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)))) 1546593454.061 * * * * [misc]progress: [ 87 / 113 ] simplifiying candidate # 1546593454.061 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546593454.061 * * [misc]simplify: iters left: 6 (11 enodes) 1546593454.063 * * [misc]simplify: iters left: 5 (17 enodes) 1546593454.065 * * [misc]simplify: iters left: 4 (26 enodes) 1546593454.070 * * [misc]simplify: iters left: 3 (27 enodes) 1546593454.073 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546593454.073 * [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)))) 1546593454.073 * * * * [misc]progress: [ 88 / 113 ] simplifiying candidate # 1546593454.073 * * * * [misc]progress: [ 89 / 113 ] simplifiying candidate # 1546593454.073 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546593454.073 * * [misc]simplify: iters left: 5 (7 enodes) 1546593454.074 * * [misc]simplify: iters left: 4 (12 enodes) 1546593454.076 * * [misc]simplify: iters left: 3 (18 enodes) 1546593454.078 * * [misc]simplify: iters left: 2 (20 enodes) 1546593454.081 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546593454.081 * [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)))) 1546593454.081 * * * * [misc]progress: [ 90 / 113 ] simplifiying candidate # 1546593454.081 * * * * [misc]progress: [ 91 / 113 ] simplifiying candidate # 1546593454.081 * * * * [misc]progress: [ 92 / 113 ] simplifiying candidate # 1546593454.081 * * * * [misc]progress: [ 93 / 113 ] simplifiying candidate # 1546593454.081 * * * * [misc]progress: [ 94 / 113 ] simplifiying candidate # 1546593454.081 * * * * [misc]progress: [ 95 / 113 ] simplifiying candidate # 1546593454.081 * * * * [misc]progress: [ 96 / 113 ] simplifiying candidate # 1546593454.081 * [enter]simplify: Simplifying (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546593454.081 * * [misc]simplify: iters left: 5 (5 enodes) 1546593454.082 * * [misc]simplify: iters left: 4 (6 enodes) 1546593454.083 * [exit]simplify: Simplified to (fabs (cbrt (sqrt k))) 1546593454.083 * [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)))))) 1546593454.083 * * * * [misc]progress: [ 97 / 113 ] simplifiying candidate # 1546593454.083 * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) 1546593454.083 * * [misc]simplify: iters left: 3 (4 enodes) 1546593454.083 * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) 1546593454.083 * [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)))))) 1546593454.083 * * * * [misc]progress: [ 98 / 113 ] simplifiying candidate # 1546593454.084 * [enter]simplify: Simplifying (sqrt 1) 1546593454.084 * * [misc]simplify: iters left: 1 (2 enodes) 1546593454.084 * [exit]simplify: Simplified to 1 1546593454.085 * [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))))) 1546593454.085 * * * * [misc]progress: [ 99 / 113 ] simplifiying candidate # 1546593454.085 * * * * [misc]progress: [ 100 / 113 ] simplifiying candidate # 1546593454.085 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546593454.085 * * [misc]simplify: iters left: 2 (3 enodes) 1546593454.085 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546593454.085 * [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))))) 1546593454.085 * * * * [misc]progress: [ 101 / 113 ] simplifiying candidate # 1546593454.085 * * * * [misc]progress: [ 102 / 113 ] simplifiying candidate # 1546593454.085 * [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))))) 1546593454.086 * * [misc]simplify: iters left: 6 (37 enodes) 1546593454.095 * * [misc]simplify: iters left: 5 (105 enodes) 1546593454.135 * * [misc]simplify: iters left: 4 (339 enodes) 1546593454.382 * [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))))) 1546593454.382 * [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)))) 1546593454.382 * * * * [misc]progress: [ 103 / 113 ] simplifiying candidate # 1546593454.383 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546593454.383 * * [misc]simplify: iters left: 6 (15 enodes) 1546593454.389 * * [misc]simplify: iters left: 5 (33 enodes) 1546593454.399 * * [misc]simplify: iters left: 4 (64 enodes) 1546593454.422 * * [misc]simplify: iters left: 3 (171 enodes) 1546593454.502 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546593454.502 * [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)))) 1546593454.502 * * * * [misc]progress: [ 104 / 113 ] simplifiying candidate # 1546593454.503 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546593454.503 * * [misc]simplify: iters left: 6 (15 enodes) 1546593454.508 * * [misc]simplify: iters left: 5 (30 enodes) 1546593454.519 * * [misc]simplify: iters left: 4 (65 enodes) 1546593454.551 * * [misc]simplify: iters left: 3 (200 enodes) 1546593454.677 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546593454.677 * [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)))) 1546593454.677 * * * * [misc]progress: [ 105 / 113 ] simplifiying candidate # 1546593454.677 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593454.677 * * [misc]simplify: iters left: 4 (5 enodes) 1546593454.678 * * [misc]simplify: iters left: 3 (9 enodes) 1546593454.679 * * [misc]simplify: iters left: 2 (15 enodes) 1546593454.681 * * [misc]simplify: iters left: 1 (17 enodes) 1546593454.683 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593454.683 * [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)))) 1546593454.683 * * * * [misc]progress: [ 106 / 113 ] simplifiying candidate # 1546593454.684 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593454.684 * * [misc]simplify: iters left: 4 (5 enodes) 1546593454.684 * * [misc]simplify: iters left: 3 (9 enodes) 1546593454.686 * * [misc]simplify: iters left: 2 (15 enodes) 1546593454.688 * * [misc]simplify: iters left: 1 (17 enodes) 1546593454.689 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593454.690 * [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)))) 1546593454.690 * * * * [misc]progress: [ 107 / 113 ] simplifiying candidate # 1546593454.690 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546593454.690 * * [misc]simplify: iters left: 4 (5 enodes) 1546593454.691 * * [misc]simplify: iters left: 3 (9 enodes) 1546593454.692 * * [misc]simplify: iters left: 2 (15 enodes) 1546593454.694 * * [misc]simplify: iters left: 1 (17 enodes) 1546593454.696 * [exit]simplify: Simplified to (* (* PI n) 2) 1546593454.696 * [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)))) 1546593454.696 * * * * [misc]progress: [ 108 / 113 ] simplifiying candidate # 1546593454.696 * [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))))) 1546593454.696 * * [misc]simplify: iters left: 6 (45 enodes) 1546593454.705 * * [misc]simplify: iters left: 5 (119 enodes) 1546593454.744 * * [misc]simplify: iters left: 4 (333 enodes) 1546593454.998 * [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))))))) 1546593454.998 * [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)))) 1546593454.999 * * * * [misc]progress: [ 109 / 113 ] simplifiying candidate # 1546593454.999 * [enter]simplify: Simplifying (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) 1546593454.999 * * [misc]simplify: iters left: 6 (19 enodes) 1546593455.006 * * [misc]simplify: iters left: 5 (38 enodes) 1546593455.022 * * [misc]simplify: iters left: 4 (69 enodes) 1546593455.046 * * [misc]simplify: iters left: 3 (176 enodes) 1546593455.131 * [exit]simplify: Simplified to (* (* (pow (/ 1 k) 1/4) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (pow n (- 1/2 (* 1/2 k)))) 1546593455.131 * [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)))) 1546593455.131 * * * * [misc]progress: [ 110 / 113 ] simplifiying candidate # 1546593455.132 * [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))))))))) 1546593455.132 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ +nan.0 (sqrt (sqrt k)))) 1546593455.132 * * * * [misc]progress: [ 111 / 113 ] simplifiying candidate # 1546593455.132 * [enter]simplify: Simplifying (pow k 1/4) 1546593455.132 * * [misc]simplify: iters left: 1 (3 enodes) 1546593455.133 * [exit]simplify: Simplified to (pow k 1/4) 1546593455.133 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (pow k 1/4))) 1546593455.133 * * * * [misc]progress: [ 112 / 113 ] simplifiying candidate # 1546593455.133 * [enter]simplify: Simplifying (pow (/ 1 k) -1/4) 1546593455.133 * * [misc]simplify: iters left: 3 (5 enodes) 1546593455.135 * * [misc]simplify: iters left: 2 (7 enodes) 1546593455.136 * [exit]simplify: Simplified to (pow (/ 1 k) -1/4) 1546593455.136 * [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))) 1546593455.137 * * * * [misc]progress: [ 113 / 113 ] simplifiying candidate # 1546593455.137 * [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))))))))) 1546593455.137 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) +nan.0)) 1546593455.137 * * * [misc]progress: adding candidates to table 1546593456.634 * [misc]progress: [Phase 3 of 3] Extracting. 1546593456.635 * * [misc]regime: Finding splitpoints for: (# # # # # #) 1546593456.636 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1546593456.636 * * * * [misc]regimes: Trying to branch on n from (# # # # # #) 1546593456.694 * * * * [misc]regimes: Trying to branch on k from (# # # # # #) 1546593456.753 * * * [misc]regime: Found split indices: #