1536754405.072 * [misc]progress: [Phase 1 of 3] Setting up. 1536754405.072 * * * [misc]progress: [1/2] Preparing points 1536754405.072 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1536754405.074 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision 1536754405.077 * * * * [misc]points: Setting MPFR precision to 64 1536754405.078 * * * * [misc]points: Setting MPFR precision to 320 1536754405.078 * * * * [misc]points: Setting MPFR precision to 576 1536754405.079 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision 1536754405.084 * * * * [misc]points: Setting MPFR precision to 320 1536754405.086 * * * * [misc]points: Setting MPFR precision to 576 1536754405.087 * * * * [misc]points: Setting MPFR precision to 832 1536754405.089 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision 1536754405.096 * * * * [misc]points: Setting MPFR precision to 576 1536754405.098 * * * * [misc]points: Setting MPFR precision to 832 1536754405.103 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.109 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.115 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision 1536754405.146 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.156 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.165 * * * * [misc]points: Computing exacts for 256 points 1536754405.185 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.213 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.232 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.232 * * * * [misc]points: Sampling 207 additional inputs, on iter 1 have 49 / 256 1536754405.233 * * * * [misc]points: Computing exacts on every 12 of 207 points to ramp up precision 1536754405.254 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.254 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.255 * * * * [misc]points: Computing exacts on every 6 of 207 points to ramp up precision 1536754405.265 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.267 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.269 * * * * [misc]points: Computing exacts on every 3 of 207 points to ramp up precision 1536754405.282 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.285 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.289 * * * * [misc]points: Computing exacts for 207 points 1536754405.298 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.320 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.343 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.343 * * * * [misc]points: Sampling 164 additional inputs, on iter 2 have 92 / 256 1536754405.344 * * * * [misc]points: Computing exacts on every 10 of 164 points to ramp up precision 1536754405.377 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.379 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.382 * * * * [misc]points: Computing exacts on every 5 of 164 points to ramp up precision 1536754405.394 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.396 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.397 * * * * [misc]points: Computing exacts on every 2 of 164 points to ramp up precision 1536754405.407 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.410 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.412 * * * * [misc]points: Computing exacts for 164 points 1536754405.428 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.437 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.446 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.446 * * * * [misc]points: Sampling 137 additional inputs, on iter 3 have 119 / 256 1536754405.446 * * * * [misc]points: Computing exacts on every 8 of 137 points to ramp up precision 1536754405.456 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.457 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.458 * * * * [misc]points: Computing exacts on every 4 of 137 points to ramp up precision 1536754405.477 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.481 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.483 * * * * [misc]points: Computing exacts on every 2 of 137 points to ramp up precision 1536754405.501 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.504 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.506 * * * * [misc]points: Computing exacts for 137 points 1536754405.516 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.530 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.537 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.537 * * * * [misc]points: Sampling 114 additional inputs, on iter 4 have 142 / 256 1536754405.538 * * * * [misc]points: Computing exacts on every 7 of 114 points to ramp up precision 1536754405.548 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.549 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.550 * * * * [misc]points: Computing exacts on every 3 of 114 points to ramp up precision 1536754405.560 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.563 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.566 * * * * [misc]points: Computing exacts for 114 points 1536754405.594 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.603 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.610 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.610 * * * * [misc]points: Sampling 89 additional inputs, on iter 5 have 167 / 256 1536754405.610 * * * * [misc]points: Computing exacts on every 5 of 89 points to ramp up precision 1536754405.620 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.621 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.622 * * * * [misc]points: Computing exacts on every 2 of 89 points to ramp up precision 1536754405.637 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.639 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.641 * * * * [misc]points: Computing exacts for 89 points 1536754405.651 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.656 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.662 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.662 * * * * [misc]points: Sampling 75 additional inputs, on iter 6 have 181 / 256 1536754405.662 * * * * [misc]points: Computing exacts on every 4 of 75 points to ramp up precision 1536754405.672 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.673 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.674 * * * * [misc]points: Computing exacts on every 2 of 75 points to ramp up precision 1536754405.689 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.690 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.692 * * * * [misc]points: Computing exacts for 75 points 1536754405.704 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.708 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.713 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.713 * * * * [misc]points: Sampling 64 additional inputs, on iter 7 have 192 / 256 1536754405.713 * * * * [misc]points: Computing exacts on every 4 of 64 points to ramp up precision 1536754405.727 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.728 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.729 * * * * [misc]points: Computing exacts on every 2 of 64 points to ramp up precision 1536754405.742 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.744 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.746 * * * * [misc]points: Computing exacts for 64 points 1536754405.767 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.773 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.780 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.780 * * * * [misc]points: Sampling 55 additional inputs, on iter 8 have 201 / 256 1536754405.780 * * * * [misc]points: Computing exacts on every 3 of 55 points to ramp up precision 1536754405.807 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.809 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.810 * * * * [misc]points: Computing exacts for 55 points 1536754405.831 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.837 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.843 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.843 * * * * [misc]points: Sampling 45 additional inputs, on iter 9 have 211 / 256 1536754405.843 * * * * [misc]points: Computing exacts on every 2 of 45 points to ramp up precision 1536754405.856 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.857 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.858 * * * * [misc]points: Computing exacts for 45 points 1536754405.867 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.870 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.873 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.873 * * * * [misc]points: Sampling 37 additional inputs, on iter 10 have 219 / 256 1536754405.873 * * * * [misc]points: Computing exacts on every 2 of 37 points to ramp up precision 1536754405.893 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.894 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.896 * * * * [misc]points: Computing exacts for 37 points 1536754405.920 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.922 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.924 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.924 * * * * [misc]points: Sampling 31 additional inputs, on iter 11 have 225 / 256 1536754405.924 * * * * [misc]points: Computing exacts for 31 points 1536754405.934 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.936 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.937 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.937 * * * * [misc]points: Sampling 26 additional inputs, on iter 12 have 230 / 256 1536754405.937 * * * * [misc]points: Computing exacts for 26 points 1536754405.954 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.957 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.960 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.960 * * * * [misc]points: Sampling 22 additional inputs, on iter 13 have 234 / 256 1536754405.960 * * * * [misc]points: Computing exacts for 22 points 1536754405.976 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.977 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.978 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.978 * * * * [misc]points: Sampling 15 additional inputs, on iter 14 have 241 / 256 1536754405.978 * * * * [misc]points: Computing exacts for 15 points 1536754405.988 * * * * [misc]points: Setting MPFR precision to 1088 1536754405.989 * * * * [misc]points: Setting MPFR precision to 1344 1536754405.990 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754405.990 * * * * [misc]points: Sampling 11 additional inputs, on iter 15 have 245 / 256 1536754405.990 * * * * [misc]points: Computing exacts for 11 points 1536754406.009 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.011 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.012 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.012 * * * * [misc]points: Sampling 11 additional inputs, on iter 16 have 245 / 256 1536754406.012 * * * * [misc]points: Computing exacts for 11 points 1536754406.032 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.033 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.034 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.034 * * * * [misc]points: Sampling 11 additional inputs, on iter 17 have 245 / 256 1536754406.035 * * * * [misc]points: Computing exacts for 11 points 1536754406.059 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.060 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.061 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.061 * * * * [misc]points: Sampling 9 additional inputs, on iter 18 have 247 / 256 1536754406.061 * * * * [misc]points: Computing exacts for 9 points 1536754406.082 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.083 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.084 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.084 * * * * [misc]points: Sampling 8 additional inputs, on iter 19 have 248 / 256 1536754406.084 * * * * [misc]points: Computing exacts for 8 points 1536754406.097 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.098 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.099 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.099 * * * * [misc]points: Sampling 6 additional inputs, on iter 20 have 250 / 256 1536754406.099 * * * * [misc]points: Computing exacts for 6 points 1536754406.112 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.112 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.113 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.113 * * * * [misc]points: Sampling 5 additional inputs, on iter 21 have 251 / 256 1536754406.113 * * * * [misc]points: Computing exacts for 5 points 1536754406.123 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.123 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.124 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.124 * * * * [misc]points: Sampling 5 additional inputs, on iter 22 have 251 / 256 1536754406.124 * * * * [misc]points: Computing exacts for 5 points 1536754406.133 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.134 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.134 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.134 * * * * [misc]points: Sampling 5 additional inputs, on iter 23 have 251 / 256 1536754406.134 * * * * [misc]points: Computing exacts for 5 points 1536754406.146 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.147 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.147 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.147 * * * * [misc]points: Sampling 4 additional inputs, on iter 24 have 252 / 256 1536754406.147 * * * * [misc]points: Computing exacts for 4 points 1536754406.157 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.157 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.157 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.157 * * * * [misc]points: Sampling 4 additional inputs, on iter 25 have 253 / 256 1536754406.157 * * * * [misc]points: Computing exacts for 4 points 1536754406.175 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.175 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.176 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.176 * * * * [misc]points: Sampling 4 additional inputs, on iter 26 have 253 / 256 1536754406.176 * * * * [misc]points: Computing exacts for 4 points 1536754406.196 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.197 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.197 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.197 * * * * [misc]points: Sampling 4 additional inputs, on iter 27 have 254 / 256 1536754406.197 * * * * [misc]points: Computing exacts for 4 points 1536754406.218 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.218 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.219 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.219 * * * * [misc]points: Sampling 4 additional inputs, on iter 28 have 255 / 256 1536754406.219 * * * * [misc]points: Computing exacts for 4 points 1536754406.242 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.243 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.244 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.244 * * * * [misc]points: Sampling 4 additional inputs, on iter 29 have 255 / 256 1536754406.244 * * * * [misc]points: Computing exacts for 4 points 1536754406.264 * * * * [misc]points: Setting MPFR precision to 1088 1536754406.265 * * * * [misc]points: Setting MPFR precision to 1344 1536754406.266 * * * * [misc]points: Filtering points with unrepresentable outputs 1536754406.266 * * * * [exit]points: Sampled 256 points with exact outputs 1536754406.266 * * * [misc]progress: [2/2] Setting up program. 1536754406.277 * [misc]progress: [Phase 2 of 3] Improving. 1536754406.277 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1536754406.279 * * [misc]simplify: iters left: 6 (13 enodes) 1536754406.286 * * [misc]simplify: iters left: 5 (28 enodes) 1536754406.298 * * [misc]simplify: iters left: 4 (44 enodes) 1536754406.314 * * [misc]simplify: iters left: 3 (54 enodes) 1536754406.328 * * [misc]simplify: iters left: 2 (57 enodes) 1536754406.347 * * [misc]simplify: iters left: 1 (65 enodes) 1536754406.370 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1536754406.390 * * [misc]progress: iteration 1 / 4 1536754406.390 * * * [misc]progress: picking best candidate 1536754406.409 * * * * [misc]pick: Picked # 1536754406.409 * * * [misc]progress: localizing error 1536754406.447 * * * [misc]progress: generating rewritten candidates 1536754406.447 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1536754406.496 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1536754406.521 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1536754406.580 * * * [misc]progress: generating series expansions 1536754406.580 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1536754406.580 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1536754406.580 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1536754406.580 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536754406.580 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536754406.580 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536754406.581 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754406.581 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.581 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.581 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754406.581 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.581 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.581 * [misc]taylor: Taking taylor expansion of k in k 1536754406.581 * [misc]backup-simplify: Simplify 0 into 0 1536754406.581 * [misc]backup-simplify: Simplify 1 into 1 1536754406.581 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536754406.581 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536754406.581 * [misc]taylor: Taking taylor expansion of 2 in k 1536754406.581 * [misc]backup-simplify: Simplify 2 into 2 1536754406.581 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536754406.581 * [misc]taylor: Taking taylor expansion of n in k 1536754406.581 * [misc]backup-simplify: Simplify n into n 1536754406.581 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.581 * [misc]backup-simplify: Simplify PI into PI 1536754406.581 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754406.581 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536754406.581 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536754406.581 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754406.581 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.581 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754406.582 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536754406.582 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536754406.582 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536754406.582 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536754406.582 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536754406.582 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754406.582 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.582 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.582 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754406.582 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.582 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.582 * [misc]taylor: Taking taylor expansion of k in n 1536754406.582 * [misc]backup-simplify: Simplify k into k 1536754406.582 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536754406.582 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754406.582 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.582 * [misc]backup-simplify: Simplify 2 into 2 1536754406.582 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754406.582 * [misc]taylor: Taking taylor expansion of n in n 1536754406.582 * [misc]backup-simplify: Simplify 0 into 0 1536754406.582 * [misc]backup-simplify: Simplify 1 into 1 1536754406.582 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.582 * [misc]backup-simplify: Simplify PI into PI 1536754406.582 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754406.582 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754406.583 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754406.583 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754406.584 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.584 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754406.584 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754406.584 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754406.584 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.585 * [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)))) 1536754406.585 * [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))))) 1536754406.585 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536754406.585 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536754406.585 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536754406.585 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754406.585 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.585 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.585 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754406.585 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.585 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.585 * [misc]taylor: Taking taylor expansion of k in n 1536754406.585 * [misc]backup-simplify: Simplify k into k 1536754406.585 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536754406.585 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754406.585 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.585 * [misc]backup-simplify: Simplify 2 into 2 1536754406.585 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754406.585 * [misc]taylor: Taking taylor expansion of n in n 1536754406.585 * [misc]backup-simplify: Simplify 0 into 0 1536754406.585 * [misc]backup-simplify: Simplify 1 into 1 1536754406.585 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.585 * [misc]backup-simplify: Simplify PI into PI 1536754406.586 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754406.586 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754406.586 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754406.587 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754406.587 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.587 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754406.587 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754406.587 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754406.588 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.588 * [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)))) 1536754406.588 * [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))))) 1536754406.589 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536754406.589 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536754406.589 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754406.589 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.589 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.589 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754406.589 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.589 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.589 * [misc]taylor: Taking taylor expansion of k in k 1536754406.589 * [misc]backup-simplify: Simplify 0 into 0 1536754406.589 * [misc]backup-simplify: Simplify 1 into 1 1536754406.589 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536754406.589 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754406.589 * [misc]taylor: Taking taylor expansion of n in k 1536754406.589 * [misc]backup-simplify: Simplify n into n 1536754406.589 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754406.589 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536754406.589 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536754406.589 * [misc]taylor: Taking taylor expansion of 2 in k 1536754406.589 * [misc]backup-simplify: Simplify 2 into 2 1536754406.589 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.589 * [misc]backup-simplify: Simplify PI into PI 1536754406.589 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.589 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.590 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754406.590 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.590 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754406.590 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.590 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536754406.591 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536754406.591 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536754406.592 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754406.593 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536754406.595 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754406.595 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536754406.595 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.595 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.595 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.596 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536754406.597 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754406.597 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.597 * [misc]backup-simplify: Simplify 0 into 0 1536754406.597 * [misc]backup-simplify: Simplify 0 into 0 1536754406.598 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536754406.598 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754406.600 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754406.600 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.600 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754406.600 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754406.600 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754406.601 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536754406.602 * [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))))))) 1536754406.603 * [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))))))) 1536754406.604 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754406.605 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536754406.609 * [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 1536754406.609 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536754406.609 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.609 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.610 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.610 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536754406.612 * [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 1536754406.612 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.612 * [misc]backup-simplify: Simplify 0 into 0 1536754406.612 * [misc]backup-simplify: Simplify 0 into 0 1536754406.612 * [misc]backup-simplify: Simplify 0 into 0 1536754406.614 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536754406.615 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754406.621 * [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 1536754406.621 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.621 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754406.622 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.622 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.623 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536754406.626 * [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))))) 1536754406.630 * [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))))) 1536754406.638 * [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))))) 1536754406.639 * [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)))) 1536754406.639 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1536754406.639 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754406.639 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536754406.639 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536754406.639 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754406.639 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.640 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.640 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754406.640 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.640 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.640 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754406.640 * [misc]taylor: Taking taylor expansion of k in k 1536754406.640 * [misc]backup-simplify: Simplify 0 into 0 1536754406.640 * [misc]backup-simplify: Simplify 1 into 1 1536754406.640 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754406.640 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536754406.640 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536754406.640 * [misc]taylor: Taking taylor expansion of 2 in k 1536754406.640 * [misc]backup-simplify: Simplify 2 into 2 1536754406.640 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754406.640 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.640 * [misc]backup-simplify: Simplify PI into PI 1536754406.640 * [misc]taylor: Taking taylor expansion of n in k 1536754406.640 * [misc]backup-simplify: Simplify n into n 1536754406.640 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754406.641 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536754406.641 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536754406.641 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754406.641 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754406.641 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754406.641 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536754406.642 * [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)))) 1536754406.642 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.642 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.642 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.642 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.642 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of k in n 1536754406.642 * [misc]backup-simplify: Simplify k into k 1536754406.642 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754406.642 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.642 * [misc]backup-simplify: Simplify 2 into 2 1536754406.642 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.642 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.642 * [misc]backup-simplify: Simplify PI into PI 1536754406.642 * [misc]taylor: Taking taylor expansion of n in n 1536754406.642 * [misc]backup-simplify: Simplify 0 into 0 1536754406.642 * [misc]backup-simplify: Simplify 1 into 1 1536754406.643 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.643 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.644 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.644 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754406.644 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754406.644 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754406.645 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754406.645 * [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))) 1536754406.646 * [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)))) 1536754406.646 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754406.646 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536754406.646 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536754406.646 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754406.646 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.646 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.646 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754406.646 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.647 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.647 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754406.647 * [misc]taylor: Taking taylor expansion of k in n 1536754406.647 * [misc]backup-simplify: Simplify k into k 1536754406.647 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754406.647 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536754406.647 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754406.647 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.647 * [misc]backup-simplify: Simplify 2 into 2 1536754406.647 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.647 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.647 * [misc]backup-simplify: Simplify PI into PI 1536754406.647 * [misc]taylor: Taking taylor expansion of n in n 1536754406.647 * [misc]backup-simplify: Simplify 0 into 0 1536754406.647 * [misc]backup-simplify: Simplify 1 into 1 1536754406.647 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.648 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.648 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.648 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754406.648 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754406.648 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754406.649 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754406.650 * [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))) 1536754406.651 * [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)))) 1536754406.651 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536754406.651 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536754406.651 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754406.651 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.651 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.651 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754406.651 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.651 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.651 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754406.651 * [misc]taylor: Taking taylor expansion of k in k 1536754406.651 * [misc]backup-simplify: Simplify 0 into 0 1536754406.651 * [misc]backup-simplify: Simplify 1 into 1 1536754406.651 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754406.651 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536754406.651 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536754406.651 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536754406.651 * [misc]taylor: Taking taylor expansion of 2 in k 1536754406.651 * [misc]backup-simplify: Simplify 2 into 2 1536754406.651 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.651 * [misc]backup-simplify: Simplify PI into PI 1536754406.652 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.652 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.652 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754406.652 * [misc]taylor: Taking taylor expansion of n in k 1536754406.652 * [misc]backup-simplify: Simplify n into n 1536754406.652 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754406.653 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754406.653 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754406.653 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754406.653 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754406.654 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536754406.654 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536754406.655 * [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)))) 1536754406.656 * [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)))) 1536754406.657 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754406.658 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754406.661 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754406.662 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754406.662 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754406.662 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.662 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.663 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754406.664 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536754406.665 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754406.665 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.665 * [misc]backup-simplify: Simplify 0 into 0 1536754406.665 * [misc]backup-simplify: Simplify 0 into 0 1536754406.665 * [misc]backup-simplify: Simplify 0 into 0 1536754406.667 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.668 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754406.674 * [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 1536754406.674 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754406.674 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754406.674 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.675 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.675 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754406.676 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536754406.679 * [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 1536754406.679 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.679 * [misc]backup-simplify: Simplify 0 into 0 1536754406.679 * [misc]backup-simplify: Simplify 0 into 0 1536754406.679 * [misc]backup-simplify: Simplify 0 into 0 1536754406.679 * [misc]backup-simplify: Simplify 0 into 0 1536754406.681 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.682 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754406.691 * [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 1536754406.692 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754406.692 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754406.692 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.692 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.693 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754406.694 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536754406.696 * [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 1536754406.696 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.696 * [misc]backup-simplify: Simplify 0 into 0 1536754406.696 * [misc]backup-simplify: Simplify 0 into 0 1536754406.697 * [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))))) 1536754406.697 * [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)) 1536754406.697 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1536754406.697 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754406.697 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536754406.697 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536754406.697 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754406.697 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754406.697 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.697 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.697 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754406.697 * [misc]taylor: Taking taylor expansion of k in k 1536754406.697 * [misc]backup-simplify: Simplify 0 into 0 1536754406.697 * [misc]backup-simplify: Simplify 1 into 1 1536754406.698 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754406.698 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.698 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.698 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536754406.698 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536754406.698 * [misc]taylor: Taking taylor expansion of -2 in k 1536754406.698 * [misc]backup-simplify: Simplify -2 into -2 1536754406.698 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754406.698 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.698 * [misc]backup-simplify: Simplify PI into PI 1536754406.698 * [misc]taylor: Taking taylor expansion of n in k 1536754406.698 * [misc]backup-simplify: Simplify n into n 1536754406.698 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754406.698 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536754406.698 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536754406.698 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754406.698 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754406.698 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536754406.698 * [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))) 1536754406.699 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.699 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.699 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of k in n 1536754406.699 * [misc]backup-simplify: Simplify k into k 1536754406.699 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754406.699 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.699 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.699 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of -2 in n 1536754406.699 * [misc]backup-simplify: Simplify -2 into -2 1536754406.699 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.699 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.699 * [misc]backup-simplify: Simplify PI into PI 1536754406.699 * [misc]taylor: Taking taylor expansion of n in n 1536754406.699 * [misc]backup-simplify: Simplify 0 into 0 1536754406.699 * [misc]backup-simplify: Simplify 1 into 1 1536754406.699 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.699 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754406.700 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754406.700 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754406.700 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754406.700 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754406.701 * [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))) 1536754406.701 * [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)))) 1536754406.701 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754406.701 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536754406.701 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536754406.701 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754406.701 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754406.701 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.701 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.701 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754406.701 * [misc]taylor: Taking taylor expansion of k in n 1536754406.701 * [misc]backup-simplify: Simplify k into k 1536754406.702 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754406.702 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.702 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.702 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536754406.702 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754406.702 * [misc]taylor: Taking taylor expansion of -2 in n 1536754406.702 * [misc]backup-simplify: Simplify -2 into -2 1536754406.702 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.702 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.702 * [misc]backup-simplify: Simplify PI into PI 1536754406.702 * [misc]taylor: Taking taylor expansion of n in n 1536754406.702 * [misc]backup-simplify: Simplify 0 into 0 1536754406.702 * [misc]backup-simplify: Simplify 1 into 1 1536754406.702 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.702 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754406.702 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754406.703 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754406.703 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754406.703 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754406.703 * [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))) 1536754406.704 * [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)))) 1536754406.704 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536754406.704 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536754406.704 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754406.704 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754406.704 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.704 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.704 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754406.704 * [misc]taylor: Taking taylor expansion of k in k 1536754406.704 * [misc]backup-simplify: Simplify 0 into 0 1536754406.704 * [misc]backup-simplify: Simplify 1 into 1 1536754406.704 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754406.704 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.704 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.705 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536754406.705 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536754406.705 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536754406.705 * [misc]taylor: Taking taylor expansion of -2 in k 1536754406.705 * [misc]backup-simplify: Simplify -2 into -2 1536754406.705 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.705 * [misc]backup-simplify: Simplify PI into PI 1536754406.705 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754406.705 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754406.705 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754406.705 * [misc]taylor: Taking taylor expansion of n in k 1536754406.705 * [misc]backup-simplify: Simplify n into n 1536754406.705 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754406.705 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754406.705 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754406.705 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754406.706 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536754406.706 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536754406.707 * [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)))) 1536754406.707 * [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)))) 1536754406.710 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754406.711 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536754406.713 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536754406.713 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754406.713 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754406.713 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.713 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754406.714 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536754406.715 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754406.715 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.715 * [misc]backup-simplify: Simplify 0 into 0 1536754406.715 * [misc]backup-simplify: Simplify 0 into 0 1536754406.715 * [misc]backup-simplify: Simplify 0 into 0 1536754406.716 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.717 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754406.721 * [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 1536754406.721 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754406.722 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754406.722 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.723 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754406.723 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536754406.726 * [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 1536754406.726 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.726 * [misc]backup-simplify: Simplify 0 into 0 1536754406.726 * [misc]backup-simplify: Simplify 0 into 0 1536754406.726 * [misc]backup-simplify: Simplify 0 into 0 1536754406.726 * [misc]backup-simplify: Simplify 0 into 0 1536754406.728 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.730 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754406.739 * [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 1536754406.739 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754406.740 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754406.740 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.741 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754406.742 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1536754406.746 * [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 1536754406.746 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.746 * [misc]backup-simplify: Simplify 0 into 0 1536754406.746 * [misc]backup-simplify: Simplify 0 into 0 1536754406.747 * [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))))) 1536754406.747 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1536754406.747 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1536754406.747 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536754406.747 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754406.747 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.747 * [misc]backup-simplify: Simplify 2 into 2 1536754406.747 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754406.747 * [misc]taylor: Taking taylor expansion of n in n 1536754406.747 * [misc]backup-simplify: Simplify 0 into 0 1536754406.747 * [misc]backup-simplify: Simplify 1 into 1 1536754406.747 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.747 * [misc]backup-simplify: Simplify PI into PI 1536754406.747 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754406.747 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.747 * [misc]backup-simplify: Simplify 2 into 2 1536754406.747 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754406.747 * [misc]taylor: Taking taylor expansion of n in n 1536754406.747 * [misc]backup-simplify: Simplify 0 into 0 1536754406.747 * [misc]backup-simplify: Simplify 1 into 1 1536754406.747 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.747 * [misc]backup-simplify: Simplify PI into PI 1536754406.748 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754406.748 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754406.748 * [misc]backup-simplify: Simplify 0 into 0 1536754406.748 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754406.749 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754406.749 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.750 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754406.750 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536754406.750 * [misc]backup-simplify: Simplify 0 into 0 1536754406.751 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754406.752 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536754406.752 * [misc]backup-simplify: Simplify 0 into 0 1536754406.754 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754406.755 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536754406.755 * [misc]backup-simplify: Simplify 0 into 0 1536754406.756 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536754406.758 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536754406.758 * [misc]backup-simplify: Simplify 0 into 0 1536754406.760 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536754406.762 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536754406.762 * [misc]backup-simplify: Simplify 0 into 0 1536754406.765 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536754406.767 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536754406.767 * [misc]backup-simplify: Simplify 0 into 0 1536754406.768 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536754406.768 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1536754406.768 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536754406.768 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754406.768 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.768 * [misc]backup-simplify: Simplify 2 into 2 1536754406.768 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.768 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.768 * [misc]backup-simplify: Simplify PI into PI 1536754406.768 * [misc]taylor: Taking taylor expansion of n in n 1536754406.768 * [misc]backup-simplify: Simplify 0 into 0 1536754406.768 * [misc]backup-simplify: Simplify 1 into 1 1536754406.768 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.768 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754406.768 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.768 * [misc]backup-simplify: Simplify 2 into 2 1536754406.768 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.768 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.768 * [misc]backup-simplify: Simplify PI into PI 1536754406.768 * [misc]taylor: Taking taylor expansion of n in n 1536754406.768 * [misc]backup-simplify: Simplify 0 into 0 1536754406.768 * [misc]backup-simplify: Simplify 1 into 1 1536754406.769 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.769 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.769 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.770 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754406.770 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754406.770 * [misc]backup-simplify: Simplify 0 into 0 1536754406.771 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.773 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754406.773 * [misc]backup-simplify: Simplify 0 into 0 1536754406.774 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.776 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754406.776 * [misc]backup-simplify: Simplify 0 into 0 1536754406.778 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.780 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754406.781 * [misc]backup-simplify: Simplify 0 into 0 1536754406.783 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.786 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536754406.786 * [misc]backup-simplify: Simplify 0 into 0 1536754406.789 * [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 1536754406.792 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536754406.792 * [misc]backup-simplify: Simplify 0 into 0 1536754406.793 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536754406.793 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1536754406.793 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536754406.793 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754406.793 * [misc]taylor: Taking taylor expansion of -2 in n 1536754406.793 * [misc]backup-simplify: Simplify -2 into -2 1536754406.793 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.793 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.793 * [misc]backup-simplify: Simplify PI into PI 1536754406.793 * [misc]taylor: Taking taylor expansion of n in n 1536754406.793 * [misc]backup-simplify: Simplify 0 into 0 1536754406.793 * [misc]backup-simplify: Simplify 1 into 1 1536754406.793 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.793 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754406.794 * [misc]taylor: Taking taylor expansion of -2 in n 1536754406.794 * [misc]backup-simplify: Simplify -2 into -2 1536754406.794 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.794 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.794 * [misc]backup-simplify: Simplify PI into PI 1536754406.794 * [misc]taylor: Taking taylor expansion of n in n 1536754406.794 * [misc]backup-simplify: Simplify 0 into 0 1536754406.794 * [misc]backup-simplify: Simplify 1 into 1 1536754406.794 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.794 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754406.795 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754406.796 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754406.797 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536754406.797 * [misc]backup-simplify: Simplify 0 into 0 1536754406.798 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.799 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754406.799 * [misc]backup-simplify: Simplify 0 into 0 1536754406.801 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.803 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754406.803 * [misc]backup-simplify: Simplify 0 into 0 1536754406.805 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.807 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754406.807 * [misc]backup-simplify: Simplify 0 into 0 1536754406.809 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.812 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536754406.812 * [misc]backup-simplify: Simplify 0 into 0 1536754406.815 * [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 1536754406.818 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536754406.818 * [misc]backup-simplify: Simplify 0 into 0 1536754406.819 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536754406.819 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1536754406.820 * [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)))) 1536754406.820 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1536754406.820 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1536754406.820 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754406.820 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754406.820 * [misc]taylor: Taking taylor expansion of k in k 1536754406.820 * [misc]backup-simplify: Simplify 0 into 0 1536754406.820 * [misc]backup-simplify: Simplify 1 into 1 1536754406.820 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754406.820 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754406.821 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754406.821 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536754406.821 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536754406.821 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536754406.821 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754406.821 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.821 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.821 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754406.821 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.821 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.821 * [misc]taylor: Taking taylor expansion of k in k 1536754406.821 * [misc]backup-simplify: Simplify 0 into 0 1536754406.821 * [misc]backup-simplify: Simplify 1 into 1 1536754406.821 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536754406.821 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536754406.821 * [misc]taylor: Taking taylor expansion of 2 in k 1536754406.821 * [misc]backup-simplify: Simplify 2 into 2 1536754406.821 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536754406.821 * [misc]taylor: Taking taylor expansion of n in k 1536754406.821 * [misc]backup-simplify: Simplify n into n 1536754406.821 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.821 * [misc]backup-simplify: Simplify PI into PI 1536754406.821 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754406.822 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536754406.822 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536754406.822 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754406.822 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.822 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754406.822 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536754406.823 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536754406.823 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536754406.823 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754406.823 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754406.823 * [misc]taylor: Taking taylor expansion of k in n 1536754406.823 * [misc]backup-simplify: Simplify k into k 1536754406.823 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754406.823 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754406.823 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754406.823 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754406.823 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536754406.823 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536754406.823 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536754406.823 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754406.823 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.823 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.823 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754406.823 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.823 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.824 * [misc]taylor: Taking taylor expansion of k in n 1536754406.824 * [misc]backup-simplify: Simplify k into k 1536754406.824 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536754406.824 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754406.824 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.824 * [misc]backup-simplify: Simplify 2 into 2 1536754406.824 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754406.824 * [misc]taylor: Taking taylor expansion of n in n 1536754406.824 * [misc]backup-simplify: Simplify 0 into 0 1536754406.824 * [misc]backup-simplify: Simplify 1 into 1 1536754406.824 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.824 * [misc]backup-simplify: Simplify PI into PI 1536754406.824 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754406.824 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754406.825 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754406.826 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754406.826 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.826 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754406.826 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754406.827 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754406.827 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.828 * [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)))) 1536754406.828 * [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))))) 1536754406.828 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536754406.828 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754406.828 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754406.828 * [misc]taylor: Taking taylor expansion of k in n 1536754406.828 * [misc]backup-simplify: Simplify k into k 1536754406.828 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754406.828 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754406.828 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754406.829 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754406.829 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536754406.829 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536754406.829 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536754406.829 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754406.829 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.829 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.829 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754406.829 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.829 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.829 * [misc]taylor: Taking taylor expansion of k in n 1536754406.829 * [misc]backup-simplify: Simplify k into k 1536754406.829 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536754406.829 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754406.829 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.829 * [misc]backup-simplify: Simplify 2 into 2 1536754406.829 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754406.829 * [misc]taylor: Taking taylor expansion of n in n 1536754406.829 * [misc]backup-simplify: Simplify 0 into 0 1536754406.829 * [misc]backup-simplify: Simplify 1 into 1 1536754406.829 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.829 * [misc]backup-simplify: Simplify PI into PI 1536754406.829 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754406.829 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754406.830 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754406.830 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754406.830 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.830 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754406.830 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754406.831 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754406.831 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.831 * [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)))) 1536754406.832 * [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))))) 1536754406.832 * [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))) 1536754406.832 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1536754406.832 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536754406.832 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536754406.832 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754406.832 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.833 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.833 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754406.833 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.833 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.833 * [misc]taylor: Taking taylor expansion of k in k 1536754406.833 * [misc]backup-simplify: Simplify 0 into 0 1536754406.833 * [misc]backup-simplify: Simplify 1 into 1 1536754406.833 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536754406.833 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754406.833 * [misc]taylor: Taking taylor expansion of n in k 1536754406.833 * [misc]backup-simplify: Simplify n into n 1536754406.833 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754406.833 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536754406.833 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536754406.833 * [misc]taylor: Taking taylor expansion of 2 in k 1536754406.833 * [misc]backup-simplify: Simplify 2 into 2 1536754406.833 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.833 * [misc]backup-simplify: Simplify PI into PI 1536754406.833 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.833 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.833 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754406.834 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.834 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754406.834 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.834 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536754406.835 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536754406.835 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754406.835 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754406.835 * [misc]taylor: Taking taylor expansion of k in k 1536754406.835 * [misc]backup-simplify: Simplify 0 into 0 1536754406.835 * [misc]backup-simplify: Simplify 1 into 1 1536754406.835 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754406.835 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754406.835 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754406.836 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1536754406.836 * [misc]backup-simplify: Simplify 0 into 0 1536754406.836 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754406.838 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536754406.840 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754406.841 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536754406.841 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.841 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.841 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.842 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536754406.843 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754406.843 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1536754406.843 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.843 * [misc]backup-simplify: Simplify 0 into 0 1536754406.844 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536754406.844 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754406.846 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754406.846 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.846 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754406.847 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754406.847 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754406.847 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536754406.848 * [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))))))) 1536754406.850 * [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))))))) 1536754406.850 * [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))))))) 1536754406.851 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754406.852 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536754406.856 * [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 1536754406.856 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536754406.856 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.857 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.857 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.858 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536754406.860 * [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 1536754406.861 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754406.861 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536754406.862 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1536754406.862 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.863 * [misc]backup-simplify: Simplify 0 into 0 1536754406.863 * [misc]backup-simplify: Simplify 0 into 0 1536754406.863 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754406.864 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754406.866 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536754406.867 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754406.873 * [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 1536754406.873 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.874 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754406.874 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.874 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.875 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536754406.878 * [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))))) 1536754406.886 * [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)))))))) 1536754406.890 * [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)))))))) 1536754406.892 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754406.894 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536754406.904 * [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 1536754406.904 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536754406.905 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.905 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.906 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754406.907 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536754406.911 * [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 1536754406.911 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754406.911 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536754406.912 * [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 1536754406.912 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.912 * [misc]backup-simplify: Simplify 0 into 0 1536754406.913 * [misc]backup-simplify: Simplify 0 into 0 1536754406.913 * [misc]backup-simplify: Simplify 0 into 0 1536754406.913 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754406.914 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754406.917 * [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 1536754406.919 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754406.929 * [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 1536754406.929 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.929 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754406.929 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.930 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.931 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536754406.938 * [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))))))) 1536754406.956 * [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)))))))))))))) 1536754406.966 * [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)))))))))))))) 1536754406.979 * [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)))))))))))))))))))))) 1536754406.980 * [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))))) 1536754406.980 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1536754406.980 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754406.980 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754406.980 * [misc]taylor: Taking taylor expansion of k in k 1536754406.980 * [misc]backup-simplify: Simplify 0 into 0 1536754406.980 * [misc]backup-simplify: Simplify 1 into 1 1536754406.980 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754406.980 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754406.980 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754406.980 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536754406.980 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536754406.980 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754406.980 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.980 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.980 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754406.980 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.980 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.980 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754406.980 * [misc]taylor: Taking taylor expansion of k in k 1536754406.980 * [misc]backup-simplify: Simplify 0 into 0 1536754406.980 * [misc]backup-simplify: Simplify 1 into 1 1536754406.981 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754406.981 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536754406.981 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536754406.981 * [misc]taylor: Taking taylor expansion of 2 in k 1536754406.981 * [misc]backup-simplify: Simplify 2 into 2 1536754406.981 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754406.981 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.981 * [misc]backup-simplify: Simplify PI into PI 1536754406.981 * [misc]taylor: Taking taylor expansion of n in k 1536754406.981 * [misc]backup-simplify: Simplify n into n 1536754406.981 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754406.981 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536754406.981 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536754406.981 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754406.981 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754406.981 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754406.981 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536754406.982 * [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)))) 1536754406.982 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of k in n 1536754406.982 * [misc]backup-simplify: Simplify k into k 1536754406.982 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754406.982 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754406.982 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.982 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.982 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.982 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.982 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of k in n 1536754406.982 * [misc]backup-simplify: Simplify k into k 1536754406.982 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754406.982 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.982 * [misc]backup-simplify: Simplify 2 into 2 1536754406.982 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.982 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.982 * [misc]backup-simplify: Simplify PI into PI 1536754406.982 * [misc]taylor: Taking taylor expansion of n in n 1536754406.982 * [misc]backup-simplify: Simplify 0 into 0 1536754406.982 * [misc]backup-simplify: Simplify 1 into 1 1536754406.982 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.983 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.983 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.983 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754406.983 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754406.983 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754406.984 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754406.984 * [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))) 1536754406.984 * [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)))) 1536754406.984 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of k in n 1536754406.985 * [misc]backup-simplify: Simplify k into k 1536754406.985 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754406.985 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754406.985 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.985 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.985 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754406.985 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.985 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of k in n 1536754406.985 * [misc]backup-simplify: Simplify k into k 1536754406.985 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754406.985 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of 2 in n 1536754406.985 * [misc]backup-simplify: Simplify 2 into 2 1536754406.985 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754406.985 * [misc]taylor: Taking taylor expansion of PI in n 1536754406.985 * [misc]backup-simplify: Simplify PI into PI 1536754406.985 * [misc]taylor: Taking taylor expansion of n in n 1536754406.985 * [misc]backup-simplify: Simplify 0 into 0 1536754406.985 * [misc]backup-simplify: Simplify 1 into 1 1536754406.985 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754406.985 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.986 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.986 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754406.986 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754406.986 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754406.987 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754406.987 * [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))) 1536754406.988 * [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)))) 1536754406.988 * [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)) 1536754406.988 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1536754406.988 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536754406.988 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536754406.988 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754406.988 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.988 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.988 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754406.988 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754406.988 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754406.988 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754406.988 * [misc]taylor: Taking taylor expansion of k in k 1536754406.988 * [misc]backup-simplify: Simplify 0 into 0 1536754406.988 * [misc]backup-simplify: Simplify 1 into 1 1536754406.989 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754406.989 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536754406.989 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536754406.989 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536754406.989 * [misc]taylor: Taking taylor expansion of 2 in k 1536754406.989 * [misc]backup-simplify: Simplify 2 into 2 1536754406.989 * [misc]taylor: Taking taylor expansion of PI in k 1536754406.989 * [misc]backup-simplify: Simplify PI into PI 1536754406.989 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754406.989 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754406.989 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754406.989 * [misc]taylor: Taking taylor expansion of n in k 1536754406.989 * [misc]backup-simplify: Simplify n into n 1536754406.989 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754406.989 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754406.989 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754406.990 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754406.990 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754406.990 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536754406.991 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536754406.991 * [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)))) 1536754406.991 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754406.991 * [misc]taylor: Taking taylor expansion of k in k 1536754406.991 * [misc]backup-simplify: Simplify 0 into 0 1536754406.991 * [misc]backup-simplify: Simplify 1 into 1 1536754406.991 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754406.991 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754406.992 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1536754406.992 * [misc]backup-simplify: Simplify 0 into 0 1536754406.993 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754406.993 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754406.995 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754406.995 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754406.995 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754406.996 * [misc]backup-simplify: Simplify (- 0) into 0 1536754406.996 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754406.996 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754406.997 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536754406.998 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754406.998 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1536754406.998 * [misc]taylor: Taking taylor expansion of 0 in k 1536754406.998 * [misc]backup-simplify: Simplify 0 into 0 1536754406.998 * [misc]backup-simplify: Simplify 0 into 0 1536754406.999 * [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)))))) 1536754406.999 * [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)))))) 1536754407.000 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754407.001 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754407.004 * [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 1536754407.005 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754407.005 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754407.005 * [misc]backup-simplify: Simplify (- 0) into 0 1536754407.005 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754407.006 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754407.006 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536754407.008 * [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 1536754407.009 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536754407.010 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1536754407.010 * [misc]taylor: Taking taylor expansion of 0 in k 1536754407.010 * [misc]backup-simplify: Simplify 0 into 0 1536754407.010 * [misc]backup-simplify: Simplify 0 into 0 1536754407.010 * [misc]backup-simplify: Simplify 0 into 0 1536754407.011 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754407.012 * [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)))))) 1536754407.013 * [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)))))) 1536754407.015 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754407.016 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754407.026 * [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 1536754407.026 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754407.027 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754407.027 * [misc]backup-simplify: Simplify (- 0) into 0 1536754407.027 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754407.028 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754407.029 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536754407.033 * [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 1536754407.033 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536754407.034 * [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 1536754407.034 * [misc]taylor: Taking taylor expansion of 0 in k 1536754407.035 * [misc]backup-simplify: Simplify 0 into 0 1536754407.035 * [misc]backup-simplify: Simplify 0 into 0 1536754407.035 * [misc]backup-simplify: Simplify 0 into 0 1536754407.035 * [misc]backup-simplify: Simplify 0 into 0 1536754407.036 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754407.037 * [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)))))) 1536754407.038 * [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)))))) 1536754407.041 * [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)))))))) 1536754407.042 * [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))) 1536754407.042 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1536754407.042 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536754407.042 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754407.042 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536754407.042 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536754407.042 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754407.042 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754407.042 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754407.042 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754407.042 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754407.042 * [misc]taylor: Taking taylor expansion of k in k 1536754407.042 * [misc]backup-simplify: Simplify 0 into 0 1536754407.042 * [misc]backup-simplify: Simplify 1 into 1 1536754407.043 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754407.043 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754407.043 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754407.043 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536754407.043 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536754407.043 * [misc]taylor: Taking taylor expansion of -2 in k 1536754407.043 * [misc]backup-simplify: Simplify -2 into -2 1536754407.043 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754407.043 * [misc]taylor: Taking taylor expansion of PI in k 1536754407.043 * [misc]backup-simplify: Simplify PI into PI 1536754407.043 * [misc]taylor: Taking taylor expansion of n in k 1536754407.043 * [misc]backup-simplify: Simplify n into n 1536754407.043 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754407.043 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536754407.043 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536754407.044 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754407.044 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754407.044 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536754407.044 * [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))) 1536754407.044 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754407.044 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754407.044 * [misc]taylor: Taking taylor expansion of -1 in k 1536754407.044 * [misc]backup-simplify: Simplify -1 into -1 1536754407.044 * [misc]taylor: Taking taylor expansion of k in k 1536754407.044 * [misc]backup-simplify: Simplify 0 into 0 1536754407.045 * [misc]backup-simplify: Simplify 1 into 1 1536754407.045 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754407.045 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754407.046 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754407.046 * [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)))) 1536754407.046 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754407.046 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754407.046 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of k in n 1536754407.046 * [misc]backup-simplify: Simplify k into k 1536754407.046 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754407.046 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754407.046 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754407.046 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754407.046 * [misc]taylor: Taking taylor expansion of -2 in n 1536754407.047 * [misc]backup-simplify: Simplify -2 into -2 1536754407.047 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754407.047 * [misc]taylor: Taking taylor expansion of PI in n 1536754407.047 * [misc]backup-simplify: Simplify PI into PI 1536754407.047 * [misc]taylor: Taking taylor expansion of n in n 1536754407.047 * [misc]backup-simplify: Simplify 0 into 0 1536754407.047 * [misc]backup-simplify: Simplify 1 into 1 1536754407.047 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754407.047 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754407.048 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754407.048 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754407.048 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754407.049 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754407.050 * [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))) 1536754407.050 * [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)))) 1536754407.050 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754407.050 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754407.050 * [misc]taylor: Taking taylor expansion of -1 in n 1536754407.050 * [misc]backup-simplify: Simplify -1 into -1 1536754407.051 * [misc]taylor: Taking taylor expansion of k in n 1536754407.051 * [misc]backup-simplify: Simplify k into k 1536754407.051 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754407.051 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754407.051 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754407.051 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754407.052 * [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))) 1536754407.052 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754407.052 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754407.052 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of k in n 1536754407.052 * [misc]backup-simplify: Simplify k into k 1536754407.052 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754407.052 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754407.052 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754407.052 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of -2 in n 1536754407.052 * [misc]backup-simplify: Simplify -2 into -2 1536754407.052 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754407.052 * [misc]taylor: Taking taylor expansion of PI in n 1536754407.052 * [misc]backup-simplify: Simplify PI into PI 1536754407.052 * [misc]taylor: Taking taylor expansion of n in n 1536754407.053 * [misc]backup-simplify: Simplify 0 into 0 1536754407.053 * [misc]backup-simplify: Simplify 1 into 1 1536754407.053 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754407.053 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754407.054 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754407.054 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754407.054 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754407.055 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754407.055 * [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))) 1536754407.056 * [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)))) 1536754407.056 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754407.056 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754407.056 * [misc]taylor: Taking taylor expansion of -1 in n 1536754407.056 * [misc]backup-simplify: Simplify -1 into -1 1536754407.056 * [misc]taylor: Taking taylor expansion of k in n 1536754407.056 * [misc]backup-simplify: Simplify k into k 1536754407.056 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754407.056 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754407.057 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754407.057 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754407.057 * [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))) 1536754407.058 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754407.058 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754407.058 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of k in k 1536754407.058 * [misc]backup-simplify: Simplify 0 into 0 1536754407.058 * [misc]backup-simplify: Simplify 1 into 1 1536754407.058 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754407.058 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754407.058 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754407.058 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536754407.058 * [misc]taylor: Taking taylor expansion of -2 in k 1536754407.058 * [misc]backup-simplify: Simplify -2 into -2 1536754407.058 * [misc]taylor: Taking taylor expansion of PI in k 1536754407.058 * [misc]backup-simplify: Simplify PI into PI 1536754407.059 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754407.059 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754407.059 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754407.059 * [misc]taylor: Taking taylor expansion of n in k 1536754407.059 * [misc]backup-simplify: Simplify n into n 1536754407.059 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754407.059 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754407.060 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754407.060 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754407.060 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536754407.061 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536754407.062 * [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)))) 1536754407.062 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754407.062 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754407.062 * [misc]taylor: Taking taylor expansion of -1 in k 1536754407.062 * [misc]backup-simplify: Simplify -1 into -1 1536754407.062 * [misc]taylor: Taking taylor expansion of k in k 1536754407.062 * [misc]backup-simplify: Simplify 0 into 0 1536754407.062 * [misc]backup-simplify: Simplify 1 into 1 1536754407.062 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754407.062 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754407.063 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754407.064 * [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))))) 1536754407.064 * [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))))) 1536754407.066 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754407.066 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536754407.069 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536754407.070 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754407.070 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754407.070 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754407.071 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754407.072 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536754407.073 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754407.075 * [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 1536754407.075 * [misc]taylor: Taking taylor expansion of 0 in k 1536754407.075 * [misc]backup-simplify: Simplify 0 into 0 1536754407.075 * [misc]backup-simplify: Simplify 0 into 0 1536754407.075 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754407.076 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754407.077 * [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)))))) 1536754407.078 * [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)))))) 1536754407.080 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754407.081 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754407.087 * [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 1536754407.087 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754407.088 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754407.088 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754407.089 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754407.090 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536754407.092 * [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 1536754407.092 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754407.093 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536754407.094 * [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 1536754407.094 * [misc]taylor: Taking taylor expansion of 0 in k 1536754407.094 * [misc]backup-simplify: Simplify 0 into 0 1536754407.094 * [misc]backup-simplify: Simplify 0 into 0 1536754407.094 * [misc]backup-simplify: Simplify 0 into 0 1536754407.095 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754407.096 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754407.099 * [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)))))) 1536754407.100 * [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)))))) 1536754407.103 * [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))))))))))) 1536754407.103 * * * [misc]progress: simplifying candidates 1536754407.103 * * * * [misc]progress: [ 1 / 83 ] simplifiying candidate # 1536754407.103 * * * * [misc]progress: [ 2 / 83 ] simplifiying candidate # 1536754407.103 * * * * [misc]progress: [ 3 / 83 ] simplifiying candidate # 1536754407.104 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1536754407.105 * * [misc]simplify: iters left: 6 (11 enodes) 1536754407.112 * * [misc]simplify: iters left: 5 (21 enodes) 1536754407.124 * * [misc]simplify: iters left: 4 (47 enodes) 1536754407.152 * * [misc]simplify: iters left: 3 (113 enodes) 1536754407.230 * * [misc]simplify: iters left: 2 (328 enodes) 1536754407.648 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1536754407.648 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1536754407.648 * * * * [misc]progress: [ 4 / 83 ] simplifiying candidate # 1536754407.648 * * * * [misc]progress: [ 5 / 83 ] simplifiying candidate # 1536754407.649 * [enter]simplify: Simplifying (* PI (* n 2)) 1536754407.649 * * [misc]simplify: iters left: 4 (5 enodes) 1536754407.652 * * [misc]simplify: iters left: 3 (9 enodes) 1536754407.656 * * [misc]simplify: iters left: 2 (15 enodes) 1536754407.661 * * [misc]simplify: iters left: 1 (17 enodes) 1536754407.666 * [exit]simplify: Simplified to (* (* 2 n) PI) 1536754407.666 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1536754407.666 * * * * [misc]progress: [ 6 / 83 ] simplifiying candidate # 1536754407.666 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1536754407.667 * * [misc]simplify: iters left: 5 (8 enodes) 1536754407.670 * * [misc]simplify: iters left: 4 (12 enodes) 1536754407.676 * * [misc]simplify: iters left: 3 (18 enodes) 1536754407.682 * * [misc]simplify: iters left: 2 (20 enodes) 1536754407.688 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1536754407.688 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1536754407.688 * * * * [misc]progress: [ 7 / 83 ] simplifiying candidate # 1536754407.689 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536754407.689 * * [misc]simplify: iters left: 5 (6 enodes) 1536754407.693 * * [misc]simplify: iters left: 4 (8 enodes) 1536754407.696 * * [misc]simplify: iters left: 3 (11 enodes) 1536754407.700 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536754407.700 * [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))) 1536754407.700 * * * * [misc]progress: [ 8 / 83 ] simplifiying candidate # 1536754407.700 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536754407.701 * * [misc]simplify: iters left: 5 (6 enodes) 1536754407.703 * * [misc]simplify: iters left: 4 (8 enodes) 1536754407.707 * * [misc]simplify: iters left: 3 (11 enodes) 1536754407.711 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536754407.711 * [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))) 1536754407.711 * * * * [misc]progress: [ 9 / 83 ] simplifiying candidate # 1536754407.711 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536754407.712 * * [misc]simplify: iters left: 4 (5 enodes) 1536754407.712 * * [misc]simplify: iters left: 3 (7 enodes) 1536754407.714 * * [misc]simplify: iters left: 2 (10 enodes) 1536754407.715 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536754407.715 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1536754407.716 * * * * [misc]progress: [ 10 / 83 ] simplifiying candidate # 1536754407.716 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1536754407.716 * * [misc]simplify: iters left: 5 (9 enodes) 1536754407.718 * * [misc]simplify: iters left: 4 (15 enodes) 1536754407.721 * * [misc]simplify: iters left: 3 (21 enodes) 1536754407.725 * * [misc]simplify: iters left: 2 (22 enodes) 1536754407.728 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1536754407.728 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1536754407.728 * * * * [misc]progress: [ 11 / 83 ] simplifiying candidate # 1536754407.729 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1536754407.729 * * [misc]simplify: iters left: 5 (9 enodes) 1536754407.731 * * [misc]simplify: iters left: 4 (15 enodes) 1536754407.734 * * [misc]simplify: iters left: 3 (21 enodes) 1536754407.737 * * [misc]simplify: iters left: 2 (22 enodes) 1536754407.741 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1536754407.741 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1536754407.741 * * * * [misc]progress: [ 12 / 83 ] simplifiying candidate # 1536754407.741 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1536754407.742 * * [misc]simplify: iters left: 5 (7 enodes) 1536754407.743 * * [misc]simplify: iters left: 4 (9 enodes) 1536754407.745 * * [misc]simplify: iters left: 3 (12 enodes) 1536754407.747 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536754407.747 * [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))) 1536754407.747 * * * * [misc]progress: [ 13 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 14 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 15 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 16 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 17 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 18 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 19 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 20 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 21 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 22 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 23 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 24 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 25 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 26 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 27 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 28 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 29 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 30 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 31 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 32 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 33 / 83 ] simplifiying candidate # 1536754407.747 * * * * [misc]progress: [ 34 / 83 ] simplifiying candidate # 1536754407.748 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754407.748 * * [misc]simplify: iters left: 6 (14 enodes) 1536754407.752 * * [misc]simplify: iters left: 5 (27 enodes) 1536754407.763 * * [misc]simplify: iters left: 4 (55 enodes) 1536754407.801 * * [misc]simplify: iters left: 3 (144 enodes) 1536754407.965 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1536754407.965 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1536754407.965 * * * * [misc]progress: [ 35 / 83 ] simplifiying candidate # 1536754407.965 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754407.966 * * [misc]simplify: iters left: 6 (14 enodes) 1536754407.970 * * [misc]simplify: iters left: 5 (27 enodes) 1536754407.977 * * [misc]simplify: iters left: 4 (55 enodes) 1536754407.996 * * [misc]simplify: iters left: 3 (144 enodes) 1536754408.165 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1536754408.165 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1536754408.165 * * * * [misc]progress: [ 36 / 83 ] simplifiying candidate # 1536754408.166 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1536754408.167 * * [misc]simplify: iters left: 6 (14 enodes) 1536754408.174 * * [misc]simplify: iters left: 5 (24 enodes) 1536754408.184 * * [misc]simplify: iters left: 4 (43 enodes) 1536754408.194 * * [misc]simplify: iters left: 3 (73 enodes) 1536754408.243 * * [misc]simplify: iters left: 2 (220 enodes) 1536754408.562 * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1536754408.562 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1536754408.562 * * * * [misc]progress: [ 37 / 83 ] simplifiying candidate # 1536754408.562 * * * * [misc]progress: [ 38 / 83 ] simplifiying candidate # 1536754408.562 * * * * [misc]progress: [ 39 / 83 ] simplifiying candidate # 1536754408.562 * [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))) 1536754408.564 * * [misc]simplify: iters left: 6 (16 enodes) 1536754408.572 * * [misc]simplify: iters left: 5 (31 enodes) 1536754408.580 * * [misc]simplify: iters left: 4 (67 enodes) 1536754408.597 * * [misc]simplify: iters left: 3 (124 enodes) 1536754408.630 * * [misc]simplify: iters left: 2 (195 enodes) 1536754408.718 * * [misc]simplify: iters left: 1 (309 enodes) 1536754409.246 * [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)))) 1536754409.246 * [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)))))) 1536754409.246 * * * * [misc]progress: [ 40 / 83 ] simplifiying candidate # 1536754409.246 * * * * [misc]progress: [ 41 / 83 ] simplifiying candidate # 1536754409.247 * * * * [misc]progress: [ 42 / 83 ] simplifiying candidate # 1536754409.247 * * * * [misc]progress: [ 43 / 83 ] simplifiying candidate # 1536754409.247 * * * * [misc]progress: [ 44 / 83 ] simplifiying candidate # 1536754409.247 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.248 * * [misc]simplify: iters left: 6 (12 enodes) 1536754409.253 * * [misc]simplify: iters left: 5 (19 enodes) 1536754409.260 * * [misc]simplify: iters left: 4 (25 enodes) 1536754409.268 * * [misc]simplify: iters left: 3 (26 enodes) 1536754409.277 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.277 * [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))))) 1536754409.278 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1536754409.279 * * [misc]simplify: iters left: 6 (12 enodes) 1536754409.284 * * [misc]simplify: iters left: 5 (18 enodes) 1536754409.291 * * [misc]simplify: iters left: 4 (24 enodes) 1536754409.299 * * [misc]simplify: iters left: 3 (25 enodes) 1536754409.307 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754409.307 * [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))))) 1536754409.307 * * * * [misc]progress: [ 45 / 83 ] simplifiying candidate # 1536754409.308 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1536754409.309 * * [misc]simplify: iters left: 6 (11 enodes) 1536754409.313 * * [misc]simplify: iters left: 5 (16 enodes) 1536754409.319 * * [misc]simplify: iters left: 4 (22 enodes) 1536754409.326 * * [misc]simplify: iters left: 3 (24 enodes) 1536754409.334 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1536754409.334 * [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))))) 1536754409.335 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1536754409.336 * * [misc]simplify: iters left: 6 (12 enodes) 1536754409.341 * * [misc]simplify: iters left: 5 (18 enodes) 1536754409.349 * * [misc]simplify: iters left: 4 (24 enodes) 1536754409.357 * * [misc]simplify: iters left: 3 (25 enodes) 1536754409.365 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754409.365 * [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))))) 1536754409.365 * * * * [misc]progress: [ 46 / 83 ] simplifiying candidate # 1536754409.365 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1536754409.366 * * [misc]simplify: iters left: 6 (9 enodes) 1536754409.370 * * [misc]simplify: iters left: 5 (16 enodes) 1536754409.377 * * [misc]simplify: iters left: 4 (24 enodes) 1536754409.386 * * [misc]simplify: iters left: 3 (26 enodes) 1536754409.393 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1536754409.393 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536754409.394 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536754409.395 * * [misc]simplify: iters left: 6 (11 enodes) 1536754409.400 * * [misc]simplify: iters left: 5 (17 enodes) 1536754409.406 * * [misc]simplify: iters left: 4 (23 enodes) 1536754409.413 * * [misc]simplify: iters left: 3 (24 enodes) 1536754409.418 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536754409.418 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536754409.418 * * * * [misc]progress: [ 47 / 83 ] simplifiying candidate # 1536754409.418 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.419 * * [misc]simplify: iters left: 6 (12 enodes) 1536754409.422 * * [misc]simplify: iters left: 5 (19 enodes) 1536754409.425 * * [misc]simplify: iters left: 4 (25 enodes) 1536754409.429 * * [misc]simplify: iters left: 3 (26 enodes) 1536754409.434 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.434 * [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))))) 1536754409.434 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1536754409.434 * * [misc]simplify: iters left: 6 (12 enodes) 1536754409.437 * * [misc]simplify: iters left: 5 (18 enodes) 1536754409.440 * * [misc]simplify: iters left: 4 (24 enodes) 1536754409.444 * * [misc]simplify: iters left: 3 (25 enodes) 1536754409.448 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754409.448 * [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))))) 1536754409.448 * * * * [misc]progress: [ 48 / 83 ] simplifiying candidate # 1536754409.448 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1536754409.449 * * [misc]simplify: iters left: 6 (11 enodes) 1536754409.451 * * [misc]simplify: iters left: 5 (16 enodes) 1536754409.454 * * [misc]simplify: iters left: 4 (22 enodes) 1536754409.458 * * [misc]simplify: iters left: 3 (24 enodes) 1536754409.462 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1536754409.462 * [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))))) 1536754409.462 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1536754409.463 * * [misc]simplify: iters left: 6 (12 enodes) 1536754409.465 * * [misc]simplify: iters left: 5 (18 enodes) 1536754409.470 * * [misc]simplify: iters left: 4 (24 enodes) 1536754409.473 * * [misc]simplify: iters left: 3 (25 enodes) 1536754409.478 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754409.478 * [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))))) 1536754409.478 * * * * [misc]progress: [ 49 / 83 ] simplifiying candidate # 1536754409.478 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1536754409.478 * * [misc]simplify: iters left: 6 (9 enodes) 1536754409.482 * * [misc]simplify: iters left: 5 (16 enodes) 1536754409.489 * * [misc]simplify: iters left: 4 (24 enodes) 1536754409.495 * * [misc]simplify: iters left: 3 (26 enodes) 1536754409.499 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1536754409.499 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536754409.499 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536754409.500 * * [misc]simplify: iters left: 6 (11 enodes) 1536754409.502 * * [misc]simplify: iters left: 5 (17 enodes) 1536754409.505 * * [misc]simplify: iters left: 4 (23 enodes) 1536754409.509 * * [misc]simplify: iters left: 3 (24 enodes) 1536754409.513 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536754409.513 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536754409.513 * * * * [misc]progress: [ 50 / 83 ] simplifiying candidate # 1536754409.513 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.514 * * [misc]simplify: iters left: 6 (11 enodes) 1536754409.516 * * [misc]simplify: iters left: 5 (15 enodes) 1536754409.519 * * [misc]simplify: iters left: 4 (18 enodes) 1536754409.522 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.522 * [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))))) 1536754409.522 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754409.523 * * [misc]simplify: iters left: 6 (11 enodes) 1536754409.526 * * [misc]simplify: iters left: 5 (14 enodes) 1536754409.530 * * [misc]simplify: iters left: 4 (17 enodes) 1536754409.536 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754409.536 * [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))))) 1536754409.536 * * * * [misc]progress: [ 51 / 83 ] simplifiying candidate # 1536754409.536 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754409.537 * * [misc]simplify: iters left: 6 (10 enodes) 1536754409.541 * * [misc]simplify: iters left: 5 (12 enodes) 1536754409.545 * * [misc]simplify: iters left: 4 (15 enodes) 1536754409.550 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754409.550 * [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))))) 1536754409.550 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754409.551 * * [misc]simplify: iters left: 6 (11 enodes) 1536754409.555 * * [misc]simplify: iters left: 5 (14 enodes) 1536754409.558 * * [misc]simplify: iters left: 4 (17 enodes) 1536754409.561 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754409.561 * [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))))) 1536754409.561 * * * * [misc]progress: [ 52 / 83 ] simplifiying candidate # 1536754409.561 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1536754409.561 * * [misc]simplify: iters left: 6 (9 enodes) 1536754409.565 * * [misc]simplify: iters left: 5 (13 enodes) 1536754409.568 * * [misc]simplify: iters left: 4 (18 enodes) 1536754409.570 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536754409.570 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1536754409.570 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1536754409.571 * * [misc]simplify: iters left: 6 (10 enodes) 1536754409.573 * * [misc]simplify: iters left: 5 (13 enodes) 1536754409.575 * * [misc]simplify: iters left: 4 (16 enodes) 1536754409.578 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1536754409.578 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1536754409.579 * * * * [misc]progress: [ 53 / 83 ] simplifiying candidate # 1536754409.579 * [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)))) 1536754409.580 * * [misc]simplify: iters left: 6 (16 enodes) 1536754409.585 * * [misc]simplify: iters left: 5 (28 enodes) 1536754409.592 * * [misc]simplify: iters left: 4 (46 enodes) 1536754409.599 * * [misc]simplify: iters left: 3 (50 enodes) 1536754409.606 * * [misc]simplify: iters left: 2 (53 enodes) 1536754409.622 * [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)))) 1536754409.622 * [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))))) 1536754409.623 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754409.624 * * [misc]simplify: iters left: 6 (14 enodes) 1536754409.626 * * [misc]simplify: iters left: 5 (20 enodes) 1536754409.630 * * [misc]simplify: iters left: 4 (29 enodes) 1536754409.635 * * [misc]simplify: iters left: 3 (30 enodes) 1536754409.639 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754409.639 * [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))))) 1536754409.640 * * * * [misc]progress: [ 54 / 83 ] simplifiying candidate # 1536754409.640 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536754409.641 * * [misc]simplify: iters left: 6 (15 enodes) 1536754409.645 * * [misc]simplify: iters left: 5 (23 enodes) 1536754409.653 * * [misc]simplify: iters left: 4 (34 enodes) 1536754409.664 * * [misc]simplify: iters left: 3 (37 enodes) 1536754409.678 * [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)))))) 1536754409.679 * [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))))) 1536754409.679 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754409.680 * * [misc]simplify: iters left: 6 (14 enodes) 1536754409.686 * * [misc]simplify: iters left: 5 (20 enodes) 1536754409.694 * * [misc]simplify: iters left: 4 (29 enodes) 1536754409.703 * * [misc]simplify: iters left: 3 (30 enodes) 1536754409.713 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754409.713 * [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))))) 1536754409.713 * * * * [misc]progress: [ 55 / 83 ] simplifiying candidate # 1536754409.714 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1536754409.715 * * [misc]simplify: iters left: 6 (14 enodes) 1536754409.721 * * [misc]simplify: iters left: 5 (24 enodes) 1536754409.732 * * [misc]simplify: iters left: 4 (39 enodes) 1536754409.745 * * [misc]simplify: iters left: 3 (54 enodes) 1536754409.763 * * [misc]simplify: iters left: 2 (80 enodes) 1536754409.790 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1536754409.790 * [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)))) 1536754409.790 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1536754409.792 * * [misc]simplify: iters left: 6 (13 enodes) 1536754409.797 * * [misc]simplify: iters left: 5 (19 enodes) 1536754409.804 * * [misc]simplify: iters left: 4 (28 enodes) 1536754409.813 * * [misc]simplify: iters left: 3 (30 enodes) 1536754409.823 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754409.823 * [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)))) 1536754409.823 * * * * [misc]progress: [ 56 / 83 ] simplifiying candidate # 1536754409.823 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.825 * * [misc]simplify: iters left: 6 (15 enodes) 1536754409.831 * * [misc]simplify: iters left: 5 (23 enodes) 1536754409.840 * * [misc]simplify: iters left: 4 (32 enodes) 1536754409.850 * * [misc]simplify: iters left: 3 (34 enodes) 1536754409.862 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.862 * [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))))) 1536754409.862 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754409.864 * * [misc]simplify: iters left: 6 (14 enodes) 1536754409.869 * * [misc]simplify: iters left: 5 (20 enodes) 1536754409.876 * * [misc]simplify: iters left: 4 (29 enodes) 1536754409.881 * * [misc]simplify: iters left: 3 (30 enodes) 1536754409.886 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754409.886 * [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))))) 1536754409.886 * * * * [misc]progress: [ 57 / 83 ] simplifiying candidate # 1536754409.886 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754409.887 * * [misc]simplify: iters left: 6 (14 enodes) 1536754409.890 * * [misc]simplify: iters left: 5 (20 enodes) 1536754409.894 * * [misc]simplify: iters left: 4 (29 enodes) 1536754409.898 * * [misc]simplify: iters left: 3 (30 enodes) 1536754409.906 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754409.906 * [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))))) 1536754409.906 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754409.907 * * [misc]simplify: iters left: 6 (14 enodes) 1536754409.913 * * [misc]simplify: iters left: 5 (20 enodes) 1536754409.921 * * [misc]simplify: iters left: 4 (29 enodes) 1536754409.929 * * [misc]simplify: iters left: 3 (30 enodes) 1536754409.937 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754409.937 * [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))))) 1536754409.937 * * * * [misc]progress: [ 58 / 83 ] simplifiying candidate # 1536754409.938 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1536754409.938 * * [misc]simplify: iters left: 6 (13 enodes) 1536754409.941 * * [misc]simplify: iters left: 5 (21 enodes) 1536754409.946 * * [misc]simplify: iters left: 4 (32 enodes) 1536754409.950 * * [misc]simplify: iters left: 3 (33 enodes) 1536754409.955 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1536754409.955 * [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)))) 1536754409.955 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1536754409.956 * * [misc]simplify: iters left: 6 (13 enodes) 1536754409.959 * * [misc]simplify: iters left: 5 (19 enodes) 1536754409.963 * * [misc]simplify: iters left: 4 (28 enodes) 1536754409.971 * * [misc]simplify: iters left: 3 (30 enodes) 1536754409.980 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754409.980 * [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)))) 1536754409.980 * * * * [misc]progress: [ 59 / 83 ] simplifiying candidate # 1536754409.980 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754409.981 * * [misc]simplify: iters left: 6 (6 enodes) 1536754409.982 * * [misc]simplify: iters left: 5 (10 enodes) 1536754409.984 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536754409.984 * [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))))) 1536754409.984 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754409.985 * * [misc]simplify: iters left: 6 (13 enodes) 1536754409.987 * * [misc]simplify: iters left: 5 (19 enodes) 1536754409.991 * * [misc]simplify: iters left: 4 (28 enodes) 1536754409.997 * * [misc]simplify: iters left: 3 (30 enodes) 1536754410.002 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754410.002 * [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))))) 1536754410.002 * * * * [misc]progress: [ 60 / 83 ] simplifiying candidate # 1536754410.002 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536754410.003 * * [misc]simplify: iters left: 4 (5 enodes) 1536754410.004 * * [misc]simplify: iters left: 3 (7 enodes) 1536754410.005 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536754410.005 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536754410.005 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754410.005 * * [misc]simplify: iters left: 6 (13 enodes) 1536754410.009 * * [misc]simplify: iters left: 5 (19 enodes) 1536754410.016 * * [misc]simplify: iters left: 4 (28 enodes) 1536754410.020 * * [misc]simplify: iters left: 3 (30 enodes) 1536754410.025 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754410.025 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536754410.025 * * * * [misc]progress: [ 61 / 83 ] simplifiying candidate # 1536754410.025 * [enter]simplify: Simplifying (/ 1 1) 1536754410.025 * * [misc]simplify: iters left: 2 (2 enodes) 1536754410.026 * * [misc]simplify: iters left: 1 (4 enodes) 1536754410.026 * [exit]simplify: Simplified to 1 1536754410.026 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1536754410.026 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1536754410.027 * * [misc]simplify: iters left: 6 (12 enodes) 1536754410.029 * * [misc]simplify: iters left: 5 (18 enodes) 1536754410.033 * * [misc]simplify: iters left: 4 (27 enodes) 1536754410.039 * * [misc]simplify: iters left: 3 (29 enodes) 1536754410.049 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754410.049 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754410.049 * * * * [misc]progress: [ 62 / 83 ] simplifiying candidate # 1536754410.049 * * * * [misc]progress: [ 63 / 83 ] simplifiying candidate # 1536754410.049 * * * * [misc]progress: [ 64 / 83 ] simplifiying candidate # 1536754410.049 * * * * [misc]progress: [ 65 / 83 ] simplifiying candidate # 1536754410.050 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536754410.050 * * [misc]simplify: iters left: 2 (3 enodes) 1536754410.051 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536754410.051 * [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)))) 1536754410.051 * * * * [misc]progress: [ 66 / 83 ] simplifiying candidate # 1536754410.052 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536754410.052 * * [misc]simplify: iters left: 2 (3 enodes) 1536754410.053 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536754410.053 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1536754410.053 * * * * [misc]progress: [ 67 / 83 ] simplifiying candidate # 1536754410.054 * [enter]simplify: Simplifying (sqrt k) 1536754410.054 * * [misc]simplify: iters left: 1 (2 enodes) 1536754410.054 * [exit]simplify: Simplified to (sqrt k) 1536754410.054 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1536754410.055 * * * * [misc]progress: [ 68 / 83 ] simplifiying candidate # 1536754410.055 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536754410.055 * * [misc]simplify: iters left: 5 (7 enodes) 1536754410.057 * * [misc]simplify: iters left: 4 (12 enodes) 1536754410.059 * * [misc]simplify: iters left: 3 (18 enodes) 1536754410.062 * * [misc]simplify: iters left: 2 (20 enodes) 1536754410.065 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536754410.066 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1536754410.066 * * * * [misc]progress: [ 69 / 83 ] simplifiying candidate # 1536754410.066 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536754410.066 * * [misc]simplify: iters left: 5 (7 enodes) 1536754410.068 * * [misc]simplify: iters left: 4 (12 enodes) 1536754410.070 * * [misc]simplify: iters left: 3 (18 enodes) 1536754410.073 * * [misc]simplify: iters left: 2 (20 enodes) 1536754410.076 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536754410.076 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1536754410.076 * * * * [misc]progress: [ 70 / 83 ] simplifiying candidate # 1536754410.076 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1536754410.077 * * [misc]simplify: iters left: 5 (7 enodes) 1536754410.078 * * [misc]simplify: iters left: 4 (9 enodes) 1536754410.081 * * [misc]simplify: iters left: 3 (12 enodes) 1536754410.083 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536754410.083 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1536754410.083 * * * * [misc]progress: [ 71 / 83 ] simplifiying candidate # 1536754410.083 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1536754410.084 * * [misc]simplify: iters left: 6 (12 enodes) 1536754410.089 * * [misc]simplify: iters left: 5 (18 enodes) 1536754410.097 * * [misc]simplify: iters left: 4 (27 enodes) 1536754410.106 * * [misc]simplify: iters left: 3 (29 enodes) 1536754410.116 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1536754410.116 * [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))))))) 1536754410.116 * * * * [misc]progress: [ 72 / 83 ] simplifiying candidate # 1536754410.117 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1536754410.118 * * [misc]simplify: iters left: 6 (11 enodes) 1536754410.122 * * [misc]simplify: iters left: 5 (17 enodes) 1536754410.129 * * [misc]simplify: iters left: 4 (26 enodes) 1536754410.137 * * [misc]simplify: iters left: 3 (27 enodes) 1536754410.146 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1536754410.146 * [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))))))) 1536754410.146 * * * * [misc]progress: [ 73 / 83 ] simplifiying candidate # 1536754410.147 * * * * [misc]progress: [ 74 / 83 ] simplifiying candidate # 1536754410.147 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536754410.147 * * [misc]simplify: iters left: 5 (7 enodes) 1536754410.149 * * [misc]simplify: iters left: 4 (12 enodes) 1536754410.151 * * [misc]simplify: iters left: 3 (18 enodes) 1536754410.154 * * [misc]simplify: iters left: 2 (20 enodes) 1536754410.157 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536754410.157 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536754410.157 * * * * [misc]progress: [ 75 / 83 ] simplifiying candidate # 1536754410.158 * [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))))) 1536754410.160 * * [misc]simplify: iters left: 6 (37 enodes) 1536754410.174 * * [misc]simplify: iters left: 5 (108 enodes) 1536754410.232 * * [misc]simplify: iters left: 4 (368 enodes) 1536754410.796 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1536754410.796 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) 1536754410.796 * * * * [misc]progress: [ 76 / 83 ] simplifiying candidate # 1536754410.796 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1536754410.797 * * [misc]simplify: iters left: 6 (15 enodes) 1536754410.802 * * [misc]simplify: iters left: 5 (33 enodes) 1536754410.811 * * [misc]simplify: iters left: 4 (64 enodes) 1536754410.847 * * [misc]simplify: iters left: 3 (179 enodes) 1536754411.027 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1536754411.027 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) 1536754411.027 * * * * [misc]progress: [ 77 / 83 ] simplifiying candidate # 1536754411.027 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1536754411.029 * * [misc]simplify: iters left: 6 (15 enodes) 1536754411.037 * * [misc]simplify: iters left: 5 (30 enodes) 1536754411.054 * * [misc]simplify: iters left: 4 (65 enodes) 1536754411.085 * * [misc]simplify: iters left: 3 (208 enodes) 1536754411.398 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1536754411.398 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1536754411.398 * * * * [misc]progress: [ 78 / 83 ] simplifiying candidate # 1536754411.399 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536754411.399 * * [misc]simplify: iters left: 4 (5 enodes) 1536754411.400 * * [misc]simplify: iters left: 3 (9 enodes) 1536754411.402 * * [misc]simplify: iters left: 2 (15 enodes) 1536754411.405 * * [misc]simplify: iters left: 1 (17 enodes) 1536754411.408 * [exit]simplify: Simplified to (* (* PI n) 2) 1536754411.408 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536754411.408 * * * * [misc]progress: [ 79 / 83 ] simplifiying candidate # 1536754411.408 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536754411.409 * * [misc]simplify: iters left: 4 (5 enodes) 1536754411.410 * * [misc]simplify: iters left: 3 (9 enodes) 1536754411.412 * * [misc]simplify: iters left: 2 (15 enodes) 1536754411.415 * * [misc]simplify: iters left: 1 (17 enodes) 1536754411.417 * [exit]simplify: Simplified to (* (* PI n) 2) 1536754411.417 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536754411.417 * * * * [misc]progress: [ 80 / 83 ] simplifiying candidate # 1536754411.417 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536754411.418 * * [misc]simplify: iters left: 4 (5 enodes) 1536754411.419 * * [misc]simplify: iters left: 3 (9 enodes) 1536754411.421 * * [misc]simplify: iters left: 2 (15 enodes) 1536754411.424 * * [misc]simplify: iters left: 1 (17 enodes) 1536754411.426 * [exit]simplify: Simplified to (* (* PI n) 2) 1536754411.426 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536754411.427 * * * * [misc]progress: [ 81 / 83 ] simplifiying candidate # 1536754411.427 * [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)))))))))))))))))))))) 1536754411.427 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754411.427 * * * * [misc]progress: [ 82 / 83 ] simplifiying candidate # 1536754411.427 * [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)))))))) 1536754411.427 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754411.427 * * * * [misc]progress: [ 83 / 83 ] simplifiying candidate # 1536754411.427 * [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))))))))))) 1536754411.427 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754411.427 * * * [misc]progress: adding candidates to table 1536754412.931 * * [misc]progress: iteration 2 / 4 1536754412.931 * * * [misc]progress: picking best candidate 1536754413.034 * * * * [misc]pick: Picked # 1536754413.034 * * * [misc]progress: localizing error 1536754413.056 * * * [misc]progress: generating rewritten candidates 1536754413.056 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1536754413.096 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1 2) 1536754413.098 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1536754413.154 * * * [misc]progress: generating series expansions 1536754413.154 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1536754413.154 * [misc]backup-simplify: Simplify (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1536754413.154 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1536754413.154 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536754413.154 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536754413.154 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536754413.154 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754413.154 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.154 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.155 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754413.155 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.155 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.155 * [misc]taylor: Taking taylor expansion of k in k 1536754413.155 * [misc]backup-simplify: Simplify 0 into 0 1536754413.155 * [misc]backup-simplify: Simplify 1 into 1 1536754413.155 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536754413.155 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536754413.155 * [misc]taylor: Taking taylor expansion of 2 in k 1536754413.155 * [misc]backup-simplify: Simplify 2 into 2 1536754413.155 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536754413.155 * [misc]taylor: Taking taylor expansion of n in k 1536754413.155 * [misc]backup-simplify: Simplify n into n 1536754413.155 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.155 * [misc]backup-simplify: Simplify PI into PI 1536754413.155 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754413.155 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536754413.155 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536754413.155 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754413.155 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.155 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754413.156 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536754413.156 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536754413.156 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536754413.156 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536754413.156 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536754413.156 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754413.156 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.156 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.156 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754413.156 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.156 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.156 * [misc]taylor: Taking taylor expansion of k in n 1536754413.156 * [misc]backup-simplify: Simplify k into k 1536754413.156 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536754413.156 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754413.156 * [misc]taylor: Taking taylor expansion of 2 in n 1536754413.156 * [misc]backup-simplify: Simplify 2 into 2 1536754413.156 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754413.156 * [misc]taylor: Taking taylor expansion of n in n 1536754413.156 * [misc]backup-simplify: Simplify 0 into 0 1536754413.156 * [misc]backup-simplify: Simplify 1 into 1 1536754413.156 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.156 * [misc]backup-simplify: Simplify PI into PI 1536754413.156 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754413.156 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754413.157 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754413.157 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754413.158 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.158 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754413.158 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754413.158 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754413.158 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.159 * [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)))) 1536754413.159 * [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))))) 1536754413.159 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536754413.159 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536754413.159 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536754413.159 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754413.159 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.159 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.159 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754413.159 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.159 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.159 * [misc]taylor: Taking taylor expansion of k in n 1536754413.159 * [misc]backup-simplify: Simplify k into k 1536754413.159 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536754413.159 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754413.159 * [misc]taylor: Taking taylor expansion of 2 in n 1536754413.159 * [misc]backup-simplify: Simplify 2 into 2 1536754413.159 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754413.159 * [misc]taylor: Taking taylor expansion of n in n 1536754413.159 * [misc]backup-simplify: Simplify 0 into 0 1536754413.159 * [misc]backup-simplify: Simplify 1 into 1 1536754413.159 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.159 * [misc]backup-simplify: Simplify PI into PI 1536754413.160 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754413.160 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754413.160 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754413.161 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754413.161 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.161 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754413.161 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754413.161 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754413.162 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.162 * [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)))) 1536754413.163 * [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))))) 1536754413.163 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536754413.163 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536754413.163 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754413.163 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.163 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.163 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754413.163 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.163 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.163 * [misc]taylor: Taking taylor expansion of k in k 1536754413.163 * [misc]backup-simplify: Simplify 0 into 0 1536754413.163 * [misc]backup-simplify: Simplify 1 into 1 1536754413.163 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536754413.163 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754413.163 * [misc]taylor: Taking taylor expansion of n in k 1536754413.163 * [misc]backup-simplify: Simplify n into n 1536754413.163 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754413.163 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536754413.163 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536754413.163 * [misc]taylor: Taking taylor expansion of 2 in k 1536754413.163 * [misc]backup-simplify: Simplify 2 into 2 1536754413.163 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.163 * [misc]backup-simplify: Simplify PI into PI 1536754413.163 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754413.164 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.164 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754413.164 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.164 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754413.164 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.165 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536754413.165 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536754413.165 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536754413.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754413.167 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536754413.170 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754413.170 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536754413.170 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.170 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.171 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.172 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536754413.174 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754413.174 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.174 * [misc]backup-simplify: Simplify 0 into 0 1536754413.174 * [misc]backup-simplify: Simplify 0 into 0 1536754413.179 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536754413.180 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754413.183 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754413.183 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.184 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754413.184 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754413.184 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754413.184 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536754413.186 * [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))))))) 1536754413.187 * [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))))))) 1536754413.188 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754413.189 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536754413.193 * [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 1536754413.193 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536754413.193 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.193 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.193 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.194 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536754413.196 * [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 1536754413.196 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.196 * [misc]backup-simplify: Simplify 0 into 0 1536754413.196 * [misc]backup-simplify: Simplify 0 into 0 1536754413.196 * [misc]backup-simplify: Simplify 0 into 0 1536754413.197 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536754413.198 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754413.201 * [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 1536754413.201 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.201 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754413.201 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.202 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.202 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536754413.204 * [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))))) 1536754413.207 * [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))))) 1536754413.212 * [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))))) 1536754413.212 * [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)))) 1536754413.212 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1536754413.212 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754413.212 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536754413.212 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536754413.212 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754413.212 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.212 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.213 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754413.213 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.213 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.213 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.213 * [misc]taylor: Taking taylor expansion of k in k 1536754413.213 * [misc]backup-simplify: Simplify 0 into 0 1536754413.213 * [misc]backup-simplify: Simplify 1 into 1 1536754413.213 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.213 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536754413.213 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536754413.213 * [misc]taylor: Taking taylor expansion of 2 in k 1536754413.213 * [misc]backup-simplify: Simplify 2 into 2 1536754413.213 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754413.213 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.213 * [misc]backup-simplify: Simplify PI into PI 1536754413.213 * [misc]taylor: Taking taylor expansion of n in k 1536754413.213 * [misc]backup-simplify: Simplify n into n 1536754413.213 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754413.213 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536754413.214 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536754413.214 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754413.214 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754413.214 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754413.214 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536754413.214 * [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)))) 1536754413.214 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.215 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.215 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.215 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.215 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of k in n 1536754413.215 * [misc]backup-simplify: Simplify k into k 1536754413.215 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.215 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of 2 in n 1536754413.215 * [misc]backup-simplify: Simplify 2 into 2 1536754413.215 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.215 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.215 * [misc]backup-simplify: Simplify PI into PI 1536754413.215 * [misc]taylor: Taking taylor expansion of n in n 1536754413.215 * [misc]backup-simplify: Simplify 0 into 0 1536754413.215 * [misc]backup-simplify: Simplify 1 into 1 1536754413.215 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.216 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754413.216 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.216 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754413.216 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754413.217 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754413.217 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.218 * [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))) 1536754413.219 * [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)))) 1536754413.219 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754413.219 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536754413.219 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536754413.219 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754413.219 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.219 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.219 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754413.219 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.219 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.219 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.219 * [misc]taylor: Taking taylor expansion of k in n 1536754413.219 * [misc]backup-simplify: Simplify k into k 1536754413.219 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.219 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536754413.219 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754413.219 * [misc]taylor: Taking taylor expansion of 2 in n 1536754413.219 * [misc]backup-simplify: Simplify 2 into 2 1536754413.220 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.220 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.220 * [misc]backup-simplify: Simplify PI into PI 1536754413.220 * [misc]taylor: Taking taylor expansion of n in n 1536754413.220 * [misc]backup-simplify: Simplify 0 into 0 1536754413.220 * [misc]backup-simplify: Simplify 1 into 1 1536754413.220 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.220 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754413.221 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.221 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754413.221 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754413.221 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754413.222 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.223 * [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))) 1536754413.223 * [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)))) 1536754413.223 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536754413.223 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536754413.224 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754413.224 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.224 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.224 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754413.224 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.224 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.224 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.224 * [misc]taylor: Taking taylor expansion of k in k 1536754413.224 * [misc]backup-simplify: Simplify 0 into 0 1536754413.224 * [misc]backup-simplify: Simplify 1 into 1 1536754413.224 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.224 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536754413.224 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536754413.224 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536754413.224 * [misc]taylor: Taking taylor expansion of 2 in k 1536754413.224 * [misc]backup-simplify: Simplify 2 into 2 1536754413.224 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.224 * [misc]backup-simplify: Simplify PI into PI 1536754413.224 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754413.225 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.225 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754413.225 * [misc]taylor: Taking taylor expansion of n in k 1536754413.225 * [misc]backup-simplify: Simplify n into n 1536754413.225 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754413.225 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754413.225 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754413.226 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754413.226 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754413.226 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536754413.227 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536754413.227 * [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)))) 1536754413.228 * [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)))) 1536754413.229 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754413.229 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754413.231 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754413.231 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754413.231 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754413.231 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.231 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.232 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.232 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536754413.233 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754413.234 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.234 * [misc]backup-simplify: Simplify 0 into 0 1536754413.234 * [misc]backup-simplify: Simplify 0 into 0 1536754413.234 * [misc]backup-simplify: Simplify 0 into 0 1536754413.234 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.235 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754413.238 * [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 1536754413.239 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.239 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754413.239 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.239 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.240 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.240 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536754413.242 * [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 1536754413.242 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.242 * [misc]backup-simplify: Simplify 0 into 0 1536754413.242 * [misc]backup-simplify: Simplify 0 into 0 1536754413.242 * [misc]backup-simplify: Simplify 0 into 0 1536754413.242 * [misc]backup-simplify: Simplify 0 into 0 1536754413.243 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.244 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754413.250 * [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 1536754413.250 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.250 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754413.250 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.250 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.251 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.251 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536754413.254 * [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 1536754413.254 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.254 * [misc]backup-simplify: Simplify 0 into 0 1536754413.254 * [misc]backup-simplify: Simplify 0 into 0 1536754413.254 * [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))))) 1536754413.255 * [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)) 1536754413.255 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1536754413.255 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.255 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.255 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of k in k 1536754413.255 * [misc]backup-simplify: Simplify 0 into 0 1536754413.255 * [misc]backup-simplify: Simplify 1 into 1 1536754413.255 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.255 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.255 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.255 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of -2 in k 1536754413.255 * [misc]backup-simplify: Simplify -2 into -2 1536754413.255 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754413.255 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.255 * [misc]backup-simplify: Simplify PI into PI 1536754413.255 * [misc]taylor: Taking taylor expansion of n in k 1536754413.255 * [misc]backup-simplify: Simplify n into n 1536754413.255 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754413.255 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536754413.255 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536754413.255 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754413.256 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754413.256 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536754413.256 * [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))) 1536754413.256 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.256 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.256 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of k in n 1536754413.256 * [misc]backup-simplify: Simplify k into k 1536754413.256 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.256 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.256 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.256 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of -2 in n 1536754413.256 * [misc]backup-simplify: Simplify -2 into -2 1536754413.256 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.256 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.256 * [misc]backup-simplify: Simplify PI into PI 1536754413.256 * [misc]taylor: Taking taylor expansion of n in n 1536754413.256 * [misc]backup-simplify: Simplify 0 into 0 1536754413.256 * [misc]backup-simplify: Simplify 1 into 1 1536754413.257 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.257 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754413.257 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754413.257 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754413.257 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754413.258 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.258 * [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))) 1536754413.258 * [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)))) 1536754413.259 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.259 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.259 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of k in n 1536754413.259 * [misc]backup-simplify: Simplify k into k 1536754413.259 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.259 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.259 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.259 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of -2 in n 1536754413.259 * [misc]backup-simplify: Simplify -2 into -2 1536754413.259 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.259 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.259 * [misc]backup-simplify: Simplify PI into PI 1536754413.259 * [misc]taylor: Taking taylor expansion of n in n 1536754413.259 * [misc]backup-simplify: Simplify 0 into 0 1536754413.259 * [misc]backup-simplify: Simplify 1 into 1 1536754413.259 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.259 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754413.260 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754413.260 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754413.260 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754413.260 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.261 * [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))) 1536754413.261 * [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)))) 1536754413.261 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536754413.261 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536754413.261 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754413.261 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754413.261 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.261 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.261 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.261 * [misc]taylor: Taking taylor expansion of k in k 1536754413.261 * [misc]backup-simplify: Simplify 0 into 0 1536754413.261 * [misc]backup-simplify: Simplify 1 into 1 1536754413.261 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.261 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.261 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.261 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536754413.261 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536754413.261 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536754413.261 * [misc]taylor: Taking taylor expansion of -2 in k 1536754413.261 * [misc]backup-simplify: Simplify -2 into -2 1536754413.262 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.262 * [misc]backup-simplify: Simplify PI into PI 1536754413.262 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754413.262 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754413.262 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754413.262 * [misc]taylor: Taking taylor expansion of n in k 1536754413.262 * [misc]backup-simplify: Simplify n into n 1536754413.262 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754413.262 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754413.262 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754413.262 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754413.263 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536754413.263 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536754413.264 * [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)))) 1536754413.265 * [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)))) 1536754413.266 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754413.266 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536754413.270 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536754413.270 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754413.270 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754413.270 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.271 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.272 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536754413.273 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754413.273 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.273 * [misc]backup-simplify: Simplify 0 into 0 1536754413.273 * [misc]backup-simplify: Simplify 0 into 0 1536754413.273 * [misc]backup-simplify: Simplify 0 into 0 1536754413.275 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.276 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754413.281 * [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 1536754413.281 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.281 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754413.281 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.282 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.282 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536754413.284 * [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 1536754413.284 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.284 * [misc]backup-simplify: Simplify 0 into 0 1536754413.284 * [misc]backup-simplify: Simplify 0 into 0 1536754413.284 * [misc]backup-simplify: Simplify 0 into 0 1536754413.284 * [misc]backup-simplify: Simplify 0 into 0 1536754413.285 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.286 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754413.293 * [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 1536754413.293 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.294 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754413.294 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.294 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.295 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1536754413.298 * [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 1536754413.298 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.298 * [misc]backup-simplify: Simplify 0 into 0 1536754413.298 * [misc]backup-simplify: Simplify 0 into 0 1536754413.298 * [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))))) 1536754413.298 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1 2) 1536754413.299 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754413.299 * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 1536754413.299 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754413.299 * [misc]taylor: Taking taylor expansion of n in n 1536754413.299 * [misc]backup-simplify: Simplify 0 into 0 1536754413.299 * [misc]backup-simplify: Simplify 1 into 1 1536754413.299 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.299 * [misc]backup-simplify: Simplify PI into PI 1536754413.299 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754413.299 * [misc]taylor: Taking taylor expansion of n in n 1536754413.299 * [misc]backup-simplify: Simplify 0 into 0 1536754413.299 * [misc]backup-simplify: Simplify 1 into 1 1536754413.299 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.299 * [misc]backup-simplify: Simplify PI into PI 1536754413.299 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754413.299 * [misc]backup-simplify: Simplify 0 into 0 1536754413.300 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754413.300 * [misc]backup-simplify: Simplify PI into PI 1536754413.301 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754413.301 * [misc]backup-simplify: Simplify 0 into 0 1536754413.302 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754413.302 * [misc]backup-simplify: Simplify 0 into 0 1536754413.303 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754413.303 * [misc]backup-simplify: Simplify 0 into 0 1536754413.305 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536754413.305 * [misc]backup-simplify: Simplify 0 into 0 1536754413.307 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536754413.307 * [misc]backup-simplify: Simplify 0 into 0 1536754413.309 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536754413.309 * [misc]backup-simplify: Simplify 0 into 0 1536754413.309 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) 1536754413.309 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) 1536754413.309 * [misc]approximate: Taking taylor expansion of (/ PI n) in (n) around 0 1536754413.309 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.309 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.309 * [misc]backup-simplify: Simplify PI into PI 1536754413.309 * [misc]taylor: Taking taylor expansion of n in n 1536754413.310 * [misc]backup-simplify: Simplify 0 into 0 1536754413.310 * [misc]backup-simplify: Simplify 1 into 1 1536754413.310 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.310 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.310 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.310 * [misc]backup-simplify: Simplify PI into PI 1536754413.310 * [misc]taylor: Taking taylor expansion of n in n 1536754413.310 * [misc]backup-simplify: Simplify 0 into 0 1536754413.310 * [misc]backup-simplify: Simplify 1 into 1 1536754413.310 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.310 * [misc]backup-simplify: Simplify PI into PI 1536754413.311 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754413.311 * [misc]backup-simplify: Simplify 0 into 0 1536754413.312 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.312 * [misc]backup-simplify: Simplify 0 into 0 1536754413.313 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.313 * [misc]backup-simplify: Simplify 0 into 0 1536754413.314 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.314 * [misc]backup-simplify: Simplify 0 into 0 1536754413.315 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.315 * [misc]backup-simplify: Simplify 0 into 0 1536754413.317 * [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 1536754413.317 * [misc]backup-simplify: Simplify 0 into 0 1536754413.317 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 1536754413.317 * [misc]backup-simplify: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 1536754413.317 * [misc]approximate: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 1536754413.317 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754413.317 * [misc]taylor: Taking taylor expansion of -1 in n 1536754413.317 * [misc]backup-simplify: Simplify -1 into -1 1536754413.317 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.317 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.317 * [misc]backup-simplify: Simplify PI into PI 1536754413.317 * [misc]taylor: Taking taylor expansion of n in n 1536754413.317 * [misc]backup-simplify: Simplify 0 into 0 1536754413.317 * [misc]backup-simplify: Simplify 1 into 1 1536754413.317 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.317 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754413.317 * [misc]taylor: Taking taylor expansion of -1 in n 1536754413.317 * [misc]backup-simplify: Simplify -1 into -1 1536754413.317 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.317 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.318 * [misc]backup-simplify: Simplify PI into PI 1536754413.318 * [misc]taylor: Taking taylor expansion of n in n 1536754413.318 * [misc]backup-simplify: Simplify 0 into 0 1536754413.318 * [misc]backup-simplify: Simplify 1 into 1 1536754413.318 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.318 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754413.318 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754413.319 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754413.319 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536754413.319 * [misc]backup-simplify: Simplify 0 into 0 1536754413.320 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.321 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1536754413.321 * [misc]backup-simplify: Simplify 0 into 0 1536754413.322 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.323 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754413.323 * [misc]backup-simplify: Simplify 0 into 0 1536754413.324 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.325 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754413.325 * [misc]backup-simplify: Simplify 0 into 0 1536754413.327 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.329 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536754413.330 * [misc]backup-simplify: Simplify 0 into 0 1536754413.332 * [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 1536754413.336 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536754413.336 * [misc]backup-simplify: Simplify 0 into 0 1536754413.336 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 1536754413.336 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1536754413.337 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1536754413.337 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1536754413.337 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1536754413.337 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754413.337 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.337 * [misc]taylor: Taking taylor expansion of k in k 1536754413.337 * [misc]backup-simplify: Simplify 0 into 0 1536754413.337 * [misc]backup-simplify: Simplify 1 into 1 1536754413.337 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.338 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754413.338 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754413.338 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536754413.338 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536754413.338 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536754413.338 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754413.338 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.338 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.338 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754413.338 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.338 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.338 * [misc]taylor: Taking taylor expansion of k in k 1536754413.338 * [misc]backup-simplify: Simplify 0 into 0 1536754413.338 * [misc]backup-simplify: Simplify 1 into 1 1536754413.338 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536754413.338 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536754413.338 * [misc]taylor: Taking taylor expansion of 2 in k 1536754413.339 * [misc]backup-simplify: Simplify 2 into 2 1536754413.339 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536754413.339 * [misc]taylor: Taking taylor expansion of n in k 1536754413.339 * [misc]backup-simplify: Simplify n into n 1536754413.339 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.339 * [misc]backup-simplify: Simplify PI into PI 1536754413.339 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754413.339 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536754413.339 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536754413.339 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754413.339 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.340 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754413.340 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536754413.340 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536754413.340 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536754413.340 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754413.340 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.340 * [misc]taylor: Taking taylor expansion of k in n 1536754413.340 * [misc]backup-simplify: Simplify k into k 1536754413.340 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.341 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754413.341 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754413.341 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754413.341 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536754413.341 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536754413.341 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536754413.341 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754413.341 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.341 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.341 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754413.341 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.341 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.341 * [misc]taylor: Taking taylor expansion of k in n 1536754413.341 * [misc]backup-simplify: Simplify k into k 1536754413.341 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536754413.341 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754413.341 * [misc]taylor: Taking taylor expansion of 2 in n 1536754413.341 * [misc]backup-simplify: Simplify 2 into 2 1536754413.341 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754413.341 * [misc]taylor: Taking taylor expansion of n in n 1536754413.341 * [misc]backup-simplify: Simplify 0 into 0 1536754413.341 * [misc]backup-simplify: Simplify 1 into 1 1536754413.341 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.341 * [misc]backup-simplify: Simplify PI into PI 1536754413.342 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754413.342 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754413.343 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754413.343 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754413.344 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.344 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754413.344 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754413.344 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754413.345 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.346 * [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)))) 1536754413.346 * [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))))) 1536754413.346 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of k in n 1536754413.347 * [misc]backup-simplify: Simplify k into k 1536754413.347 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.347 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754413.347 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754413.347 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754413.347 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.347 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.347 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.347 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.347 * [misc]taylor: Taking taylor expansion of k in n 1536754413.347 * [misc]backup-simplify: Simplify k into k 1536754413.347 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536754413.347 * [misc]taylor: Taking taylor expansion of 2 in n 1536754413.347 * [misc]backup-simplify: Simplify 2 into 2 1536754413.347 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754413.348 * [misc]taylor: Taking taylor expansion of n in n 1536754413.348 * [misc]backup-simplify: Simplify 0 into 0 1536754413.348 * [misc]backup-simplify: Simplify 1 into 1 1536754413.348 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.348 * [misc]backup-simplify: Simplify PI into PI 1536754413.348 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754413.348 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536754413.349 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754413.350 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536754413.350 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.351 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754413.351 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754413.351 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754413.352 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.352 * [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)))) 1536754413.353 * [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))))) 1536754413.354 * [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))) 1536754413.354 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1536754413.354 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536754413.354 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536754413.354 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754413.354 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.354 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.354 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754413.354 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.354 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.354 * [misc]taylor: Taking taylor expansion of k in k 1536754413.354 * [misc]backup-simplify: Simplify 0 into 0 1536754413.354 * [misc]backup-simplify: Simplify 1 into 1 1536754413.354 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536754413.354 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754413.354 * [misc]taylor: Taking taylor expansion of n in k 1536754413.354 * [misc]backup-simplify: Simplify n into n 1536754413.354 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754413.354 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536754413.355 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536754413.355 * [misc]taylor: Taking taylor expansion of 2 in k 1536754413.355 * [misc]backup-simplify: Simplify 2 into 2 1536754413.355 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.355 * [misc]backup-simplify: Simplify PI into PI 1536754413.355 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754413.356 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.356 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754413.356 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.356 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754413.357 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.357 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536754413.359 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536754413.359 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754413.359 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.359 * [misc]taylor: Taking taylor expansion of k in k 1536754413.359 * [misc]backup-simplify: Simplify 0 into 0 1536754413.359 * [misc]backup-simplify: Simplify 1 into 1 1536754413.359 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.359 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754413.359 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754413.360 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1536754413.360 * [misc]backup-simplify: Simplify 0 into 0 1536754413.361 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754413.361 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536754413.363 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754413.363 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536754413.363 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.363 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.364 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.364 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536754413.365 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754413.366 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1536754413.366 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.366 * [misc]backup-simplify: Simplify 0 into 0 1536754413.367 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536754413.367 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754413.369 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754413.369 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.369 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754413.369 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754413.369 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754413.370 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536754413.371 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536754413.372 * [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))))))) 1536754413.373 * [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))))))) 1536754413.374 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754413.375 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536754413.378 * [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 1536754413.379 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536754413.379 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.379 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.379 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.380 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536754413.381 * [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 1536754413.381 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.382 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536754413.382 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1536754413.382 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.382 * [misc]backup-simplify: Simplify 0 into 0 1536754413.383 * [misc]backup-simplify: Simplify 0 into 0 1536754413.383 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754413.383 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754413.384 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536754413.385 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754413.389 * [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 1536754413.389 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.389 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754413.389 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.389 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.390 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536754413.392 * [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))))) 1536754413.396 * [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)))))))) 1536754413.398 * [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)))))))) 1536754413.399 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754413.402 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536754413.407 * [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 1536754413.408 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536754413.408 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.408 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.409 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536754413.410 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536754413.412 * [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 1536754413.412 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.413 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536754413.413 * [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 1536754413.413 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.413 * [misc]backup-simplify: Simplify 0 into 0 1536754413.413 * [misc]backup-simplify: Simplify 0 into 0 1536754413.413 * [misc]backup-simplify: Simplify 0 into 0 1536754413.414 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.414 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754413.416 * [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 1536754413.417 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754413.423 * [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 1536754413.423 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.423 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754413.423 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.423 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.424 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536754413.428 * [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))))))) 1536754413.439 * [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)))))))))))))) 1536754413.447 * [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)))))))))))))) 1536754413.458 * [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)))))))))))))))))))))) 1536754413.458 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754413.458 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1536754413.458 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754413.458 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754413.458 * [misc]taylor: Taking taylor expansion of k in k 1536754413.458 * [misc]backup-simplify: Simplify 0 into 0 1536754413.458 * [misc]backup-simplify: Simplify 1 into 1 1536754413.458 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754413.459 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754413.459 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.459 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.459 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.459 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.459 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of k in k 1536754413.459 * [misc]backup-simplify: Simplify 0 into 0 1536754413.459 * [misc]backup-simplify: Simplify 1 into 1 1536754413.459 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.459 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of 2 in k 1536754413.459 * [misc]backup-simplify: Simplify 2 into 2 1536754413.459 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754413.459 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.459 * [misc]backup-simplify: Simplify PI into PI 1536754413.459 * [misc]taylor: Taking taylor expansion of n in k 1536754413.459 * [misc]backup-simplify: Simplify n into n 1536754413.459 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754413.460 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536754413.460 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536754413.460 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754413.460 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754413.460 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754413.460 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536754413.460 * [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)))) 1536754413.460 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754413.460 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754413.460 * [misc]taylor: Taking taylor expansion of k in n 1536754413.460 * [misc]backup-simplify: Simplify k into k 1536754413.460 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754413.460 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754413.460 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754413.460 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536754413.460 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536754413.460 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754413.461 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.461 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.461 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754413.461 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.461 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.461 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.461 * [misc]taylor: Taking taylor expansion of k in n 1536754413.461 * [misc]backup-simplify: Simplify k into k 1536754413.461 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.461 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536754413.461 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754413.461 * [misc]taylor: Taking taylor expansion of 2 in n 1536754413.461 * [misc]backup-simplify: Simplify 2 into 2 1536754413.461 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.461 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.461 * [misc]backup-simplify: Simplify PI into PI 1536754413.461 * [misc]taylor: Taking taylor expansion of n in n 1536754413.461 * [misc]backup-simplify: Simplify 0 into 0 1536754413.461 * [misc]backup-simplify: Simplify 1 into 1 1536754413.461 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.461 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754413.462 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.462 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754413.462 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754413.462 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754413.463 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.463 * [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))) 1536754413.464 * [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)))) 1536754413.464 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of k in n 1536754413.464 * [misc]backup-simplify: Simplify k into k 1536754413.464 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754413.464 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754413.464 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.464 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.464 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.464 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.464 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of k in n 1536754413.464 * [misc]backup-simplify: Simplify k into k 1536754413.464 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.464 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of 2 in n 1536754413.464 * [misc]backup-simplify: Simplify 2 into 2 1536754413.464 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.464 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.464 * [misc]backup-simplify: Simplify PI into PI 1536754413.464 * [misc]taylor: Taking taylor expansion of n in n 1536754413.464 * [misc]backup-simplify: Simplify 0 into 0 1536754413.464 * [misc]backup-simplify: Simplify 1 into 1 1536754413.464 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.464 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754413.465 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.465 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754413.465 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754413.465 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754413.465 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.466 * [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))) 1536754413.466 * [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)))) 1536754413.467 * [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)) 1536754413.467 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.467 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.467 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.467 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.467 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of k in k 1536754413.467 * [misc]backup-simplify: Simplify 0 into 0 1536754413.467 * [misc]backup-simplify: Simplify 1 into 1 1536754413.467 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.467 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536754413.467 * [misc]taylor: Taking taylor expansion of 2 in k 1536754413.467 * [misc]backup-simplify: Simplify 2 into 2 1536754413.467 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.467 * [misc]backup-simplify: Simplify PI into PI 1536754413.468 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536754413.468 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536754413.468 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754413.468 * [misc]taylor: Taking taylor expansion of n in k 1536754413.468 * [misc]backup-simplify: Simplify n into n 1536754413.468 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754413.468 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754413.468 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754413.468 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754413.468 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754413.469 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536754413.469 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536754413.470 * [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)))) 1536754413.470 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754413.470 * [misc]taylor: Taking taylor expansion of k in k 1536754413.470 * [misc]backup-simplify: Simplify 0 into 0 1536754413.470 * [misc]backup-simplify: Simplify 1 into 1 1536754413.470 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754413.470 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754413.470 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1536754413.471 * [misc]backup-simplify: Simplify 0 into 0 1536754413.471 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754413.472 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536754413.474 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536754413.474 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754413.474 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754413.474 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.474 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.475 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.475 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536754413.476 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754413.477 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1536754413.477 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.477 * [misc]backup-simplify: Simplify 0 into 0 1536754413.477 * [misc]backup-simplify: Simplify 0 into 0 1536754413.477 * [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)))))) 1536754413.478 * [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)))))) 1536754413.479 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.479 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754413.483 * [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 1536754413.483 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.483 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754413.484 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.484 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.484 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.485 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536754413.486 * [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 1536754413.487 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536754413.487 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1536754413.487 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.487 * [misc]backup-simplify: Simplify 0 into 0 1536754413.487 * [misc]backup-simplify: Simplify 0 into 0 1536754413.487 * [misc]backup-simplify: Simplify 0 into 0 1536754413.488 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754413.489 * [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)))))) 1536754413.489 * [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)))))) 1536754413.490 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.491 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754413.498 * [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 1536754413.499 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.499 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754413.499 * [misc]backup-simplify: Simplify (- 0) into 0 1536754413.499 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.500 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536754413.501 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536754413.505 * [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 1536754413.505 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536754413.507 * [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 1536754413.507 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.507 * [misc]backup-simplify: Simplify 0 into 0 1536754413.507 * [misc]backup-simplify: Simplify 0 into 0 1536754413.507 * [misc]backup-simplify: Simplify 0 into 0 1536754413.507 * [misc]backup-simplify: Simplify 0 into 0 1536754413.508 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754413.509 * [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)))))) 1536754413.510 * [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)))))) 1536754413.514 * [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)))))))) 1536754413.514 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1536754413.514 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1536754413.514 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536754413.514 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754413.514 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536754413.514 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536754413.515 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754413.515 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754413.515 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.515 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.515 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.515 * [misc]taylor: Taking taylor expansion of k in k 1536754413.515 * [misc]backup-simplify: Simplify 0 into 0 1536754413.515 * [misc]backup-simplify: Simplify 1 into 1 1536754413.515 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.515 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.515 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.515 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536754413.515 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536754413.515 * [misc]taylor: Taking taylor expansion of -2 in k 1536754413.515 * [misc]backup-simplify: Simplify -2 into -2 1536754413.515 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754413.515 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.515 * [misc]backup-simplify: Simplify PI into PI 1536754413.515 * [misc]taylor: Taking taylor expansion of n in k 1536754413.515 * [misc]backup-simplify: Simplify n into n 1536754413.515 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754413.516 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536754413.516 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536754413.516 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754413.516 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754413.516 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536754413.517 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754413.517 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754413.517 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754413.517 * [misc]taylor: Taking taylor expansion of -1 in k 1536754413.517 * [misc]backup-simplify: Simplify -1 into -1 1536754413.517 * [misc]taylor: Taking taylor expansion of k in k 1536754413.517 * [misc]backup-simplify: Simplify 0 into 0 1536754413.517 * [misc]backup-simplify: Simplify 1 into 1 1536754413.517 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754413.517 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754413.518 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754413.518 * [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)))) 1536754413.518 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536754413.518 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754413.518 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536754413.518 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536754413.518 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754413.518 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754413.518 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.518 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.518 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.518 * [misc]taylor: Taking taylor expansion of k in n 1536754413.519 * [misc]backup-simplify: Simplify k into k 1536754413.519 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.519 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.519 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.519 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536754413.519 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754413.519 * [misc]taylor: Taking taylor expansion of -2 in n 1536754413.519 * [misc]backup-simplify: Simplify -2 into -2 1536754413.519 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.519 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.519 * [misc]backup-simplify: Simplify PI into PI 1536754413.519 * [misc]taylor: Taking taylor expansion of n in n 1536754413.519 * [misc]backup-simplify: Simplify 0 into 0 1536754413.519 * [misc]backup-simplify: Simplify 1 into 1 1536754413.519 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.520 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754413.520 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754413.520 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754413.520 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754413.521 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.522 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536754413.523 * [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)))) 1536754413.523 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754413.523 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754413.523 * [misc]taylor: Taking taylor expansion of -1 in n 1536754413.523 * [misc]backup-simplify: Simplify -1 into -1 1536754413.523 * [misc]taylor: Taking taylor expansion of k in n 1536754413.523 * [misc]backup-simplify: Simplify k into k 1536754413.523 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754413.523 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754413.523 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754413.523 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754413.524 * [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))) 1536754413.524 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536754413.524 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754413.524 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536754413.524 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536754413.524 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754413.524 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754413.524 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.524 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.524 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754413.524 * [misc]taylor: Taking taylor expansion of k in n 1536754413.524 * [misc]backup-simplify: Simplify k into k 1536754413.524 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754413.525 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754413.525 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.525 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536754413.525 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536754413.525 * [misc]taylor: Taking taylor expansion of -2 in n 1536754413.525 * [misc]backup-simplify: Simplify -2 into -2 1536754413.525 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754413.525 * [misc]taylor: Taking taylor expansion of PI in n 1536754413.525 * [misc]backup-simplify: Simplify PI into PI 1536754413.525 * [misc]taylor: Taking taylor expansion of n in n 1536754413.525 * [misc]backup-simplify: Simplify 0 into 0 1536754413.525 * [misc]backup-simplify: Simplify 1 into 1 1536754413.525 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754413.525 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754413.526 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754413.526 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754413.526 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754413.527 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.528 * [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))) 1536754413.528 * [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)))) 1536754413.528 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754413.528 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754413.528 * [misc]taylor: Taking taylor expansion of -1 in n 1536754413.528 * [misc]backup-simplify: Simplify -1 into -1 1536754413.528 * [misc]taylor: Taking taylor expansion of k in n 1536754413.529 * [misc]backup-simplify: Simplify k into k 1536754413.529 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754413.529 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754413.529 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754413.529 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754413.530 * [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))) 1536754413.530 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1536754413.530 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536754413.530 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536754413.530 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754413.530 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754413.530 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.530 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.530 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754413.530 * [misc]taylor: Taking taylor expansion of k in k 1536754413.530 * [misc]backup-simplify: Simplify 0 into 0 1536754413.530 * [misc]backup-simplify: Simplify 1 into 1 1536754413.530 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754413.530 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754413.530 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754413.530 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536754413.530 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536754413.530 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536754413.531 * [misc]taylor: Taking taylor expansion of -2 in k 1536754413.531 * [misc]backup-simplify: Simplify -2 into -2 1536754413.531 * [misc]taylor: Taking taylor expansion of PI in k 1536754413.531 * [misc]backup-simplify: Simplify PI into PI 1536754413.531 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536754413.531 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536754413.531 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754413.532 * [misc]taylor: Taking taylor expansion of n in k 1536754413.532 * [misc]backup-simplify: Simplify n into n 1536754413.532 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754413.532 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754413.532 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754413.532 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754413.533 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536754413.533 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536754413.534 * [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)))) 1536754413.534 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754413.534 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754413.534 * [misc]taylor: Taking taylor expansion of -1 in k 1536754413.534 * [misc]backup-simplify: Simplify -1 into -1 1536754413.534 * [misc]taylor: Taking taylor expansion of k in k 1536754413.534 * [misc]backup-simplify: Simplify 0 into 0 1536754413.534 * [misc]backup-simplify: Simplify 1 into 1 1536754413.534 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754413.534 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754413.535 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754413.536 * [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))))) 1536754413.536 * [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))))) 1536754413.538 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754413.538 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536754413.541 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536754413.542 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754413.542 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754413.542 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.543 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.544 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536754413.546 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754413.547 * [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 1536754413.547 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.547 * [misc]backup-simplify: Simplify 0 into 0 1536754413.547 * [misc]backup-simplify: Simplify 0 into 0 1536754413.547 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754413.548 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754413.549 * [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)))))) 1536754413.550 * [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)))))) 1536754413.552 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.553 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536754413.559 * [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 1536754413.559 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.559 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754413.559 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754413.560 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536754413.560 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536754413.562 * [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 1536754413.562 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754413.562 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536754413.563 * [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 1536754413.563 * [misc]taylor: Taking taylor expansion of 0 in k 1536754413.563 * [misc]backup-simplify: Simplify 0 into 0 1536754413.563 * [misc]backup-simplify: Simplify 0 into 0 1536754413.563 * [misc]backup-simplify: Simplify 0 into 0 1536754413.563 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754413.564 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754413.566 * [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)))))) 1536754413.566 * [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)))))) 1536754413.568 * [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))))))))))) 1536754413.569 * * * [misc]progress: simplifying candidates 1536754413.569 * * * * [misc]progress: [ 1 / 82 ] simplifiying candidate # 1536754413.569 * * * * [misc]progress: [ 2 / 82 ] simplifiying candidate # 1536754413.569 * * * * [misc]progress: [ 3 / 82 ] simplifiying candidate # 1536754413.569 * [enter]simplify: Simplifying (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) 1536754413.570 * * [misc]simplify: iters left: 6 (11 enodes) 1536754413.573 * * [misc]simplify: iters left: 5 (21 enodes) 1536754413.579 * * [misc]simplify: iters left: 4 (47 enodes) 1536754413.596 * * [misc]simplify: iters left: 3 (113 enodes) 1536754413.660 * * [misc]simplify: iters left: 2 (328 enodes) 1536754414.042 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) 1536754414.043 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* PI n) 2)))) (sqrt k))) 1536754414.043 * * * * [misc]progress: [ 4 / 82 ] simplifiying candidate # 1536754414.043 * * * * [misc]progress: [ 5 / 82 ] simplifiying candidate # 1536754414.043 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536754414.043 * * [misc]simplify: iters left: 4 (5 enodes) 1536754414.045 * * [misc]simplify: iters left: 3 (9 enodes) 1536754414.047 * * [misc]simplify: iters left: 2 (15 enodes) 1536754414.049 * * [misc]simplify: iters left: 1 (17 enodes) 1536754414.052 * [exit]simplify: Simplified to (* (* PI n) 2) 1536754414.052 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1536754414.052 * * * * [misc]progress: [ 6 / 82 ] simplifiying candidate # 1536754414.052 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (/ k 2)) 1536754414.052 * * [misc]simplify: iters left: 5 (8 enodes) 1536754414.054 * * [misc]simplify: iters left: 4 (12 enodes) 1536754414.057 * * [misc]simplify: iters left: 3 (18 enodes) 1536754414.060 * * [misc]simplify: iters left: 2 (20 enodes) 1536754414.063 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) 1536754414.063 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) 1/2) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) 1536754414.063 * * * * [misc]progress: [ 7 / 82 ] simplifiying candidate # 1536754414.064 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536754414.064 * * [misc]simplify: iters left: 5 (6 enodes) 1536754414.065 * * [misc]simplify: iters left: 4 (8 enodes) 1536754414.067 * * [misc]simplify: iters left: 3 (11 enodes) 1536754414.068 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536754414.068 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) 1536754414.068 * * * * [misc]progress: [ 8 / 82 ] simplifiying candidate # 1536754414.069 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536754414.069 * * [misc]simplify: iters left: 5 (6 enodes) 1536754414.070 * * [misc]simplify: iters left: 4 (8 enodes) 1536754414.072 * * [misc]simplify: iters left: 3 (11 enodes) 1536754414.075 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536754414.075 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) 1536754414.075 * * * * [misc]progress: [ 9 / 82 ] simplifiying candidate # 1536754414.076 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536754414.076 * * [misc]simplify: iters left: 4 (5 enodes) 1536754414.078 * * [misc]simplify: iters left: 3 (7 enodes) 1536754414.081 * * [misc]simplify: iters left: 2 (10 enodes) 1536754414.084 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536754414.084 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1536754414.084 * * * * [misc]progress: [ 10 / 82 ] simplifiying candidate # 1536754414.085 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- (/ k 2))) 1536754414.086 * * [misc]simplify: iters left: 5 (9 enodes) 1536754414.090 * * [misc]simplify: iters left: 4 (15 enodes) 1536754414.096 * * [misc]simplify: iters left: 3 (21 enodes) 1536754414.103 * * [misc]simplify: iters left: 2 (22 enodes) 1536754414.111 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1536754414.111 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k))) 1536754414.111 * * * * [misc]progress: [ 11 / 82 ] simplifiying candidate # 1536754414.111 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- (/ k 2))) 1536754414.112 * * [misc]simplify: iters left: 5 (9 enodes) 1536754414.116 * * [misc]simplify: iters left: 4 (15 enodes) 1536754414.122 * * [misc]simplify: iters left: 3 (21 enodes) 1536754414.129 * * [misc]simplify: iters left: 2 (22 enodes) 1536754414.136 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1536754414.136 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k))) 1536754414.136 * * * * [misc]progress: [ 12 / 82 ] simplifiying candidate # 1536754414.138 * [enter]simplify: Simplifying (pow 2 (- 1/2 (/ k 2))) 1536754414.139 * * [misc]simplify: iters left: 5 (6 enodes) 1536754414.141 * * [misc]simplify: iters left: 4 (8 enodes) 1536754414.144 * * [misc]simplify: iters left: 3 (11 enodes) 1536754414.148 * [exit]simplify: Simplified to (pow 2 (- 1/2 (/ k 2))) 1536754414.148 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) 1536754414.148 * * * * [misc]progress: [ 13 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 14 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 15 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 16 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 17 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 18 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 19 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 20 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 21 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 22 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 23 / 82 ] simplifiying candidate # 1536754414.148 * * * * [misc]progress: [ 24 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 25 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 26 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 27 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 28 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 29 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 30 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 31 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 32 / 82 ] simplifiying candidate # 1536754414.149 * * * * [misc]progress: [ 33 / 82 ] simplifiying candidate # 1536754414.149 * [enter]simplify: Simplifying (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754414.151 * * [misc]simplify: iters left: 6 (14 enodes) 1536754414.158 * * [misc]simplify: iters left: 5 (27 enodes) 1536754414.173 * * [misc]simplify: iters left: 4 (55 enodes) 1536754414.208 * * [misc]simplify: iters left: 3 (144 enodes) 1536754414.397 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) 1536754414.397 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))))) 1536754414.397 * * * * [misc]progress: [ 34 / 82 ] simplifiying candidate # 1536754414.398 * [enter]simplify: Simplifying (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754414.399 * * [misc]simplify: iters left: 6 (14 enodes) 1536754414.403 * * [misc]simplify: iters left: 5 (27 enodes) 1536754414.410 * * [misc]simplify: iters left: 4 (55 enodes) 1536754414.428 * * [misc]simplify: iters left: 3 (144 enodes) 1536754414.584 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) 1536754414.584 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))))) 1536754414.584 * * * * [misc]progress: [ 35 / 82 ] simplifiying candidate # 1536754414.585 * [enter]simplify: Simplifying (- (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1536754414.586 * * [misc]simplify: iters left: 6 (14 enodes) 1536754414.592 * * [misc]simplify: iters left: 5 (24 enodes) 1536754414.604 * * [misc]simplify: iters left: 4 (43 enodes) 1536754414.622 * * [misc]simplify: iters left: 3 (73 enodes) 1536754414.661 * * [misc]simplify: iters left: 2 (220 enodes) 1536754414.991 * [exit]simplify: Simplified to (fma (log (* (* 2 PI) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1536754414.992 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 PI) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1536754414.992 * * * * [misc]progress: [ 36 / 82 ] simplifiying candidate # 1536754414.992 * * * * [misc]progress: [ 37 / 82 ] simplifiying candidate # 1536754414.992 * * * * [misc]progress: [ 38 / 82 ] simplifiying candidate # 1536754414.992 * [enter]simplify: Simplifying (/ (* (* (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 k)) (sqrt k))) 1536754414.994 * * [misc]simplify: iters left: 6 (16 enodes) 1536754415.003 * * [misc]simplify: iters left: 5 (31 enodes) 1536754415.018 * * [misc]simplify: iters left: 4 (67 enodes) 1536754415.050 * * [misc]simplify: iters left: 3 (124 enodes) 1536754415.107 * * [misc]simplify: iters left: 2 (195 enodes) 1536754415.166 * * [misc]simplify: iters left: 1 (309 enodes) 1536754415.357 * [exit]simplify: Simplified to (* (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (* k (sqrt k)))) 1536754415.357 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (* k (sqrt k)))))) 1536754415.357 * * * * [misc]progress: [ 39 / 82 ] simplifiying candidate # 1536754415.357 * * * * [misc]progress: [ 40 / 82 ] simplifiying candidate # 1536754415.357 * * * * [misc]progress: [ 41 / 82 ] simplifiying candidate # 1536754415.357 * * * * [misc]progress: [ 42 / 82 ] simplifiying candidate # 1536754415.357 * * * * [misc]progress: [ 43 / 82 ] simplifiying candidate # 1536754415.357 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.358 * * [misc]simplify: iters left: 6 (12 enodes) 1536754415.362 * * [misc]simplify: iters left: 5 (19 enodes) 1536754415.370 * * [misc]simplify: iters left: 4 (25 enodes) 1536754415.377 * * [misc]simplify: iters left: 3 (26 enodes) 1536754415.386 * [exit]simplify: Simplified to (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.386 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k))))) 1536754415.386 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k))) 1536754415.388 * * [misc]simplify: iters left: 6 (12 enodes) 1536754415.392 * * [misc]simplify: iters left: 5 (18 enodes) 1536754415.397 * * [misc]simplify: iters left: 4 (24 enodes) 1536754415.401 * * [misc]simplify: iters left: 3 (25 enodes) 1536754415.405 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k))) 1536754415.405 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k))))) 1536754415.405 * * * * [misc]progress: [ 44 / 82 ] simplifiying candidate # 1536754415.405 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) 1536754415.406 * * [misc]simplify: iters left: 6 (11 enodes) 1536754415.408 * * [misc]simplify: iters left: 5 (16 enodes) 1536754415.411 * * [misc]simplify: iters left: 4 (22 enodes) 1536754415.415 * * [misc]simplify: iters left: 3 (24 enodes) 1536754415.419 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) 1536754415.419 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k))))) 1536754415.419 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k))) 1536754415.421 * * [misc]simplify: iters left: 6 (12 enodes) 1536754415.423 * * [misc]simplify: iters left: 5 (18 enodes) 1536754415.430 * * [misc]simplify: iters left: 4 (24 enodes) 1536754415.437 * * [misc]simplify: iters left: 3 (25 enodes) 1536754415.444 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k))) 1536754415.444 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k))))) 1536754415.445 * * * * [misc]progress: [ 45 / 82 ] simplifiying candidate # 1536754415.445 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) 1) 1536754415.445 * * [misc]simplify: iters left: 6 (9 enodes) 1536754415.447 * * [misc]simplify: iters left: 5 (16 enodes) 1536754415.451 * * [misc]simplify: iters left: 4 (24 enodes) 1536754415.454 * * [misc]simplify: iters left: 3 (26 enodes) 1536754415.458 * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) 1536754415.458 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k)))) 1536754415.458 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k)) 1536754415.458 * * [misc]simplify: iters left: 6 (11 enodes) 1536754415.461 * * [misc]simplify: iters left: 5 (17 enodes) 1536754415.464 * * [misc]simplify: iters left: 4 (23 enodes) 1536754415.468 * * [misc]simplify: iters left: 3 (24 enodes) 1536754415.472 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)) 1536754415.472 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1536754415.472 * * * * [misc]progress: [ 46 / 82 ] simplifiying candidate # 1536754415.472 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.473 * * [misc]simplify: iters left: 6 (12 enodes) 1536754415.478 * * [misc]simplify: iters left: 5 (19 enodes) 1536754415.485 * * [misc]simplify: iters left: 4 (25 enodes) 1536754415.493 * * [misc]simplify: iters left: 3 (26 enodes) 1536754415.502 * [exit]simplify: Simplified to (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.502 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k))))) 1536754415.502 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k))) 1536754415.503 * * [misc]simplify: iters left: 6 (12 enodes) 1536754415.508 * * [misc]simplify: iters left: 5 (18 enodes) 1536754415.515 * * [misc]simplify: iters left: 4 (24 enodes) 1536754415.523 * * [misc]simplify: iters left: 3 (25 enodes) 1536754415.533 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k))) 1536754415.533 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k))))) 1536754415.533 * * * * [misc]progress: [ 47 / 82 ] simplifiying candidate # 1536754415.533 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) 1536754415.534 * * [misc]simplify: iters left: 6 (11 enodes) 1536754415.537 * * [misc]simplify: iters left: 5 (16 enodes) 1536754415.540 * * [misc]simplify: iters left: 4 (22 enodes) 1536754415.543 * * [misc]simplify: iters left: 3 (24 enodes) 1536754415.547 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) 1536754415.547 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k))))) 1536754415.547 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k))) 1536754415.548 * * [misc]simplify: iters left: 6 (12 enodes) 1536754415.550 * * [misc]simplify: iters left: 5 (18 enodes) 1536754415.554 * * [misc]simplify: iters left: 4 (24 enodes) 1536754415.557 * * [misc]simplify: iters left: 3 (25 enodes) 1536754415.561 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k))) 1536754415.561 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k))))) 1536754415.561 * * * * [misc]progress: [ 48 / 82 ] simplifiying candidate # 1536754415.562 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) 1) 1536754415.562 * * [misc]simplify: iters left: 6 (9 enodes) 1536754415.565 * * [misc]simplify: iters left: 5 (16 enodes) 1536754415.572 * * [misc]simplify: iters left: 4 (24 enodes) 1536754415.578 * * [misc]simplify: iters left: 3 (26 enodes) 1536754415.585 * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) 1536754415.585 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k)))) 1536754415.586 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k)) 1536754415.587 * * [misc]simplify: iters left: 6 (11 enodes) 1536754415.589 * * [misc]simplify: iters left: 5 (17 enodes) 1536754415.593 * * [misc]simplify: iters left: 4 (23 enodes) 1536754415.596 * * [misc]simplify: iters left: 3 (24 enodes) 1536754415.600 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)) 1536754415.600 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1536754415.600 * * * * [misc]progress: [ 49 / 82 ] simplifiying candidate # 1536754415.600 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.601 * * [misc]simplify: iters left: 6 (10 enodes) 1536754415.603 * * [misc]simplify: iters left: 5 (14 enodes) 1536754415.605 * * [misc]simplify: iters left: 4 (17 enodes) 1536754415.608 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.608 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536754415.609 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754415.609 * * [misc]simplify: iters left: 6 (12 enodes) 1536754415.611 * * [misc]simplify: iters left: 5 (15 enodes) 1536754415.615 * * [misc]simplify: iters left: 4 (18 enodes) 1536754415.619 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754415.619 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536754415.619 * * * * [misc]progress: [ 50 / 82 ] simplifiying candidate # 1536754415.619 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754415.620 * * [misc]simplify: iters left: 6 (9 enodes) 1536754415.621 * * [misc]simplify: iters left: 5 (11 enodes) 1536754415.623 * * [misc]simplify: iters left: 4 (14 enodes) 1536754415.625 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754415.625 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536754415.625 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754415.626 * * [misc]simplify: iters left: 6 (12 enodes) 1536754415.628 * * [misc]simplify: iters left: 5 (15 enodes) 1536754415.631 * * [misc]simplify: iters left: 4 (18 enodes) 1536754415.634 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754415.634 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536754415.634 * * * * [misc]progress: [ 51 / 82 ] simplifiying candidate # 1536754415.634 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) 1) 1536754415.634 * * [misc]simplify: iters left: 6 (8 enodes) 1536754415.636 * * [misc]simplify: iters left: 5 (12 enodes) 1536754415.639 * * [misc]simplify: iters left: 4 (17 enodes) 1536754415.642 * [exit]simplify: Simplified to (pow 2 (- 1/2 (/ k 2))) 1536754415.642 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754415.643 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754415.644 * * [misc]simplify: iters left: 6 (11 enodes) 1536754415.648 * * [misc]simplify: iters left: 5 (14 enodes) 1536754415.652 * * [misc]simplify: iters left: 4 (17 enodes) 1536754415.658 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754415.658 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754415.658 * * * * [misc]progress: [ 52 / 82 ] simplifiying candidate # 1536754415.659 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.660 * * [misc]simplify: iters left: 6 (16 enodes) 1536754415.663 * * [misc]simplify: iters left: 5 (28 enodes) 1536754415.670 * * [misc]simplify: iters left: 4 (46 enodes) 1536754415.677 * * [misc]simplify: iters left: 3 (50 enodes) 1536754415.689 * * [misc]simplify: iters left: 2 (53 enodes) 1536754415.708 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1536754415.708 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (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 (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536754415.709 * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754415.712 * * [misc]simplify: iters left: 6 (14 enodes) 1536754415.718 * * [misc]simplify: iters left: 5 (20 enodes) 1536754415.726 * * [misc]simplify: iters left: 4 (29 enodes) 1536754415.734 * * [misc]simplify: iters left: 3 (30 enodes) 1536754415.744 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754415.744 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536754415.744 * * * * [misc]progress: [ 53 / 82 ] simplifiying candidate # 1536754415.745 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536754415.746 * * [misc]simplify: iters left: 6 (15 enodes) 1536754415.752 * * [misc]simplify: iters left: 5 (23 enodes) 1536754415.761 * * [misc]simplify: iters left: 4 (34 enodes) 1536754415.772 * * [misc]simplify: iters left: 3 (37 enodes) 1536754415.786 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1536754415.786 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536754415.787 * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754415.788 * * [misc]simplify: iters left: 6 (14 enodes) 1536754415.793 * * [misc]simplify: iters left: 5 (20 enodes) 1536754415.801 * * [misc]simplify: iters left: 4 (29 enodes) 1536754415.809 * * [misc]simplify: iters left: 3 (30 enodes) 1536754415.813 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754415.813 * [misc]simplify: Simplified (2 2) 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))))) 1536754415.813 * * * * [misc]progress: [ 54 / 82 ] simplifiying candidate # 1536754415.814 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1) 1536754415.814 * * [misc]simplify: iters left: 6 (14 enodes) 1536754415.817 * * [misc]simplify: iters left: 5 (24 enodes) 1536754415.823 * * [misc]simplify: iters left: 4 (39 enodes) 1536754415.834 * * [misc]simplify: iters left: 3 (54 enodes) 1536754415.852 * * [misc]simplify: iters left: 2 (80 enodes) 1536754415.866 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) 1536754415.866 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)))) 1536754415.866 * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)) 1536754415.867 * * [misc]simplify: iters left: 6 (13 enodes) 1536754415.869 * * [misc]simplify: iters left: 5 (19 enodes) 1536754415.873 * * [misc]simplify: iters left: 4 (28 enodes) 1536754415.878 * * [misc]simplify: iters left: 3 (30 enodes) 1536754415.883 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1536754415.883 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1536754415.883 * * * * [misc]progress: [ 55 / 82 ] simplifiying candidate # 1536754415.883 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.884 * * [misc]simplify: iters left: 6 (15 enodes) 1536754415.887 * * [misc]simplify: iters left: 5 (23 enodes) 1536754415.892 * * [misc]simplify: iters left: 4 (32 enodes) 1536754415.898 * * [misc]simplify: iters left: 3 (34 enodes) 1536754415.909 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754415.909 * [misc]simplify: Simplified (2 1) 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))))) 1536754415.910 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754415.911 * * [misc]simplify: iters left: 6 (14 enodes) 1536754415.916 * * [misc]simplify: iters left: 5 (20 enodes) 1536754415.925 * * [misc]simplify: iters left: 4 (29 enodes) 1536754415.935 * * [misc]simplify: iters left: 3 (30 enodes) 1536754415.940 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754415.940 * [misc]simplify: Simplified (2 2) 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))))) 1536754415.940 * * * * [misc]progress: [ 56 / 82 ] simplifiying candidate # 1536754415.941 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754415.941 * * [misc]simplify: iters left: 6 (14 enodes) 1536754415.944 * * [misc]simplify: iters left: 5 (20 enodes) 1536754415.948 * * [misc]simplify: iters left: 4 (29 enodes) 1536754415.952 * * [misc]simplify: iters left: 3 (30 enodes) 1536754415.957 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754415.957 * [misc]simplify: Simplified (2 1) 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))))) 1536754415.957 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754415.958 * * [misc]simplify: iters left: 6 (14 enodes) 1536754415.961 * * [misc]simplify: iters left: 5 (20 enodes) 1536754415.966 * * [misc]simplify: iters left: 4 (29 enodes) 1536754415.975 * * [misc]simplify: iters left: 3 (30 enodes) 1536754415.985 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754415.985 * [misc]simplify: Simplified (2 2) 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))))) 1536754415.985 * * * * [misc]progress: [ 57 / 82 ] simplifiying candidate # 1536754415.985 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1) 1536754415.986 * * [misc]simplify: iters left: 6 (13 enodes) 1536754415.992 * * [misc]simplify: iters left: 5 (21 enodes) 1536754416.000 * * [misc]simplify: iters left: 4 (32 enodes) 1536754416.005 * * [misc]simplify: iters left: 3 (33 enodes) 1536754416.009 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1536754416.009 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)))) 1536754416.009 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)) 1536754416.010 * * [misc]simplify: iters left: 6 (13 enodes) 1536754416.013 * * [misc]simplify: iters left: 5 (19 enodes) 1536754416.016 * * [misc]simplify: iters left: 4 (28 enodes) 1536754416.022 * * [misc]simplify: iters left: 3 (30 enodes) 1536754416.031 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1536754416.031 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1536754416.032 * * * * [misc]progress: [ 58 / 82 ] simplifiying candidate # 1536754416.032 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754416.032 * * [misc]simplify: iters left: 6 (6 enodes) 1536754416.035 * * [misc]simplify: iters left: 5 (10 enodes) 1536754416.039 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536754416.039 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536754416.040 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754416.041 * * [misc]simplify: iters left: 6 (13 enodes) 1536754416.046 * * [misc]simplify: iters left: 5 (19 enodes) 1536754416.050 * * [misc]simplify: iters left: 4 (28 enodes) 1536754416.055 * * [misc]simplify: iters left: 3 (30 enodes) 1536754416.059 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754416.059 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536754416.060 * * * * [misc]progress: [ 59 / 82 ] simplifiying candidate # 1536754416.060 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536754416.060 * * [misc]simplify: iters left: 4 (5 enodes) 1536754416.061 * * [misc]simplify: iters left: 3 (7 enodes) 1536754416.062 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536754416.062 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536754416.062 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754416.063 * * [misc]simplify: iters left: 6 (13 enodes) 1536754416.065 * * [misc]simplify: iters left: 5 (19 enodes) 1536754416.069 * * [misc]simplify: iters left: 4 (28 enodes) 1536754416.073 * * [misc]simplify: iters left: 3 (30 enodes) 1536754416.078 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754416.078 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536754416.078 * * * * [misc]progress: [ 60 / 82 ] simplifiying candidate # 1536754416.078 * [enter]simplify: Simplifying (/ 1 1) 1536754416.078 * * [misc]simplify: iters left: 2 (2 enodes) 1536754416.079 * * [misc]simplify: iters left: 1 (4 enodes) 1536754416.079 * [exit]simplify: Simplified to 1 1536754416.079 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))) 1536754416.079 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) 1536754416.080 * * [misc]simplify: iters left: 6 (12 enodes) 1536754416.083 * * [misc]simplify: iters left: 5 (18 enodes) 1536754416.087 * * [misc]simplify: iters left: 4 (27 enodes) 1536754416.091 * * [misc]simplify: iters left: 3 (29 enodes) 1536754416.095 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k)) 1536754416.095 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k)))) 1536754416.095 * * * * [misc]progress: [ 61 / 82 ] simplifiying candidate # 1536754416.095 * * * * [misc]progress: [ 62 / 82 ] simplifiying candidate # 1536754416.096 * * * * [misc]progress: [ 63 / 82 ] simplifiying candidate # 1536754416.096 * * * * [misc]progress: [ 64 / 82 ] simplifiying candidate # 1536754416.096 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536754416.096 * * [misc]simplify: iters left: 2 (3 enodes) 1536754416.096 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536754416.096 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) 1536754416.097 * * * * [misc]progress: [ 65 / 82 ] simplifiying candidate # 1536754416.097 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536754416.097 * * [misc]simplify: iters left: 2 (3 enodes) 1536754416.097 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536754416.097 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1536754416.097 * * * * [misc]progress: [ 66 / 82 ] simplifiying candidate # 1536754416.098 * [enter]simplify: Simplifying (sqrt k) 1536754416.098 * * [misc]simplify: iters left: 1 (2 enodes) 1536754416.098 * [exit]simplify: Simplified to (sqrt k) 1536754416.098 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1536754416.098 * * * * [misc]progress: [ 67 / 82 ] simplifiying candidate # 1536754416.098 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) 1/2) 1536754416.098 * * [misc]simplify: iters left: 5 (7 enodes) 1536754416.101 * * [misc]simplify: iters left: 4 (12 enodes) 1536754416.107 * * [misc]simplify: iters left: 3 (18 enodes) 1536754416.113 * * [misc]simplify: iters left: 2 (20 enodes) 1536754416.119 * [exit]simplify: Simplified to (sqrt (* (* PI n) 2)) 1536754416.119 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2)))))) 1536754416.119 * * * * [misc]progress: [ 68 / 82 ] simplifiying candidate # 1536754416.120 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) 1/2) 1536754416.120 * * [misc]simplify: iters left: 5 (7 enodes) 1536754416.123 * * [misc]simplify: iters left: 4 (12 enodes) 1536754416.128 * * [misc]simplify: iters left: 3 (18 enodes) 1536754416.134 * * [misc]simplify: iters left: 2 (20 enodes) 1536754416.141 * [exit]simplify: Simplified to (sqrt (* (* PI n) 2)) 1536754416.141 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2)))))) 1536754416.141 * * * * [misc]progress: [ 69 / 82 ] simplifiying candidate # 1536754416.141 * [enter]simplify: Simplifying (pow 2 (- 1/2 (/ k 2))) 1536754416.142 * * [misc]simplify: iters left: 5 (6 enodes) 1536754416.144 * * [misc]simplify: iters left: 4 (8 enodes) 1536754416.147 * * [misc]simplify: iters left: 3 (11 enodes) 1536754416.150 * [exit]simplify: Simplified to (pow 2 (- 1/2 (/ k 2))) 1536754416.150 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow 2 (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))))) 1536754416.150 * * * * [misc]progress: [ 70 / 82 ] simplifiying candidate # 1536754416.151 * [enter]simplify: Simplifying (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1536754416.152 * * [misc]simplify: iters left: 6 (12 enodes) 1536754416.157 * * [misc]simplify: iters left: 5 (18 enodes) 1536754416.164 * * [misc]simplify: iters left: 4 (27 enodes) 1536754416.172 * * [misc]simplify: iters left: 3 (29 enodes) 1536754416.182 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1536754416.182 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (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))))))) 1536754416.182 * * * * [misc]progress: [ 71 / 82 ] simplifiying candidate # 1536754416.182 * [enter]simplify: Simplifying (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1536754416.183 * * [misc]simplify: iters left: 6 (11 enodes) 1536754416.188 * * [misc]simplify: iters left: 5 (17 enodes) 1536754416.193 * * [misc]simplify: iters left: 4 (26 enodes) 1536754416.197 * * [misc]simplify: iters left: 3 (27 enodes) 1536754416.202 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1536754416.202 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) 1536754416.202 * * * * [misc]progress: [ 72 / 82 ] simplifiying candidate # 1536754416.202 * * * * [misc]progress: [ 73 / 82 ] simplifiying candidate # 1536754416.202 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) 1/2) 1536754416.203 * * [misc]simplify: iters left: 5 (7 enodes) 1536754416.204 * * [misc]simplify: iters left: 4 (12 enodes) 1536754416.206 * * [misc]simplify: iters left: 3 (18 enodes) 1536754416.209 * * [misc]simplify: iters left: 2 (20 enodes) 1536754416.212 * [exit]simplify: Simplified to (sqrt (* (* PI n) 2)) 1536754416.212 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))))) 1536754416.212 * * * * [misc]progress: [ 74 / 82 ] simplifiying candidate # 1536754416.213 * [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))))) 1536754416.215 * * [misc]simplify: iters left: 6 (37 enodes) 1536754416.232 * * [misc]simplify: iters left: 5 (108 enodes) 1536754416.291 * * [misc]simplify: iters left: 4 (368 enodes) 1536754416.863 * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) 1536754416.863 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) 1536754416.863 * * * * [misc]progress: [ 75 / 82 ] simplifiying candidate # 1536754416.863 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1536754416.864 * * [misc]simplify: iters left: 6 (15 enodes) 1536754416.869 * * [misc]simplify: iters left: 5 (33 enodes) 1536754416.880 * * [misc]simplify: iters left: 4 (64 enodes) 1536754416.903 * * [misc]simplify: iters left: 3 (179 enodes) 1536754417.086 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1536754417.086 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) 1536754417.086 * * * * [misc]progress: [ 76 / 82 ] simplifiying candidate # 1536754417.087 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1536754417.089 * * [misc]simplify: iters left: 6 (15 enodes) 1536754417.097 * * [misc]simplify: iters left: 5 (30 enodes) 1536754417.114 * * [misc]simplify: iters left: 4 (65 enodes) 1536754417.157 * * [misc]simplify: iters left: 3 (208 enodes) 1536754417.437 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1536754417.437 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1536754417.437 * * * * [misc]progress: [ 77 / 82 ] simplifiying candidate # 1536754417.438 * [enter]simplify: Simplifying (* n PI) 1536754417.438 * * [misc]simplify: iters left: 2 (3 enodes) 1536754417.439 * * [misc]simplify: iters left: 1 (4 enodes) 1536754417.441 * [exit]simplify: Simplified to (* n PI) 1536754417.441 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) 1536754417.441 * * * * [misc]progress: [ 78 / 82 ] simplifiying candidate # 1536754417.441 * [enter]simplify: Simplifying (* n PI) 1536754417.441 * * [misc]simplify: iters left: 2 (3 enodes) 1536754417.443 * * [misc]simplify: iters left: 1 (4 enodes) 1536754417.444 * [exit]simplify: Simplified to (* n PI) 1536754417.444 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) 1536754417.444 * * * * [misc]progress: [ 79 / 82 ] simplifiying candidate # 1536754417.444 * [enter]simplify: Simplifying (* n PI) 1536754417.444 * * [misc]simplify: iters left: 2 (3 enodes) 1536754417.446 * * [misc]simplify: iters left: 1 (4 enodes) 1536754417.447 * [exit]simplify: Simplified to (* n PI) 1536754417.447 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) 1536754417.447 * * * * [misc]progress: [ 80 / 82 ] simplifiying candidate # 1536754417.448 * [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)))))))))))))))))))))) 1536754417.448 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754417.448 * * * * [misc]progress: [ 81 / 82 ] simplifiying candidate # 1536754417.448 * [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)))))))) 1536754417.448 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754417.448 * * * * [misc]progress: [ 82 / 82 ] simplifiying candidate # 1536754417.448 * [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))))))))))) 1536754417.448 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754417.448 * * * [misc]progress: adding candidates to table 1536754419.264 * * [misc]progress: iteration 3 / 4 1536754419.264 * * * [misc]progress: picking best candidate 1536754419.383 * * * * [misc]pick: Picked # 1536754419.383 * * * [misc]progress: localizing error 1536754419.436 * * * [misc]progress: generating rewritten candidates 1536754419.436 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2) 1536754419.549 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1) 1536754419.577 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1 1) 1536754419.578 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) 1536754419.652 * * * [misc]progress: generating series expansions 1536754419.652 * * * * [misc]progress: [ 1 / 4 ] generating series at (2) 1536754419.653 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1536754419.653 * [misc]approximate: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (k n) around 0 1536754419.653 * [misc]taylor: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.653 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.653 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.653 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.653 * [misc]taylor: Taking taylor expansion of k in n 1536754419.653 * [misc]backup-simplify: Simplify k into k 1536754419.653 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.653 * [misc]taylor: Taking taylor expansion of n in n 1536754419.653 * [misc]backup-simplify: Simplify 0 into 0 1536754419.653 * [misc]backup-simplify: Simplify 1 into 1 1536754419.653 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.653 * [misc]backup-simplify: Simplify PI into PI 1536754419.654 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.655 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.655 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.655 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754419.655 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754419.655 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754419.656 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.656 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536754419.657 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536754419.657 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n 1536754419.657 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n 1536754419.657 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n 1536754419.657 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754419.657 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.657 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754419.657 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.657 * [misc]taylor: Taking taylor expansion of k in n 1536754419.657 * [misc]backup-simplify: Simplify k into k 1536754419.657 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.657 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.657 * [misc]backup-simplify: Simplify 2 into 2 1536754419.657 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.657 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754419.657 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754419.657 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754419.658 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k))) 1536754419.658 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k)))) 1536754419.658 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754419.658 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.658 * [misc]taylor: Taking taylor expansion of k in n 1536754419.658 * [misc]backup-simplify: Simplify k into k 1536754419.658 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.658 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754419.658 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754419.659 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754419.659 * [misc]taylor: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.659 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.659 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.659 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.659 * [misc]taylor: Taking taylor expansion of k in k 1536754419.659 * [misc]backup-simplify: Simplify 0 into 0 1536754419.659 * [misc]backup-simplify: Simplify 1 into 1 1536754419.659 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536754419.659 * [misc]taylor: Taking taylor expansion of n in k 1536754419.659 * [misc]backup-simplify: Simplify n into n 1536754419.659 * [misc]taylor: Taking taylor expansion of PI in k 1536754419.659 * [misc]backup-simplify: Simplify PI into PI 1536754419.659 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754419.659 * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) 1536754419.660 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754419.660 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.660 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.660 * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) 1536754419.660 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) 1536754419.660 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 1536754419.660 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 1536754419.660 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 1536754419.660 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754419.660 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.660 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.660 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754419.660 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.661 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.661 * [misc]taylor: Taking taylor expansion of k in k 1536754419.661 * [misc]backup-simplify: Simplify 0 into 0 1536754419.661 * [misc]backup-simplify: Simplify 1 into 1 1536754419.661 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754419.661 * [misc]taylor: Taking taylor expansion of 2 in k 1536754419.661 * [misc]backup-simplify: Simplify 2 into 2 1536754419.661 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.661 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754419.661 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.661 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.662 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536754419.662 * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 1536754419.662 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754419.662 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.662 * [misc]taylor: Taking taylor expansion of k in k 1536754419.662 * [misc]backup-simplify: Simplify 0 into 0 1536754419.662 * [misc]backup-simplify: Simplify 1 into 1 1536754419.663 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.663 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.663 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754419.663 * [misc]taylor: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1536754419.663 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k 1536754419.663 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k 1536754419.663 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k 1536754419.663 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k 1536754419.663 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754419.663 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.664 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.664 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754419.664 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.664 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.664 * [misc]taylor: Taking taylor expansion of k in k 1536754419.664 * [misc]backup-simplify: Simplify 0 into 0 1536754419.664 * [misc]backup-simplify: Simplify 1 into 1 1536754419.664 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k 1536754419.664 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536754419.664 * [misc]taylor: Taking taylor expansion of n in k 1536754419.664 * [misc]backup-simplify: Simplify n into n 1536754419.664 * [misc]taylor: Taking taylor expansion of PI in k 1536754419.664 * [misc]backup-simplify: Simplify PI into PI 1536754419.664 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754419.664 * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) 1536754419.664 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754419.664 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.665 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.665 * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) 1536754419.665 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) 1536754419.665 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 1536754419.665 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 1536754419.665 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 1536754419.665 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754419.665 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.665 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.665 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754419.665 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.665 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.665 * [misc]taylor: Taking taylor expansion of k in k 1536754419.665 * [misc]backup-simplify: Simplify 0 into 0 1536754419.665 * [misc]backup-simplify: Simplify 1 into 1 1536754419.665 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754419.665 * [misc]taylor: Taking taylor expansion of 2 in k 1536754419.665 * [misc]backup-simplify: Simplify 2 into 2 1536754419.666 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.666 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754419.666 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.666 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.666 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536754419.667 * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 1536754419.667 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754419.667 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.667 * [misc]taylor: Taking taylor expansion of k in k 1536754419.667 * [misc]backup-simplify: Simplify 0 into 0 1536754419.667 * [misc]backup-simplify: Simplify 1 into 1 1536754419.667 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.667 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.668 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754419.669 * [misc]backup-simplify: Simplify (* (pow (* n PI) 1/2) (pow 2 1/2)) into (sqrt (* n (* PI 2))) 1536754419.670 * [misc]backup-simplify: Simplify (* (sqrt (* n (* PI 2))) 0) into 0 1536754419.670 * [misc]taylor: Taking taylor expansion of 0 in n 1536754419.670 * [misc]backup-simplify: Simplify 0 into 0 1536754419.670 * [misc]backup-simplify: Simplify 0 into 0 1536754419.672 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536754419.673 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754419.673 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754419.673 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754419.674 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2))) 1536754419.677 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2))) 1536754419.677 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1536754419.679 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* n PI) 1)))) 1) into 0 1536754419.679 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754419.679 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754419.679 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754419.680 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* n PI)))) into (- (* 1/2 (log (* n PI)))) 1536754419.680 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1)))) into (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) 1536754419.682 * [misc]backup-simplify: Simplify (+ (* (pow (* n PI) 1/2) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (pow 2 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) 1536754419.684 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1536754419.684 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1536754419.684 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536754419.684 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.684 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.684 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536754419.684 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.684 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.684 * [misc]backup-simplify: Simplify 2 into 2 1536754419.684 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.685 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.685 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.685 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.685 * [misc]taylor: Taking taylor expansion of n in n 1536754419.685 * [misc]backup-simplify: Simplify 0 into 0 1536754419.685 * [misc]backup-simplify: Simplify 1 into 1 1536754419.685 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.685 * [misc]backup-simplify: Simplify PI into PI 1536754419.685 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.686 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.686 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.687 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.687 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536754419.687 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.687 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.687 * [misc]backup-simplify: Simplify 0 into 0 1536754419.687 * [misc]backup-simplify: Simplify 0 into 0 1536754419.688 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754419.689 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754419.693 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1536754419.694 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754419.694 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.694 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.694 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0 1536754419.699 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) 1536754419.700 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1536754419.702 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* n PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* n PI) 1)))) 2) into 0 1536754419.702 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754419.703 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.703 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.703 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* n PI))))) into 0 1536754419.705 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) 1536754419.712 * [misc]backup-simplify: Simplify (+ (* (pow (* n PI) 1/2) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (pow 2 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) 1536754419.719 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) +nan.0) (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 1536754419.720 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 1536754419.720 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 1536754419.720 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536754419.720 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.720 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.720 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 1536754419.720 * [misc]taylor: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 1536754419.720 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.720 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.720 * [misc]backup-simplify: Simplify 2 into 2 1536754419.720 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.720 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.720 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.720 * [misc]backup-simplify: Simplify 2 into 2 1536754419.720 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.721 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.721 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.721 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.721 * [misc]taylor: Taking taylor expansion of n in n 1536754419.721 * [misc]backup-simplify: Simplify 0 into 0 1536754419.721 * [misc]backup-simplify: Simplify 1 into 1 1536754419.721 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.721 * [misc]backup-simplify: Simplify PI into PI 1536754419.721 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.722 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.722 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.723 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.723 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1536754419.723 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1536754419.723 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n 1536754419.723 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.723 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.723 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n 1536754419.723 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n 1536754419.723 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.723 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.723 * [misc]backup-simplify: Simplify 2 into 2 1536754419.723 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.724 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.724 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754419.724 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.724 * [misc]taylor: Taking taylor expansion of n in n 1536754419.724 * [misc]backup-simplify: Simplify 0 into 0 1536754419.724 * [misc]backup-simplify: Simplify 1 into 1 1536754419.724 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.724 * [misc]backup-simplify: Simplify PI into PI 1536754419.724 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.725 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.725 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.726 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.726 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.726 * [misc]taylor: Taking taylor expansion of n in n 1536754419.726 * [misc]backup-simplify: Simplify 0 into 0 1536754419.726 * [misc]backup-simplify: Simplify 1 into 1 1536754419.726 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.726 * [misc]backup-simplify: Simplify PI into PI 1536754419.726 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.727 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.727 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.727 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.727 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1536754419.727 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536754419.727 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.727 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.727 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536754419.728 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.728 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.728 * [misc]backup-simplify: Simplify 2 into 2 1536754419.728 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.728 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.728 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.728 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.728 * [misc]taylor: Taking taylor expansion of n in n 1536754419.728 * [misc]backup-simplify: Simplify 0 into 0 1536754419.728 * [misc]backup-simplify: Simplify 1 into 1 1536754419.728 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.728 * [misc]backup-simplify: Simplify PI into PI 1536754419.728 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.729 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.729 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.730 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.730 * [misc]backup-simplify: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 1536754419.731 * [misc]backup-simplify: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 1536754419.731 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.731 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.732 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n))) 1536754419.732 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0 1536754419.733 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.733 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536754419.733 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.733 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.733 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.733 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.734 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.734 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.734 * [misc]backup-simplify: Simplify 0 into 0 1536754419.735 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754419.737 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754419.739 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754419.740 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754419.740 * [misc]backup-simplify: Simplify 0 into 0 1536754419.740 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754419.741 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754419.746 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1536754419.747 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754419.747 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.747 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.747 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0 1536754419.751 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2))) 1536754419.752 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754419.754 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* n PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* n PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* n PI) 1)))) 6) into 0 1536754419.754 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754419.755 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.755 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.755 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* n PI)))))) into 0 1536754419.757 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log (* n PI)) 3) (sqrt (* n PI)))) 1536754419.765 * [misc]backup-simplify: Simplify (+ (* (pow (* n PI) 1/2) (* -1/48 (* (pow (log 2) 3) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/48 (* (pow (log (* n PI)) 3) (sqrt (* n PI)))) (pow 2 1/2))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log (* n PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* n PI)) 3)) (sqrt (* n PI)))))))) 1536754419.785 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) +nan.0) (* (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log (* n PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* n PI)) 3)) (sqrt (* n PI)))))))) 0)))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))))) 1536754419.785 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))))) in n 1536754419.785 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))))) in n 1536754419.785 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536754419.786 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.786 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.786 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 1536754419.786 * [misc]taylor: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 1536754419.786 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.786 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.786 * [misc]backup-simplify: Simplify 2 into 2 1536754419.786 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.786 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.786 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.786 * [misc]backup-simplify: Simplify 2 into 2 1536754419.786 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.786 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.786 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.786 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.786 * [misc]taylor: Taking taylor expansion of n in n 1536754419.786 * [misc]backup-simplify: Simplify 0 into 0 1536754419.786 * [misc]backup-simplify: Simplify 1 into 1 1536754419.786 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.786 * [misc]backup-simplify: Simplify PI into PI 1536754419.787 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.787 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.787 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.787 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.788 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.788 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.788 * [misc]taylor: Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of (pow (log 2) 2) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.788 * [misc]backup-simplify: Simplify 2 into 2 1536754419.788 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.788 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.788 * [misc]backup-simplify: Simplify 2 into 2 1536754419.788 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.788 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.788 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.788 * [misc]taylor: Taking taylor expansion of n in n 1536754419.788 * [misc]backup-simplify: Simplify 0 into 0 1536754419.788 * [misc]backup-simplify: Simplify 1 into 1 1536754419.788 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.788 * [misc]backup-simplify: Simplify PI into PI 1536754419.788 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.789 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.789 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.789 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.789 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))) in n 1536754419.789 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))) in n 1536754419.789 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) in n 1536754419.789 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.789 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.789 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI))) in n 1536754419.789 * [misc]taylor: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log (* n PI)))) in n 1536754419.789 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.790 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.790 * [misc]backup-simplify: Simplify 2 into 2 1536754419.790 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.790 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n 1536754419.790 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.790 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.790 * [misc]backup-simplify: Simplify 2 into 2 1536754419.790 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.790 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.790 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754419.790 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.790 * [misc]taylor: Taking taylor expansion of n in n 1536754419.790 * [misc]backup-simplify: Simplify 0 into 0 1536754419.790 * [misc]backup-simplify: Simplify 1 into 1 1536754419.790 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.790 * [misc]backup-simplify: Simplify PI into PI 1536754419.790 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.791 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.791 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.791 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.791 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.791 * [misc]taylor: Taking taylor expansion of n in n 1536754419.791 * [misc]backup-simplify: Simplify 0 into 0 1536754419.791 * [misc]backup-simplify: Simplify 1 into 1 1536754419.791 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.791 * [misc]backup-simplify: Simplify PI into PI 1536754419.791 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.792 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.792 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.792 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.792 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))) in n 1536754419.792 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))) in n 1536754419.792 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) in n 1536754419.792 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.792 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.792 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))) in n 1536754419.792 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* n PI)) 2)) in n 1536754419.792 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.792 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.792 * [misc]backup-simplify: Simplify 2 into 2 1536754419.792 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.792 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.793 * [misc]taylor: Taking taylor expansion of (pow (log (* n PI)) 2) in n 1536754419.793 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754419.793 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.793 * [misc]taylor: Taking taylor expansion of n in n 1536754419.793 * [misc]backup-simplify: Simplify 0 into 0 1536754419.793 * [misc]backup-simplify: Simplify 1 into 1 1536754419.793 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.793 * [misc]backup-simplify: Simplify PI into PI 1536754419.793 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.793 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.793 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.794 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.794 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.794 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.794 * [misc]taylor: Taking taylor expansion of n in n 1536754419.794 * [misc]backup-simplify: Simplify 0 into 0 1536754419.794 * [misc]backup-simplify: Simplify 1 into 1 1536754419.794 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.794 * [misc]backup-simplify: Simplify PI into PI 1536754419.794 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.794 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.795 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.795 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.795 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))) in n 1536754419.795 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) in n 1536754419.795 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536754419.795 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.795 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.795 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536754419.795 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.795 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.795 * [misc]backup-simplify: Simplify 2 into 2 1536754419.795 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.795 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.795 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.795 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.795 * [misc]taylor: Taking taylor expansion of n in n 1536754419.795 * [misc]backup-simplify: Simplify 0 into 0 1536754419.795 * [misc]backup-simplify: Simplify 1 into 1 1536754419.795 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.795 * [misc]backup-simplify: Simplify PI into PI 1536754419.796 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.796 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.796 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.796 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.796 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))) in n 1536754419.797 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n 1536754419.797 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.797 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.797 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n 1536754419.797 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n 1536754419.797 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754419.797 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.797 * [misc]backup-simplify: Simplify 2 into 2 1536754419.797 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754419.797 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754419.797 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754419.797 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.797 * [misc]taylor: Taking taylor expansion of n in n 1536754419.797 * [misc]backup-simplify: Simplify 0 into 0 1536754419.797 * [misc]backup-simplify: Simplify 1 into 1 1536754419.797 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.797 * [misc]backup-simplify: Simplify PI into PI 1536754419.797 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.798 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.798 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.798 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754419.798 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.798 * [misc]taylor: Taking taylor expansion of n in n 1536754419.798 * [misc]backup-simplify: Simplify 0 into 0 1536754419.798 * [misc]backup-simplify: Simplify 1 into 1 1536754419.798 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.798 * [misc]backup-simplify: Simplify PI into PI 1536754419.798 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.799 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.799 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.799 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754419.799 * [misc]backup-simplify: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 1536754419.799 * [misc]backup-simplify: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 1536754419.800 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.800 * [misc]backup-simplify: Simplify (* (log 2) (log 2)) into (pow (log 2) 2) 1536754419.801 * [misc]backup-simplify: Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2)) 1536754419.802 * [misc]backup-simplify: Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0 1536754419.802 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.802 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.802 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n))) 1536754419.803 * [misc]backup-simplify: Simplify (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) into (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) 1536754419.803 * [misc]backup-simplify: Simplify (* (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) 0) into 0 1536754419.803 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.804 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.804 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.805 * [misc]backup-simplify: Simplify (* (+ (log PI) (log n)) (+ (log PI) (log n))) into (pow (+ (log PI) (log n)) 2) 1536754419.805 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) into (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) 1536754419.806 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) 0) into 0 1536754419.806 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.806 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536754419.806 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.806 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.807 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n))) 1536754419.807 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0 1536754419.807 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754419.807 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.807 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.808 * [misc]backup-simplify: Simplify 0 into 0 1536754419.810 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536754419.810 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0 1536754419.811 * [misc]backup-simplify: Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 1536754419.813 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 1536754419.814 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754419.815 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754419.816 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.816 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log PI) (log n)))) into 0 1536754419.817 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log PI) (log n))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) 1536754419.818 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) 1536754419.819 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754419.820 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754419.821 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754419.823 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536754419.826 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536754419.830 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536754419.834 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536754419.839 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536754419.839 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754419.841 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536754419.841 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536754419.843 * [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)))) 1536754419.846 * [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)))) 1536754419.848 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536754419.849 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536754419.856 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1536754419.856 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1536754419.856 * [misc]approximate: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (k n) around 0 1536754419.856 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.856 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.856 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.856 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.856 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of k in n 1536754419.856 * [misc]backup-simplify: Simplify k into k 1536754419.856 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.856 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.856 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.856 * [misc]backup-simplify: Simplify 2 into 2 1536754419.857 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.857 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.857 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754419.857 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754419.857 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.857 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.857 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754419.857 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536754419.857 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536754419.857 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754419.857 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.857 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.857 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.857 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.857 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.857 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.857 * [misc]taylor: Taking taylor expansion of k in n 1536754419.857 * [misc]backup-simplify: Simplify k into k 1536754419.857 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.857 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536754419.857 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754419.857 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.858 * [misc]backup-simplify: Simplify PI into PI 1536754419.858 * [misc]taylor: Taking taylor expansion of n in n 1536754419.858 * [misc]backup-simplify: Simplify 0 into 0 1536754419.858 * [misc]backup-simplify: Simplify 1 into 1 1536754419.858 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754419.858 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.858 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.858 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754419.858 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754419.858 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754419.859 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.859 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.859 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754419.859 * [misc]taylor: Taking taylor expansion of k in n 1536754419.859 * [misc]backup-simplify: Simplify k into k 1536754419.859 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754419.859 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754419.859 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536754419.859 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754419.859 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754419.859 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 1536754419.859 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 1536754419.859 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754419.859 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.859 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.859 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754419.859 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.859 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.859 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.859 * [misc]taylor: Taking taylor expansion of k in k 1536754419.860 * [misc]backup-simplify: Simplify 0 into 0 1536754419.860 * [misc]backup-simplify: Simplify 1 into 1 1536754419.860 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.860 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754419.860 * [misc]taylor: Taking taylor expansion of 2 in k 1536754419.860 * [misc]backup-simplify: Simplify 2 into 2 1536754419.860 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.860 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754419.860 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754419.860 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754419.860 * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 1536754419.861 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.861 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754419.861 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k 1536754419.861 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k 1536754419.861 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754419.861 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.861 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.861 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754419.861 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.861 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.861 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.861 * [misc]taylor: Taking taylor expansion of k in k 1536754419.861 * [misc]backup-simplify: Simplify 0 into 0 1536754419.861 * [misc]backup-simplify: Simplify 1 into 1 1536754419.861 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.861 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in k 1536754419.861 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754419.861 * [misc]taylor: Taking taylor expansion of PI in k 1536754419.861 * [misc]backup-simplify: Simplify PI into PI 1536754419.861 * [misc]taylor: Taking taylor expansion of n in k 1536754419.861 * [misc]backup-simplify: Simplify n into n 1536754419.861 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754419.861 * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) 1536754419.861 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754419.861 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754419.861 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754419.862 * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) 1536754419.862 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.862 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of k in k 1536754419.862 * [misc]backup-simplify: Simplify 0 into 0 1536754419.862 * [misc]backup-simplify: Simplify 1 into 1 1536754419.862 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.862 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754419.862 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.862 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.862 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.862 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.862 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.862 * [misc]taylor: Taking taylor expansion of k in k 1536754419.862 * [misc]backup-simplify: Simplify 0 into 0 1536754419.862 * [misc]backup-simplify: Simplify 1 into 1 1536754419.862 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.863 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754419.863 * [misc]taylor: Taking taylor expansion of 2 in k 1536754419.863 * [misc]backup-simplify: Simplify 2 into 2 1536754419.863 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.863 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754419.863 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754419.863 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754419.863 * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 1536754419.863 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.863 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754419.863 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k 1536754419.863 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k 1536754419.863 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754419.865 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.865 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.865 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754419.865 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.865 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.865 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.865 * [misc]taylor: Taking taylor expansion of k in k 1536754419.866 * [misc]backup-simplify: Simplify 0 into 0 1536754419.866 * [misc]backup-simplify: Simplify 1 into 1 1536754419.866 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.866 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in k 1536754419.866 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754419.866 * [misc]taylor: Taking taylor expansion of PI in k 1536754419.866 * [misc]backup-simplify: Simplify PI into PI 1536754419.866 * [misc]taylor: Taking taylor expansion of n in k 1536754419.866 * [misc]backup-simplify: Simplify n into n 1536754419.866 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754419.866 * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) 1536754419.866 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754419.866 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754419.866 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754419.866 * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) 1536754419.867 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.867 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754419.867 * [misc]taylor: Taking taylor expansion of k in k 1536754419.867 * [misc]backup-simplify: Simplify 0 into 0 1536754419.867 * [misc]backup-simplify: Simplify 1 into 1 1536754419.867 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.867 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754419.867 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.868 * [misc]backup-simplify: Simplify (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1536754419.868 * [misc]taylor: Taking taylor expansion of 0 in n 1536754419.868 * [misc]backup-simplify: Simplify 0 into 0 1536754419.868 * [misc]backup-simplify: Simplify 0 into 0 1536754419.868 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1536754419.869 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754419.869 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.869 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.869 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.869 * [misc]backup-simplify: Simplify 2 into 2 1536754419.869 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.869 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.869 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.869 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.869 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.869 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.869 * [misc]taylor: Taking taylor expansion of k in n 1536754419.869 * [misc]backup-simplify: Simplify k into k 1536754419.869 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.869 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.869 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754419.869 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754419.869 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.870 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.870 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754419.870 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536754419.870 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536754419.870 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754419.870 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.870 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.870 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.870 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.870 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.870 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.870 * [misc]taylor: Taking taylor expansion of k in n 1536754419.870 * [misc]backup-simplify: Simplify k into k 1536754419.870 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.870 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536754419.870 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754419.870 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.870 * [misc]backup-simplify: Simplify PI into PI 1536754419.870 * [misc]taylor: Taking taylor expansion of n in n 1536754419.870 * [misc]backup-simplify: Simplify 0 into 0 1536754419.870 * [misc]backup-simplify: Simplify 1 into 1 1536754419.870 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754419.870 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.870 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.871 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754419.871 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754419.871 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754419.871 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.872 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.872 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1536754419.872 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754419.873 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754419.874 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754419.874 * [misc]backup-simplify: Simplify 0 into 0 1536754419.874 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754419.875 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536754419.875 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754419.875 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536754419.875 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536754419.875 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.875 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.876 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754419.876 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754419.876 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754419.876 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.876 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.876 * [misc]backup-simplify: Simplify 2 into 2 1536754419.876 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.876 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754419.876 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.876 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.876 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.876 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.876 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.876 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.876 * [misc]taylor: Taking taylor expansion of k in n 1536754419.876 * [misc]backup-simplify: Simplify k into k 1536754419.876 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.876 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.876 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754419.876 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754419.876 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.877 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.877 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754419.877 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536754419.877 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536754419.877 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754419.877 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.877 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.877 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.877 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.877 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.877 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.877 * [misc]taylor: Taking taylor expansion of k in n 1536754419.877 * [misc]backup-simplify: Simplify k into k 1536754419.877 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.877 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536754419.877 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754419.877 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.877 * [misc]backup-simplify: Simplify PI into PI 1536754419.877 * [misc]taylor: Taking taylor expansion of n in n 1536754419.877 * [misc]backup-simplify: Simplify 0 into 0 1536754419.877 * [misc]backup-simplify: Simplify 1 into 1 1536754419.877 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754419.877 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.877 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.877 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754419.878 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754419.878 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754419.878 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.878 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.879 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1536754419.879 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754419.880 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754419.880 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754419.881 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754419.883 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754419.883 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754419.883 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754419.884 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.884 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.884 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754419.884 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 1536754419.885 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754419.885 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754419.886 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754419.886 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.886 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.887 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536754419.887 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 1536754419.888 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754419.889 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536754419.889 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536754419.889 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.889 * [misc]backup-simplify: Simplify 0 into 0 1536754419.889 * [misc]backup-simplify: Simplify 0 into 0 1536754419.890 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754419.891 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536754419.891 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754419.891 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536754419.891 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536754419.891 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.891 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.891 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754419.891 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.892 * [misc]backup-simplify: Simplify 2 into 2 1536754419.892 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.892 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.892 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.892 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.892 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.892 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of k in n 1536754419.892 * [misc]backup-simplify: Simplify k into k 1536754419.892 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.892 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.892 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754419.892 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754419.892 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.892 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.892 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754419.892 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.892 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.893 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.893 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.893 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.893 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.893 * [misc]taylor: Taking taylor expansion of k in n 1536754419.893 * [misc]backup-simplify: Simplify k into k 1536754419.893 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.893 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536754419.893 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754419.893 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.893 * [misc]backup-simplify: Simplify PI into PI 1536754419.893 * [misc]taylor: Taking taylor expansion of n in n 1536754419.893 * [misc]backup-simplify: Simplify 0 into 0 1536754419.893 * [misc]backup-simplify: Simplify 1 into 1 1536754419.893 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754419.893 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.893 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.893 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754419.893 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754419.894 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754419.894 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536754419.894 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754419.895 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1536754419.896 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754419.896 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754419.897 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754419.901 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1536754419.902 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1536754419.902 * [misc]approximate: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (k n) around 0 1536754419.902 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.902 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.902 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of k in n 1536754419.902 * [misc]backup-simplify: Simplify k into k 1536754419.902 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.902 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.902 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.902 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of -1 in n 1536754419.902 * [misc]backup-simplify: Simplify -1 into -1 1536754419.902 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754419.902 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.902 * [misc]backup-simplify: Simplify PI into PI 1536754419.902 * [misc]taylor: Taking taylor expansion of n in n 1536754419.903 * [misc]backup-simplify: Simplify 0 into 0 1536754419.903 * [misc]backup-simplify: Simplify 1 into 1 1536754419.903 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754419.903 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754419.904 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754419.904 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.904 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754419.905 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754419.906 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536754419.907 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754419.907 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754419.907 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n 1536754419.907 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n 1536754419.907 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754419.907 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.907 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.907 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.907 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.907 * [misc]taylor: Taking taylor expansion of k in n 1536754419.907 * [misc]backup-simplify: Simplify k into k 1536754419.907 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.907 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.907 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.907 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.907 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.907 * [misc]backup-simplify: Simplify 2 into 2 1536754419.907 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.907 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.907 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754419.908 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754419.908 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754419.908 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754419.908 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754419.908 * [misc]taylor: Taking taylor expansion of -1 in n 1536754419.908 * [misc]backup-simplify: Simplify -1 into -1 1536754419.908 * [misc]taylor: Taking taylor expansion of k in n 1536754419.908 * [misc]backup-simplify: Simplify k into k 1536754419.908 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754419.908 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754419.909 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754419.909 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754419.910 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536754419.911 * [misc]backup-simplify: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (sqrt (/ -1 k))) 1536754419.911 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1536754419.911 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536754419.911 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754419.911 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k 1536754419.911 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k 1536754419.911 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754419.911 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754419.911 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.911 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.911 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.911 * [misc]taylor: Taking taylor expansion of k in k 1536754419.911 * [misc]backup-simplify: Simplify 0 into 0 1536754419.911 * [misc]backup-simplify: Simplify 1 into 1 1536754419.911 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.912 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.912 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.912 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in k 1536754419.912 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in k 1536754419.912 * [misc]taylor: Taking taylor expansion of -1 in k 1536754419.912 * [misc]backup-simplify: Simplify -1 into -1 1536754419.912 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754419.912 * [misc]taylor: Taking taylor expansion of PI in k 1536754419.912 * [misc]backup-simplify: Simplify PI into PI 1536754419.912 * [misc]taylor: Taking taylor expansion of n in k 1536754419.912 * [misc]backup-simplify: Simplify n into n 1536754419.912 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754419.912 * [misc]backup-simplify: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 1536754419.912 * [misc]backup-simplify: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 1536754419.912 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754419.913 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.913 * [misc]backup-simplify: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n)))) 1536754419.913 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754419.913 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754419.913 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 1536754419.913 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 1536754419.913 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754419.913 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754419.913 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.913 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.913 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.913 * [misc]taylor: Taking taylor expansion of k in k 1536754419.913 * [misc]backup-simplify: Simplify 0 into 0 1536754419.913 * [misc]backup-simplify: Simplify 1 into 1 1536754419.914 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.914 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.914 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.914 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754419.914 * [misc]taylor: Taking taylor expansion of 2 in k 1536754419.914 * [misc]backup-simplify: Simplify 2 into 2 1536754419.914 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.914 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754419.914 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.914 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536754419.915 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754419.915 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754419.915 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754419.915 * [misc]taylor: Taking taylor expansion of -1 in k 1536754419.915 * [misc]backup-simplify: Simplify -1 into -1 1536754419.915 * [misc]taylor: Taking taylor expansion of k in k 1536754419.915 * [misc]backup-simplify: Simplify 0 into 0 1536754419.915 * [misc]backup-simplify: Simplify 1 into 1 1536754419.915 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754419.915 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.916 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754419.916 * [misc]backup-simplify: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754419.917 * [misc]backup-simplify: Simplify (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754419.917 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1536754419.917 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536754419.917 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754419.917 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k 1536754419.917 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k 1536754419.917 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754419.917 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754419.917 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.917 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.917 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.917 * [misc]taylor: Taking taylor expansion of k in k 1536754419.917 * [misc]backup-simplify: Simplify 0 into 0 1536754419.917 * [misc]backup-simplify: Simplify 1 into 1 1536754419.917 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.917 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.918 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.918 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in k 1536754419.918 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in k 1536754419.918 * [misc]taylor: Taking taylor expansion of -1 in k 1536754419.918 * [misc]backup-simplify: Simplify -1 into -1 1536754419.918 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754419.918 * [misc]taylor: Taking taylor expansion of PI in k 1536754419.918 * [misc]backup-simplify: Simplify PI into PI 1536754419.918 * [misc]taylor: Taking taylor expansion of n in k 1536754419.918 * [misc]backup-simplify: Simplify n into n 1536754419.918 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754419.918 * [misc]backup-simplify: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 1536754419.918 * [misc]backup-simplify: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 1536754419.918 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754419.919 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.919 * [misc]backup-simplify: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n)))) 1536754419.919 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754419.919 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754419.919 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 1536754419.919 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 1536754419.919 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754419.919 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754419.919 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.919 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.919 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754419.919 * [misc]taylor: Taking taylor expansion of k in k 1536754419.919 * [misc]backup-simplify: Simplify 0 into 0 1536754419.919 * [misc]backup-simplify: Simplify 1 into 1 1536754419.919 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754419.919 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.919 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.919 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754419.919 * [misc]taylor: Taking taylor expansion of 2 in k 1536754419.919 * [misc]backup-simplify: Simplify 2 into 2 1536754419.920 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.920 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754419.920 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.920 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536754419.920 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754419.920 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754419.920 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754419.920 * [misc]taylor: Taking taylor expansion of -1 in k 1536754419.920 * [misc]backup-simplify: Simplify -1 into -1 1536754419.920 * [misc]taylor: Taking taylor expansion of k in k 1536754419.920 * [misc]backup-simplify: Simplify 0 into 0 1536754419.920 * [misc]backup-simplify: Simplify 1 into 1 1536754419.920 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754419.921 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754419.921 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754419.921 * [misc]backup-simplify: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754419.921 * [misc]backup-simplify: Simplify (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754419.922 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.922 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.922 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.922 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.922 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of k in n 1536754419.922 * [misc]backup-simplify: Simplify k into k 1536754419.922 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.922 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.922 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.922 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of -1 in n 1536754419.922 * [misc]backup-simplify: Simplify -1 into -1 1536754419.922 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754419.922 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.922 * [misc]backup-simplify: Simplify PI into PI 1536754419.922 * [misc]taylor: Taking taylor expansion of n in n 1536754419.922 * [misc]backup-simplify: Simplify 0 into 0 1536754419.922 * [misc]backup-simplify: Simplify 1 into 1 1536754419.922 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754419.922 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754419.923 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754419.923 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.923 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754419.923 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754419.924 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536754419.924 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754419.924 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754419.924 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754419.924 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.924 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.924 * [misc]backup-simplify: Simplify 2 into 2 1536754419.924 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.924 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754419.924 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.924 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.924 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.924 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.925 * [misc]taylor: Taking taylor expansion of k in n 1536754419.925 * [misc]backup-simplify: Simplify k into k 1536754419.925 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.925 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.925 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.925 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.925 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754419.925 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754419.925 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754419.926 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536754419.926 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536754419.927 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536754419.927 * [misc]backup-simplify: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536754419.928 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754419.928 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754419.929 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754419.929 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.929 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.929 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.929 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of k in n 1536754419.929 * [misc]backup-simplify: Simplify k into k 1536754419.929 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.929 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.929 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of -1 in n 1536754419.929 * [misc]backup-simplify: Simplify -1 into -1 1536754419.929 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754419.929 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.929 * [misc]backup-simplify: Simplify PI into PI 1536754419.929 * [misc]taylor: Taking taylor expansion of n in n 1536754419.929 * [misc]backup-simplify: Simplify 0 into 0 1536754419.929 * [misc]backup-simplify: Simplify 1 into 1 1536754419.930 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754419.930 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754419.930 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754419.930 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.930 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754419.931 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754419.931 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536754419.932 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754419.932 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754419.932 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754419.932 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.932 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.932 * [misc]backup-simplify: Simplify 2 into 2 1536754419.932 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.932 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754419.932 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.932 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.932 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.932 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.932 * [misc]taylor: Taking taylor expansion of k in n 1536754419.932 * [misc]backup-simplify: Simplify k into k 1536754419.932 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.932 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.932 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.932 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.932 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754419.932 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754419.932 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754419.933 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536754419.934 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536754419.934 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) 1536754419.935 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) 1536754419.935 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754419.935 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754419.935 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.937 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536754419.937 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1536754419.938 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754419.939 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754419.939 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536754419.941 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 1536754419.941 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754419.941 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754419.942 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.942 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754419.942 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 1536754419.943 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754419.944 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536754419.945 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into 0 1536754419.945 * [misc]backup-simplify: Simplify 0 into 0 1536754419.945 * [misc]backup-simplify: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 1536754419.946 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754419.946 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754419.948 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754419.948 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754419.948 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754419.948 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.948 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.948 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of k in n 1536754419.948 * [misc]backup-simplify: Simplify k into k 1536754419.948 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.948 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.948 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.948 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of -1 in n 1536754419.948 * [misc]backup-simplify: Simplify -1 into -1 1536754419.948 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754419.948 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.948 * [misc]backup-simplify: Simplify PI into PI 1536754419.949 * [misc]taylor: Taking taylor expansion of n in n 1536754419.949 * [misc]backup-simplify: Simplify 0 into 0 1536754419.949 * [misc]backup-simplify: Simplify 1 into 1 1536754419.949 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754419.949 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754419.950 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754419.950 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.950 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754419.951 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754419.951 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536754419.952 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754419.952 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754419.952 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754419.952 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754419.952 * [misc]taylor: Taking taylor expansion of 2 in n 1536754419.952 * [misc]backup-simplify: Simplify 2 into 2 1536754419.952 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754419.952 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754419.952 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754419.953 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.953 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.953 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754419.953 * [misc]taylor: Taking taylor expansion of k in n 1536754419.953 * [misc]backup-simplify: Simplify k into k 1536754419.953 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754419.953 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.953 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.953 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754419.953 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754419.953 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754419.953 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754419.955 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536754419.956 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536754419.957 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) 1536754419.958 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) 1536754419.962 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))))) 1536754419.963 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1) 1536754419.963 * [misc]backup-simplify: Simplify (pow (* n PI) (- 1/2 (/ k 2))) into (pow (* n PI) (- 1/2 (* 1/2 k))) 1536754419.963 * [misc]approximate: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in (n k) around 0 1536754419.963 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k 1536754419.963 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k 1536754419.963 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k 1536754419.963 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754419.963 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.963 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.963 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754419.963 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.963 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.964 * [misc]taylor: Taking taylor expansion of k in k 1536754419.964 * [misc]backup-simplify: Simplify 0 into 0 1536754419.964 * [misc]backup-simplify: Simplify 1 into 1 1536754419.964 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k 1536754419.964 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536754419.964 * [misc]taylor: Taking taylor expansion of n in k 1536754419.964 * [misc]backup-simplify: Simplify n into n 1536754419.964 * [misc]taylor: Taking taylor expansion of PI in k 1536754419.964 * [misc]backup-simplify: Simplify PI into PI 1536754419.964 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754419.964 * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) 1536754419.964 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754419.964 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.965 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.965 * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) 1536754419.965 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) 1536754419.965 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536754419.965 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536754419.965 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536754419.965 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754419.965 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.965 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.965 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754419.965 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.965 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.965 * [misc]taylor: Taking taylor expansion of k in n 1536754419.965 * [misc]backup-simplify: Simplify k into k 1536754419.965 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754419.965 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.965 * [misc]taylor: Taking taylor expansion of n in n 1536754419.965 * [misc]backup-simplify: Simplify 0 into 0 1536754419.965 * [misc]backup-simplify: Simplify 1 into 1 1536754419.965 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.965 * [misc]backup-simplify: Simplify PI into PI 1536754419.966 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.966 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.967 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.967 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754419.967 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754419.967 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754419.967 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.968 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536754419.968 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536754419.968 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536754419.968 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536754419.968 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536754419.969 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754419.969 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.969 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.969 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754419.969 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754419.969 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.969 * [misc]taylor: Taking taylor expansion of k in n 1536754419.969 * [misc]backup-simplify: Simplify k into k 1536754419.969 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754419.969 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754419.969 * [misc]taylor: Taking taylor expansion of n in n 1536754419.969 * [misc]backup-simplify: Simplify 0 into 0 1536754419.969 * [misc]backup-simplify: Simplify 1 into 1 1536754419.969 * [misc]taylor: Taking taylor expansion of PI in n 1536754419.969 * [misc]backup-simplify: Simplify PI into PI 1536754419.969 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754419.970 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754419.970 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.970 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754419.970 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754419.970 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754419.971 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.971 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536754419.972 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536754419.972 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k 1536754419.972 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k 1536754419.972 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754419.972 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.972 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.972 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754419.972 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754419.972 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754419.972 * [misc]taylor: Taking taylor expansion of k in k 1536754419.972 * [misc]backup-simplify: Simplify 0 into 0 1536754419.972 * [misc]backup-simplify: Simplify 1 into 1 1536754419.972 * [misc]taylor: Taking taylor expansion of (+ (log PI) (log n)) in k 1536754419.972 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754419.972 * [misc]taylor: Taking taylor expansion of PI in k 1536754419.972 * [misc]backup-simplify: Simplify PI into PI 1536754419.972 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754419.972 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754419.972 * [misc]taylor: Taking taylor expansion of n in k 1536754419.972 * [misc]backup-simplify: Simplify n into n 1536754419.972 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754419.972 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754419.972 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.973 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754419.973 * [misc]backup-simplify: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n)) 1536754419.973 * [misc]backup-simplify: Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n))) 1536754419.973 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n)))) 1536754419.974 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n)))) 1536754419.974 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754419.976 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754419.976 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536754419.976 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.976 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.977 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.977 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0 1536754419.978 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754419.978 * [misc]taylor: Taking taylor expansion of 0 in k 1536754419.978 * [misc]backup-simplify: Simplify 0 into 0 1536754419.978 * [misc]backup-simplify: Simplify 0 into 0 1536754419.980 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754419.980 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536754419.980 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.980 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754419.981 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754419.981 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754419.981 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1536754419.982 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 1536754419.985 * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 1536754419.986 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754419.990 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754419.991 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536754419.991 * [misc]backup-simplify: Simplify (- 0) into 0 1536754419.991 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754419.991 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754419.992 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0 1536754419.995 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754419.995 * [misc]taylor: Taking taylor expansion of 0 in k 1536754419.995 * [misc]backup-simplify: Simplify 0 into 0 1536754419.995 * [misc]backup-simplify: Simplify 0 into 0 1536754419.995 * [misc]backup-simplify: Simplify 0 into 0 1536754420.000 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754420.002 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536754420.002 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.002 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754420.002 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.003 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.003 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0 1536754420.007 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 1536754420.010 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 1536754420.016 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log PI) (log n)))))) into (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))))) 1536754420.017 * [misc]backup-simplify: Simplify (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536754420.017 * [misc]approximate: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1536754420.017 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754420.017 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k 1536754420.017 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k 1536754420.017 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754420.017 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.017 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.017 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754420.017 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.017 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.017 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.017 * [misc]taylor: Taking taylor expansion of k in k 1536754420.017 * [misc]backup-simplify: Simplify 0 into 0 1536754420.017 * [misc]backup-simplify: Simplify 1 into 1 1536754420.017 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.017 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in k 1536754420.017 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754420.017 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.017 * [misc]backup-simplify: Simplify PI into PI 1536754420.017 * [misc]taylor: Taking taylor expansion of n in k 1536754420.017 * [misc]backup-simplify: Simplify n into n 1536754420.018 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754420.018 * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) 1536754420.018 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754420.018 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754420.018 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754420.018 * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) 1536754420.019 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536754420.019 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754420.019 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536754420.019 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536754420.019 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754420.019 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.019 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.019 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754420.019 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.019 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.019 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.019 * [misc]taylor: Taking taylor expansion of k in n 1536754420.019 * [misc]backup-simplify: Simplify k into k 1536754420.019 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.019 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536754420.019 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.019 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.019 * [misc]backup-simplify: Simplify PI into PI 1536754420.019 * [misc]taylor: Taking taylor expansion of n in n 1536754420.019 * [misc]backup-simplify: Simplify 0 into 0 1536754420.019 * [misc]backup-simplify: Simplify 1 into 1 1536754420.020 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.020 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.020 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754420.020 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754420.020 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754420.021 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.021 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536754420.022 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754420.022 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754420.022 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536754420.022 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536754420.022 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754420.022 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.022 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.022 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754420.022 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.022 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.022 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.022 * [misc]taylor: Taking taylor expansion of k in n 1536754420.022 * [misc]backup-simplify: Simplify k into k 1536754420.022 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.022 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536754420.022 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.022 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.022 * [misc]backup-simplify: Simplify PI into PI 1536754420.022 * [misc]taylor: Taking taylor expansion of n in n 1536754420.022 * [misc]backup-simplify: Simplify 0 into 0 1536754420.022 * [misc]backup-simplify: Simplify 1 into 1 1536754420.023 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.023 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.023 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754420.023 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754420.023 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754420.024 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.024 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536754420.025 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754420.025 * [misc]taylor: Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754420.025 * [misc]taylor: Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754420.025 * [misc]taylor: Taking taylor expansion of (- (log PI) (log n)) in k 1536754420.025 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754420.025 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.025 * [misc]backup-simplify: Simplify PI into PI 1536754420.025 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.025 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754420.025 * [misc]taylor: Taking taylor expansion of n in k 1536754420.025 * [misc]backup-simplify: Simplify n into n 1536754420.025 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754420.025 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754420.025 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.025 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.025 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754420.025 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.026 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.026 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.026 * [misc]taylor: Taking taylor expansion of k in k 1536754420.026 * [misc]backup-simplify: Simplify 0 into 0 1536754420.026 * [misc]backup-simplify: Simplify 1 into 1 1536754420.026 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.026 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754420.026 * [misc]backup-simplify: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 1536754420.026 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754420.027 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754420.027 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754420.027 * [misc]backup-simplify: Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n))) 1536754420.028 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754420.028 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754420.029 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754420.032 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754420.032 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754420.032 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754420.033 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.033 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.033 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.034 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 1536754420.035 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754420.035 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.035 * [misc]backup-simplify: Simplify 0 into 0 1536754420.035 * [misc]backup-simplify: Simplify 0 into 0 1536754420.035 * [misc]backup-simplify: Simplify 0 into 0 1536754420.037 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.042 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754420.042 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.042 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754420.042 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.043 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.043 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.044 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 1536754420.046 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754420.046 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.046 * [misc]backup-simplify: Simplify 0 into 0 1536754420.047 * [misc]backup-simplify: Simplify 0 into 0 1536754420.047 * [misc]backup-simplify: Simplify 0 into 0 1536754420.047 * [misc]backup-simplify: Simplify 0 into 0 1536754420.048 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.056 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754420.057 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.057 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754420.057 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.057 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.058 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.059 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 1536754420.062 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536754420.063 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.063 * [misc]backup-simplify: Simplify 0 into 0 1536754420.063 * [misc]backup-simplify: Simplify 0 into 0 1536754420.063 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) 1536754420.064 * [misc]backup-simplify: Simplify (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754420.064 * [misc]approximate: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1536754420.064 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.064 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.064 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of k in k 1536754420.064 * [misc]backup-simplify: Simplify 0 into 0 1536754420.064 * [misc]backup-simplify: Simplify 1 into 1 1536754420.064 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.064 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.064 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.064 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of -1 in k 1536754420.064 * [misc]backup-simplify: Simplify -1 into -1 1536754420.064 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754420.064 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.065 * [misc]backup-simplify: Simplify PI into PI 1536754420.065 * [misc]taylor: Taking taylor expansion of n in k 1536754420.065 * [misc]backup-simplify: Simplify n into n 1536754420.065 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754420.065 * [misc]backup-simplify: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 1536754420.065 * [misc]backup-simplify: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 1536754420.065 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754420.065 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754420.065 * [misc]backup-simplify: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n)))) 1536754420.066 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754420.066 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.066 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.066 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of k in n 1536754420.066 * [misc]backup-simplify: Simplify k into k 1536754420.066 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.066 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.066 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.066 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of -1 in n 1536754420.066 * [misc]backup-simplify: Simplify -1 into -1 1536754420.066 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.066 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.066 * [misc]backup-simplify: Simplify PI into PI 1536754420.066 * [misc]taylor: Taking taylor expansion of n in n 1536754420.066 * [misc]backup-simplify: Simplify 0 into 0 1536754420.066 * [misc]backup-simplify: Simplify 1 into 1 1536754420.067 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.067 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754420.068 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754420.068 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754420.068 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754420.069 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.069 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536754420.070 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754420.070 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754420.070 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536754420.070 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536754420.070 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754420.070 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754420.070 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.070 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.070 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.070 * [misc]taylor: Taking taylor expansion of k in n 1536754420.070 * [misc]backup-simplify: Simplify k into k 1536754420.070 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.071 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.071 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.071 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536754420.071 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754420.071 * [misc]taylor: Taking taylor expansion of -1 in n 1536754420.071 * [misc]backup-simplify: Simplify -1 into -1 1536754420.071 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.071 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.071 * [misc]backup-simplify: Simplify PI into PI 1536754420.071 * [misc]taylor: Taking taylor expansion of n in n 1536754420.071 * [misc]backup-simplify: Simplify 0 into 0 1536754420.071 * [misc]backup-simplify: Simplify 1 into 1 1536754420.071 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.071 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754420.072 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754420.072 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754420.072 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754420.073 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.074 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536754420.075 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754420.075 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k 1536754420.075 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k 1536754420.075 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754420.075 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754420.075 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.075 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.075 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.075 * [misc]taylor: Taking taylor expansion of k in k 1536754420.075 * [misc]backup-simplify: Simplify 0 into 0 1536754420.075 * [misc]backup-simplify: Simplify 1 into 1 1536754420.075 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.075 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.075 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.075 * [misc]taylor: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 1536754420.075 * [misc]taylor: Taking taylor expansion of (log (* -1 PI)) in k 1536754420.075 * [misc]taylor: Taking taylor expansion of (* -1 PI) in k 1536754420.075 * [misc]taylor: Taking taylor expansion of -1 in k 1536754420.075 * [misc]backup-simplify: Simplify -1 into -1 1536754420.075 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.075 * [misc]backup-simplify: Simplify PI into PI 1536754420.076 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754420.076 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754420.076 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754420.076 * [misc]taylor: Taking taylor expansion of n in k 1536754420.076 * [misc]backup-simplify: Simplify n into n 1536754420.076 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754420.077 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754420.077 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754420.077 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754420.077 * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 1536754420.078 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n))) 1536754420.079 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754420.079 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754420.081 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754420.081 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536754420.085 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 1536754420.085 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754420.085 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754420.085 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.086 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.087 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 1536754420.088 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754420.088 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.088 * [misc]backup-simplify: Simplify 0 into 0 1536754420.088 * [misc]backup-simplify: Simplify 0 into 0 1536754420.088 * [misc]backup-simplify: Simplify 0 into 0 1536754420.089 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.090 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1536754420.093 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 1536754420.093 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.093 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754420.093 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.094 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.095 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 1536754420.096 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754420.096 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.096 * [misc]backup-simplify: Simplify 0 into 0 1536754420.096 * [misc]backup-simplify: Simplify 0 into 0 1536754420.096 * [misc]backup-simplify: Simplify 0 into 0 1536754420.096 * [misc]backup-simplify: Simplify 0 into 0 1536754420.098 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.099 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754420.108 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0 1536754420.108 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.109 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754420.109 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.110 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.111 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0 1536754420.114 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536754420.114 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.114 * [misc]backup-simplify: Simplify 0 into 0 1536754420.114 * [misc]backup-simplify: Simplify 0 into 0 1536754420.115 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))) into (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) 1536754420.115 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1 1) 1536754420.116 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754420.116 * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 1536754420.116 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754420.116 * [misc]taylor: Taking taylor expansion of n in n 1536754420.116 * [misc]backup-simplify: Simplify 0 into 0 1536754420.116 * [misc]backup-simplify: Simplify 1 into 1 1536754420.116 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.116 * [misc]backup-simplify: Simplify PI into PI 1536754420.116 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754420.116 * [misc]taylor: Taking taylor expansion of n in n 1536754420.116 * [misc]backup-simplify: Simplify 0 into 0 1536754420.116 * [misc]backup-simplify: Simplify 1 into 1 1536754420.116 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.116 * [misc]backup-simplify: Simplify PI into PI 1536754420.116 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754420.116 * [misc]backup-simplify: Simplify 0 into 0 1536754420.117 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754420.117 * [misc]backup-simplify: Simplify PI into PI 1536754420.118 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754420.118 * [misc]backup-simplify: Simplify 0 into 0 1536754420.119 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754420.119 * [misc]backup-simplify: Simplify 0 into 0 1536754420.120 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754420.120 * [misc]backup-simplify: Simplify 0 into 0 1536754420.122 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536754420.122 * [misc]backup-simplify: Simplify 0 into 0 1536754420.124 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536754420.124 * [misc]backup-simplify: Simplify 0 into 0 1536754420.126 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536754420.126 * [misc]backup-simplify: Simplify 0 into 0 1536754420.126 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) 1536754420.126 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) 1536754420.126 * [misc]approximate: Taking taylor expansion of (/ PI n) in (n) around 0 1536754420.126 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.126 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.126 * [misc]backup-simplify: Simplify PI into PI 1536754420.127 * [misc]taylor: Taking taylor expansion of n in n 1536754420.127 * [misc]backup-simplify: Simplify 0 into 0 1536754420.127 * [misc]backup-simplify: Simplify 1 into 1 1536754420.127 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.127 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.127 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.127 * [misc]backup-simplify: Simplify PI into PI 1536754420.127 * [misc]taylor: Taking taylor expansion of n in n 1536754420.127 * [misc]backup-simplify: Simplify 0 into 0 1536754420.127 * [misc]backup-simplify: Simplify 1 into 1 1536754420.127 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.127 * [misc]backup-simplify: Simplify PI into PI 1536754420.128 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754420.128 * [misc]backup-simplify: Simplify 0 into 0 1536754420.130 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.130 * [misc]backup-simplify: Simplify 0 into 0 1536754420.131 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.131 * [misc]backup-simplify: Simplify 0 into 0 1536754420.132 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.132 * [misc]backup-simplify: Simplify 0 into 0 1536754420.134 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.134 * [misc]backup-simplify: Simplify 0 into 0 1536754420.135 * [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 1536754420.135 * [misc]backup-simplify: Simplify 0 into 0 1536754420.135 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 1536754420.135 * [misc]backup-simplify: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 1536754420.135 * [misc]approximate: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 1536754420.135 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754420.136 * [misc]taylor: Taking taylor expansion of -1 in n 1536754420.136 * [misc]backup-simplify: Simplify -1 into -1 1536754420.136 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.136 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.136 * [misc]backup-simplify: Simplify PI into PI 1536754420.136 * [misc]taylor: Taking taylor expansion of n in n 1536754420.136 * [misc]backup-simplify: Simplify 0 into 0 1536754420.136 * [misc]backup-simplify: Simplify 1 into 1 1536754420.136 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.136 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754420.136 * [misc]taylor: Taking taylor expansion of -1 in n 1536754420.136 * [misc]backup-simplify: Simplify -1 into -1 1536754420.136 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.136 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.136 * [misc]backup-simplify: Simplify PI into PI 1536754420.136 * [misc]taylor: Taking taylor expansion of n in n 1536754420.136 * [misc]backup-simplify: Simplify 0 into 0 1536754420.136 * [misc]backup-simplify: Simplify 1 into 1 1536754420.136 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.136 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754420.137 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754420.137 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754420.138 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536754420.138 * [misc]backup-simplify: Simplify 0 into 0 1536754420.139 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.139 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1536754420.139 * [misc]backup-simplify: Simplify 0 into 0 1536754420.140 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.141 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754420.141 * [misc]backup-simplify: Simplify 0 into 0 1536754420.143 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.145 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754420.145 * [misc]backup-simplify: Simplify 0 into 0 1536754420.147 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.150 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536754420.150 * [misc]backup-simplify: Simplify 0 into 0 1536754420.152 * [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 1536754420.156 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536754420.156 * [misc]backup-simplify: Simplify 0 into 0 1536754420.157 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 1536754420.157 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) 1536754420.157 * [misc]backup-simplify: Simplify (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 1536754420.158 * [misc]approximate: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 1536754420.158 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 1536754420.158 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k 1536754420.158 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k 1536754420.158 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k 1536754420.158 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754420.158 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.158 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.158 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754420.158 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.158 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.158 * [misc]taylor: Taking taylor expansion of k in k 1536754420.158 * [misc]backup-simplify: Simplify 0 into 0 1536754420.158 * [misc]backup-simplify: Simplify 1 into 1 1536754420.158 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k 1536754420.158 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536754420.158 * [misc]taylor: Taking taylor expansion of n in k 1536754420.158 * [misc]backup-simplify: Simplify n into n 1536754420.158 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.158 * [misc]backup-simplify: Simplify PI into PI 1536754420.158 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536754420.158 * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) 1536754420.158 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754420.159 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.159 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754420.159 * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) 1536754420.159 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) 1536754420.159 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754420.159 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.159 * [misc]taylor: Taking taylor expansion of k in k 1536754420.159 * [misc]backup-simplify: Simplify 0 into 0 1536754420.159 * [misc]backup-simplify: Simplify 1 into 1 1536754420.159 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.160 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754420.160 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754420.160 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1536754420.160 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536754420.160 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536754420.160 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536754420.160 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754420.160 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.160 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.160 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754420.160 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.160 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.160 * [misc]taylor: Taking taylor expansion of k in n 1536754420.160 * [misc]backup-simplify: Simplify k into k 1536754420.160 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754420.161 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754420.161 * [misc]taylor: Taking taylor expansion of n in n 1536754420.161 * [misc]backup-simplify: Simplify 0 into 0 1536754420.161 * [misc]backup-simplify: Simplify 1 into 1 1536754420.161 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.161 * [misc]backup-simplify: Simplify PI into PI 1536754420.161 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754420.162 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754420.162 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.162 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754420.162 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754420.162 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754420.163 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754420.163 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536754420.164 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536754420.164 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754420.164 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.164 * [misc]taylor: Taking taylor expansion of k in n 1536754420.164 * [misc]backup-simplify: Simplify k into k 1536754420.164 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.164 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754420.164 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754420.164 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754420.164 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1536754420.164 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536754420.164 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536754420.164 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536754420.164 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754420.164 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.164 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.164 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754420.164 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.164 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.164 * [misc]taylor: Taking taylor expansion of k in n 1536754420.164 * [misc]backup-simplify: Simplify k into k 1536754420.164 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536754420.165 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754420.165 * [misc]taylor: Taking taylor expansion of n in n 1536754420.165 * [misc]backup-simplify: Simplify 0 into 0 1536754420.165 * [misc]backup-simplify: Simplify 1 into 1 1536754420.165 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.165 * [misc]backup-simplify: Simplify PI into PI 1536754420.165 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754420.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754420.166 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.166 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754420.166 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754420.166 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754420.167 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754420.167 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536754420.168 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536754420.168 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754420.168 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.168 * [misc]taylor: Taking taylor expansion of k in n 1536754420.168 * [misc]backup-simplify: Simplify k into k 1536754420.168 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.168 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754420.168 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754420.168 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754420.169 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) 1536754420.169 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) in k 1536754420.169 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k 1536754420.169 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k 1536754420.169 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754420.169 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.169 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.169 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754420.169 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.169 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.169 * [misc]taylor: Taking taylor expansion of k in k 1536754420.169 * [misc]backup-simplify: Simplify 0 into 0 1536754420.169 * [misc]backup-simplify: Simplify 1 into 1 1536754420.169 * [misc]taylor: Taking taylor expansion of (+ (log PI) (log n)) in k 1536754420.169 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754420.169 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.169 * [misc]backup-simplify: Simplify PI into PI 1536754420.170 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.170 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754420.170 * [misc]taylor: Taking taylor expansion of n in k 1536754420.170 * [misc]backup-simplify: Simplify n into n 1536754420.170 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754420.170 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754420.170 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.170 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754420.171 * [misc]backup-simplify: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n)) 1536754420.171 * [misc]backup-simplify: Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n))) 1536754420.171 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n)))) 1536754420.171 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754420.171 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.171 * [misc]taylor: Taking taylor expansion of k in k 1536754420.171 * [misc]backup-simplify: Simplify 0 into 0 1536754420.171 * [misc]backup-simplify: Simplify 1 into 1 1536754420.172 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.172 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754420.172 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754420.173 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) 0) into 0 1536754420.173 * [misc]backup-simplify: Simplify 0 into 0 1536754420.174 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754420.177 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754420.177 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536754420.177 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.177 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.178 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754420.178 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0 1536754420.180 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754420.181 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1536754420.181 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.181 * [misc]backup-simplify: Simplify 0 into 0 1536754420.183 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754420.184 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536754420.185 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.185 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754420.185 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754420.185 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754420.186 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1536754420.187 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 1536754420.189 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))) 1536754420.189 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))) 1536754420.190 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.190 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536754420.192 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536754420.195 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754420.195 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536754420.195 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.195 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.195 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754420.196 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0 1536754420.197 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754420.198 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1536754420.198 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.198 * [misc]backup-simplify: Simplify 0 into 0 1536754420.198 * [misc]backup-simplify: Simplify 0 into 0 1536754420.198 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754420.199 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754420.202 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754420.203 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536754420.203 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.203 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754420.203 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.203 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.204 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0 1536754420.206 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 1536754420.209 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) +nan.0) (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) 1536754420.210 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) 1536754420.210 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.211 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536754420.212 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536754420.217 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754420.217 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536754420.217 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.217 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.218 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536754420.218 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log PI) (log n)))))) into 0 1536754420.221 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536754420.222 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1536754420.222 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.222 * [misc]backup-simplify: Simplify 0 into 0 1536754420.222 * [misc]backup-simplify: Simplify 0 into 0 1536754420.222 * [misc]backup-simplify: Simplify 0 into 0 1536754420.222 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.223 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754420.232 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754420.235 * [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 1536754420.235 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.235 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754420.235 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.236 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.236 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log PI) (log n)))))) into 0 1536754420.243 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (* 1/16 (* (log PI) (pow (log n) 2)))))) (exp (* 1/2 (+ (log PI) (log n)))))) 1536754420.259 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (* 1/16 (* (log PI) (pow (log n) 2)))))) (exp (* 1/2 (+ (log PI) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) 1536754420.268 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) 1536754420.279 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2))))))))))))))))))))))) 1536754420.279 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 1536754420.279 * [misc]approximate: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 1536754420.279 * [misc]taylor: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.279 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.279 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.279 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.279 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of k in k 1536754420.279 * [misc]backup-simplify: Simplify 0 into 0 1536754420.279 * [misc]backup-simplify: Simplify 1 into 1 1536754420.279 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.279 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754420.279 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.280 * [misc]backup-simplify: Simplify PI into PI 1536754420.280 * [misc]taylor: Taking taylor expansion of n in k 1536754420.280 * [misc]backup-simplify: Simplify n into n 1536754420.280 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754420.280 * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) 1536754420.280 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754420.280 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754420.280 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754420.280 * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) 1536754420.280 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536754420.280 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754420.280 * [misc]taylor: Taking taylor expansion of k in k 1536754420.280 * [misc]backup-simplify: Simplify 0 into 0 1536754420.280 * [misc]backup-simplify: Simplify 1 into 1 1536754420.280 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754420.281 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754420.281 * [misc]taylor: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.281 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.281 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.281 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.281 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of k in n 1536754420.281 * [misc]backup-simplify: Simplify k into k 1536754420.281 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.281 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.281 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.281 * [misc]backup-simplify: Simplify PI into PI 1536754420.281 * [misc]taylor: Taking taylor expansion of n in n 1536754420.281 * [misc]backup-simplify: Simplify 0 into 0 1536754420.281 * [misc]backup-simplify: Simplify 1 into 1 1536754420.281 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.282 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.282 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754420.282 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754420.282 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754420.282 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.282 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536754420.283 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754420.283 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of k in n 1536754420.283 * [misc]backup-simplify: Simplify k into k 1536754420.283 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754420.283 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754420.283 * [misc]taylor: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.283 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.283 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.283 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.283 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of k in n 1536754420.283 * [misc]backup-simplify: Simplify k into k 1536754420.283 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.283 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.283 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.283 * [misc]backup-simplify: Simplify PI into PI 1536754420.283 * [misc]taylor: Taking taylor expansion of n in n 1536754420.283 * [misc]backup-simplify: Simplify 0 into 0 1536754420.283 * [misc]backup-simplify: Simplify 1 into 1 1536754420.284 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.284 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.284 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754420.284 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754420.284 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754420.284 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.284 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536754420.285 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754420.285 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754420.285 * [misc]taylor: Taking taylor expansion of k in n 1536754420.285 * [misc]backup-simplify: Simplify k into k 1536754420.285 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754420.285 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754420.285 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) into (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1536754420.285 * [misc]taylor: Taking taylor expansion of (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536754420.285 * [misc]taylor: Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754420.285 * [misc]taylor: Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754420.285 * [misc]taylor: Taking taylor expansion of (- (log PI) (log n)) in k 1536754420.285 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754420.285 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.285 * [misc]backup-simplify: Simplify PI into PI 1536754420.286 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754420.286 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754420.286 * [misc]taylor: Taking taylor expansion of n in k 1536754420.286 * [misc]backup-simplify: Simplify n into n 1536754420.286 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754420.286 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754420.286 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.286 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.286 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754420.286 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.286 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.286 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.286 * [misc]taylor: Taking taylor expansion of k in k 1536754420.286 * [misc]backup-simplify: Simplify 0 into 0 1536754420.286 * [misc]backup-simplify: Simplify 1 into 1 1536754420.286 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.286 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754420.286 * [misc]backup-simplify: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 1536754420.286 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754420.286 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754420.287 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754420.287 * [misc]backup-simplify: Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n))) 1536754420.287 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536754420.287 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754420.287 * [misc]taylor: Taking taylor expansion of k in k 1536754420.287 * [misc]backup-simplify: Simplify 0 into 0 1536754420.287 * [misc]backup-simplify: Simplify 1 into 1 1536754420.287 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754420.288 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754420.288 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1536754420.288 * [misc]backup-simplify: Simplify 0 into 0 1536754420.289 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754420.291 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754420.291 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754420.291 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754420.291 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.291 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.291 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.292 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 1536754420.293 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754420.293 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (sqrt k))) into 0 1536754420.293 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.293 * [misc]backup-simplify: Simplify 0 into 0 1536754420.293 * [misc]backup-simplify: Simplify 0 into 0 1536754420.293 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754420.294 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754420.294 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536754420.295 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.298 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754420.298 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.298 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754420.299 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.299 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.299 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.299 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 1536754420.301 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754420.301 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1536754420.301 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.301 * [misc]backup-simplify: Simplify 0 into 0 1536754420.301 * [misc]backup-simplify: Simplify 0 into 0 1536754420.301 * [misc]backup-simplify: Simplify 0 into 0 1536754420.302 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754420.302 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754420.303 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754420.303 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536754420.304 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.309 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754420.309 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.309 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754420.309 * [misc]backup-simplify: Simplify (- 0) into 0 1536754420.309 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.310 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536754420.310 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 1536754420.312 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536754420.313 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1536754420.313 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.313 * [misc]backup-simplify: Simplify 0 into 0 1536754420.313 * [misc]backup-simplify: Simplify 0 into 0 1536754420.313 * [misc]backup-simplify: Simplify 0 into 0 1536754420.313 * [misc]backup-simplify: Simplify 0 into 0 1536754420.314 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754420.314 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754420.314 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536754420.316 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3)))))))) 1536754420.316 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1536754420.316 * [misc]approximate: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1536754420.316 * [misc]taylor: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536754420.316 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754420.316 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k 1536754420.316 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k 1536754420.316 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754420.316 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754420.316 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.317 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.317 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.317 * [misc]taylor: Taking taylor expansion of k in k 1536754420.317 * [misc]backup-simplify: Simplify 0 into 0 1536754420.317 * [misc]backup-simplify: Simplify 1 into 1 1536754420.317 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.317 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.317 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.317 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in k 1536754420.317 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in k 1536754420.317 * [misc]taylor: Taking taylor expansion of -1 in k 1536754420.317 * [misc]backup-simplify: Simplify -1 into -1 1536754420.317 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536754420.317 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.317 * [misc]backup-simplify: Simplify PI into PI 1536754420.317 * [misc]taylor: Taking taylor expansion of n in k 1536754420.317 * [misc]backup-simplify: Simplify n into n 1536754420.317 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536754420.317 * [misc]backup-simplify: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 1536754420.317 * [misc]backup-simplify: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 1536754420.317 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754420.317 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754420.317 * [misc]backup-simplify: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n)))) 1536754420.318 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754420.318 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754420.318 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754420.318 * [misc]taylor: Taking taylor expansion of -1 in k 1536754420.318 * [misc]backup-simplify: Simplify -1 into -1 1536754420.318 * [misc]taylor: Taking taylor expansion of k in k 1536754420.318 * [misc]backup-simplify: Simplify 0 into 0 1536754420.318 * [misc]backup-simplify: Simplify 1 into 1 1536754420.318 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754420.318 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754420.318 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754420.318 * [misc]backup-simplify: Simplify (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754420.318 * [misc]taylor: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536754420.318 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754420.318 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536754420.318 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536754420.318 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754420.318 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754420.318 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.319 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.319 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.319 * [misc]taylor: Taking taylor expansion of k in n 1536754420.319 * [misc]backup-simplify: Simplify k into k 1536754420.319 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.319 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.319 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.319 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536754420.319 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754420.319 * [misc]taylor: Taking taylor expansion of -1 in n 1536754420.319 * [misc]backup-simplify: Simplify -1 into -1 1536754420.319 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.319 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.319 * [misc]backup-simplify: Simplify PI into PI 1536754420.319 * [misc]taylor: Taking taylor expansion of n in n 1536754420.319 * [misc]backup-simplify: Simplify 0 into 0 1536754420.319 * [misc]backup-simplify: Simplify 1 into 1 1536754420.319 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.319 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754420.320 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754420.320 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754420.320 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754420.321 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.322 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536754420.322 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754420.323 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754420.323 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754420.323 * [misc]taylor: Taking taylor expansion of -1 in n 1536754420.323 * [misc]backup-simplify: Simplify -1 into -1 1536754420.323 * [misc]taylor: Taking taylor expansion of k in n 1536754420.323 * [misc]backup-simplify: Simplify k into k 1536754420.323 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754420.323 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754420.323 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754420.323 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754420.324 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) 1536754420.324 * [misc]taylor: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.324 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.324 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of k in n 1536754420.324 * [misc]backup-simplify: Simplify k into k 1536754420.324 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754420.324 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754420.324 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.324 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536754420.324 * [misc]taylor: Taking taylor expansion of -1 in n 1536754420.325 * [misc]backup-simplify: Simplify -1 into -1 1536754420.325 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536754420.325 * [misc]taylor: Taking taylor expansion of PI in n 1536754420.325 * [misc]backup-simplify: Simplify PI into PI 1536754420.325 * [misc]taylor: Taking taylor expansion of n in n 1536754420.325 * [misc]backup-simplify: Simplify 0 into 0 1536754420.325 * [misc]backup-simplify: Simplify 1 into 1 1536754420.325 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536754420.325 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754420.326 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754420.326 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754420.326 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754420.327 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.328 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536754420.328 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754420.328 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754420.328 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754420.328 * [misc]taylor: Taking taylor expansion of -1 in n 1536754420.328 * [misc]backup-simplify: Simplify -1 into -1 1536754420.328 * [misc]taylor: Taking taylor expansion of k in n 1536754420.328 * [misc]backup-simplify: Simplify k into k 1536754420.329 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754420.329 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754420.329 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754420.329 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754420.330 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) 1536754420.330 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.330 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.330 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of k in k 1536754420.330 * [misc]backup-simplify: Simplify 0 into 0 1536754420.330 * [misc]backup-simplify: Simplify 1 into 1 1536754420.330 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754420.330 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754420.330 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754420.330 * [misc]taylor: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of (log (* -1 PI)) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of (* -1 PI) in k 1536754420.330 * [misc]taylor: Taking taylor expansion of -1 in k 1536754420.330 * [misc]backup-simplify: Simplify -1 into -1 1536754420.331 * [misc]taylor: Taking taylor expansion of PI in k 1536754420.331 * [misc]backup-simplify: Simplify PI into PI 1536754420.331 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536754420.331 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536754420.331 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754420.331 * [misc]taylor: Taking taylor expansion of n in k 1536754420.332 * [misc]backup-simplify: Simplify n into n 1536754420.332 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754420.332 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754420.332 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754420.332 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754420.333 * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 1536754420.333 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n))) 1536754420.334 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536754420.334 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754420.334 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754420.334 * [misc]taylor: Taking taylor expansion of -1 in k 1536754420.334 * [misc]backup-simplify: Simplify -1 into -1 1536754420.334 * [misc]taylor: Taking taylor expansion of k in k 1536754420.334 * [misc]backup-simplify: Simplify 0 into 0 1536754420.334 * [misc]backup-simplify: Simplify 1 into 1 1536754420.334 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754420.334 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754420.335 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754420.336 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536754420.336 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536754420.338 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536754420.338 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536754420.341 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 1536754420.342 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754420.342 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754420.342 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.343 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.343 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 1536754420.345 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754420.346 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536754420.346 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.346 * [misc]backup-simplify: Simplify 0 into 0 1536754420.346 * [misc]backup-simplify: Simplify 0 into 0 1536754420.346 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754420.348 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754420.349 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536754420.350 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536754420.351 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.352 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1536754420.358 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 1536754420.358 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.359 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754420.359 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754420.360 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536754420.361 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 1536754420.363 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754420.363 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754420.364 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536754420.365 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536754420.365 * [misc]taylor: Taking taylor expansion of 0 in k 1536754420.365 * [misc]backup-simplify: Simplify 0 into 0 1536754420.365 * [misc]backup-simplify: Simplify 0 into 0 1536754420.365 * [misc]backup-simplify: Simplify 0 into 0 1536754420.366 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754420.367 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754420.369 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536754420.371 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536754420.377 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))))))))) 1536754420.378 * * * [misc]progress: simplifying candidates 1536754420.378 * * * * [misc]progress: [ 1 / 135 ] simplifiying candidate # 1536754420.378 * * * * [misc]progress: [ 2 / 135 ] simplifiying candidate # 1536754420.378 * * * * [misc]progress: [ 3 / 135 ] simplifiying candidate # 1536754420.378 * * * * [misc]progress: [ 4 / 135 ] simplifiying candidate # 1536754420.378 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536754420.380 * * [misc]simplify: iters left: 6 (16 enodes) 1536754420.389 * * [misc]simplify: iters left: 5 (31 enodes) 1536754420.406 * * [misc]simplify: iters left: 4 (66 enodes) 1536754420.439 * * [misc]simplify: iters left: 3 (212 enodes) 1536754420.652 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))) 1536754420.652 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))))) 1536754420.652 * * * * [misc]progress: [ 5 / 135 ] simplifiying candidate # 1536754420.653 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536754420.655 * * [misc]simplify: iters left: 6 (16 enodes) 1536754420.663 * * [misc]simplify: iters left: 5 (31 enodes) 1536754420.679 * * [misc]simplify: iters left: 4 (66 enodes) 1536754420.735 * * [misc]simplify: iters left: 3 (212 enodes) 1536754420.925 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))) 1536754420.925 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))))) 1536754420.925 * * * * [misc]progress: [ 6 / 135 ] simplifiying candidate # 1536754420.926 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1536754420.927 * * [misc]simplify: iters left: 6 (16 enodes) 1536754420.932 * * [misc]simplify: iters left: 5 (28 enodes) 1536754420.939 * * [misc]simplify: iters left: 4 (55 enodes) 1536754420.958 * * [misc]simplify: iters left: 3 (129 enodes) 1536754421.078 * * [misc]simplify: iters left: 2 (438 enodes) 1536754421.678 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))) 1536754421.679 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))))) 1536754421.679 * * * * [misc]progress: [ 7 / 135 ] simplifiying candidate # 1536754421.679 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754421.680 * * [misc]simplify: iters left: 6 (15 enodes) 1536754421.684 * * [misc]simplify: iters left: 5 (24 enodes) 1536754421.690 * * [misc]simplify: iters left: 4 (42 enodes) 1536754421.703 * * [misc]simplify: iters left: 3 (90 enodes) 1536754421.732 * * [misc]simplify: iters left: 2 (207 enodes) 1536754421.955 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))) 1536754421.955 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))))) 1536754421.955 * * * * [misc]progress: [ 8 / 135 ] simplifiying candidate # 1536754421.955 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536754421.957 * * [misc]simplify: iters left: 6 (16 enodes) 1536754421.965 * * [misc]simplify: iters left: 5 (31 enodes) 1536754421.979 * * [misc]simplify: iters left: 4 (60 enodes) 1536754422.016 * * [misc]simplify: iters left: 3 (180 enodes) 1536754422.236 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))) 1536754422.236 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))))) 1536754422.236 * * * * [misc]progress: [ 9 / 135 ] simplifiying candidate # 1536754422.236 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536754422.238 * * [misc]simplify: iters left: 6 (16 enodes) 1536754422.247 * * [misc]simplify: iters left: 5 (31 enodes) 1536754422.263 * * [misc]simplify: iters left: 4 (60 enodes) 1536754422.310 * * [misc]simplify: iters left: 3 (180 enodes) 1536754422.574 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))) 1536754422.574 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))))) 1536754422.574 * * * * [misc]progress: [ 10 / 135 ] simplifiying candidate # 1536754422.574 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1536754422.575 * * [misc]simplify: iters left: 6 (16 enodes) 1536754422.580 * * [misc]simplify: iters left: 5 (28 enodes) 1536754422.586 * * [misc]simplify: iters left: 4 (49 enodes) 1536754422.603 * * [misc]simplify: iters left: 3 (97 enodes) 1536754422.704 * * [misc]simplify: iters left: 2 (353 enodes) 1536754423.204 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log (* n PI)) (log 2)) (- (log (sqrt k)))) 1536754423.204 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log (* n PI)) (log 2)) (- (log (sqrt k)))))) 1536754423.204 * * * * [misc]progress: [ 11 / 135 ] simplifiying candidate # 1536754423.205 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754423.206 * * [misc]simplify: iters left: 6 (15 enodes) 1536754423.209 * * [misc]simplify: iters left: 5 (24 enodes) 1536754423.215 * * [misc]simplify: iters left: 4 (37 enodes) 1536754423.224 * * [misc]simplify: iters left: 3 (66 enodes) 1536754423.248 * * [misc]simplify: iters left: 2 (180 enodes) 1536754423.404 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))) 1536754423.404 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI))) (- (log (sqrt k)))))) 1536754423.404 * * * * [misc]progress: [ 12 / 135 ] simplifiying candidate # 1536754423.404 * * * * [misc]progress: [ 13 / 135 ] simplifiying candidate # 1536754423.404 * * * * [misc]progress: [ 14 / 135 ] simplifiying candidate # 1536754423.404 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1536754423.406 * * [misc]simplify: iters left: 6 (19 enodes) 1536754423.411 * * [misc]simplify: iters left: 5 (37 enodes) 1536754423.424 * * [misc]simplify: iters left: 4 (114 enodes) 1536754423.534 * * [misc]simplify: iters left: 3 (443 enodes) 1536754424.297 * [exit]simplify: Simplified to (* (* (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* PI n) (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow 2 (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))))) 1536754424.297 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* PI n) (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow 2 (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))))))) 1536754424.297 * * * * [misc]progress: [ 15 / 135 ] simplifiying candidate # 1536754424.297 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754424.299 * * [misc]simplify: iters left: 6 (17 enodes) 1536754424.306 * * [misc]simplify: iters left: 5 (33 enodes) 1536754424.317 * * [misc]simplify: iters left: 4 (87 enodes) 1536754424.365 * * [misc]simplify: iters left: 3 (228 enodes) 1536754424.592 * [exit]simplify: Simplified to (* (/ (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow (* PI n) (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2)))))) 1536754424.592 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow (* PI n) (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2)))))))) 1536754424.592 * * * * [misc]progress: [ 16 / 135 ] simplifiying candidate # 1536754424.592 * * * * [misc]progress: [ 17 / 135 ] simplifiying candidate # 1536754424.592 * * * * [misc]progress: [ 18 / 135 ] simplifiying candidate # 1536754424.592 * * * * [misc]progress: [ 19 / 135 ] simplifiying candidate # 1536754424.593 * [enter]simplify: Simplifying (* (pow 2 1/2) (pow (* n PI) (- 1/2 (/ k 2)))) 1536754424.594 * * [misc]simplify: iters left: 6 (11 enodes) 1536754424.599 * * [misc]simplify: iters left: 5 (16 enodes) 1536754424.606 * * [misc]simplify: iters left: 4 (19 enodes) 1536754424.613 * [exit]simplify: Simplified to (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2)))) 1536754424.613 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k)))) 1536754424.614 * [enter]simplify: Simplifying (* (pow 2 (/ k 2)) (sqrt k)) 1536754424.614 * * [misc]simplify: iters left: 5 (6 enodes) 1536754424.616 * * [misc]simplify: iters left: 4 (7 enodes) 1536754424.617 * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (sqrt k)) 1536754424.617 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k)))) 1536754424.617 * * * * [misc]progress: [ 20 / 135 ] simplifiying candidate # 1536754424.617 * * * * [misc]progress: [ 21 / 135 ] simplifiying candidate # 1536754424.617 * [enter]simplify: Simplifying (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536754424.618 * * [misc]simplify: iters left: 6 (12 enodes) 1536754424.620 * * [misc]simplify: iters left: 5 (15 enodes) 1536754424.624 * * [misc]simplify: iters left: 4 (18 enodes) 1536754424.627 * [exit]simplify: Simplified to (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536754424.627 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (* (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536754424.627 * * * * [misc]progress: [ 22 / 135 ] simplifiying candidate # 1536754424.628 * [enter]simplify: Simplifying (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536754424.628 * * [misc]simplify: iters left: 6 (12 enodes) 1536754424.630 * * [misc]simplify: iters left: 5 (15 enodes) 1536754424.633 * * [misc]simplify: iters left: 4 (18 enodes) 1536754424.636 * [exit]simplify: Simplified to (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536754424.636 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536754424.636 * * * * [misc]progress: [ 23 / 135 ] simplifiying candidate # 1536754424.636 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754424.637 * * [misc]simplify: iters left: 6 (11 enodes) 1536754424.639 * * [misc]simplify: iters left: 5 (14 enodes) 1536754424.642 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754424.642 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536754424.642 * * * * [misc]progress: [ 24 / 135 ] simplifiying candidate # 1536754424.642 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754424.643 * * [misc]simplify: iters left: 6 (11 enodes) 1536754424.645 * * [misc]simplify: iters left: 5 (14 enodes) 1536754424.647 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754424.647 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536754424.647 * * * * [misc]progress: [ 25 / 135 ] simplifiying candidate # 1536754424.647 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k)) 1536754424.648 * * [misc]simplify: iters left: 6 (10 enodes) 1536754424.650 * * [misc]simplify: iters left: 5 (13 enodes) 1536754424.652 * [exit]simplify: Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)) 1536754424.652 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)))) 1536754424.652 * * * * [misc]progress: [ 26 / 135 ] simplifiying candidate # 1536754424.652 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754424.653 * * [misc]simplify: iters left: 6 (11 enodes) 1536754424.655 * * [misc]simplify: iters left: 5 (14 enodes) 1536754424.657 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754424.657 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536754424.658 * * * * [misc]progress: [ 27 / 135 ] simplifiying candidate # 1536754424.658 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754424.658 * * [misc]simplify: iters left: 6 (11 enodes) 1536754424.660 * * [misc]simplify: iters left: 5 (14 enodes) 1536754424.663 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754424.663 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536754424.663 * * * * [misc]progress: [ 28 / 135 ] simplifiying candidate # 1536754424.663 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k)) 1536754424.663 * * [misc]simplify: iters left: 6 (10 enodes) 1536754424.665 * * [misc]simplify: iters left: 5 (13 enodes) 1536754424.667 * [exit]simplify: Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)) 1536754424.667 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)))) 1536754424.668 * * * * [misc]progress: [ 29 / 135 ] simplifiying candidate # 1536754424.668 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754424.668 * * [misc]simplify: iters left: 6 (10 enodes) 1536754424.670 * * [misc]simplify: iters left: 5 (12 enodes) 1536754424.672 * * [misc]simplify: iters left: 4 (15 enodes) 1536754424.678 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754424.678 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536754424.678 * * * * [misc]progress: [ 30 / 135 ] simplifiying candidate # 1536754424.678 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754424.679 * * [misc]simplify: iters left: 6 (10 enodes) 1536754424.682 * * [misc]simplify: iters left: 5 (12 enodes) 1536754424.687 * * [misc]simplify: iters left: 4 (15 enodes) 1536754424.692 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754424.692 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536754424.692 * * * * [misc]progress: [ 31 / 135 ] simplifiying candidate # 1536754424.693 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754424.693 * * [misc]simplify: iters left: 6 (9 enodes) 1536754424.697 * * [misc]simplify: iters left: 5 (11 enodes) 1536754424.701 * * [misc]simplify: iters left: 4 (14 enodes) 1536754424.706 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754424.706 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536754424.706 * * * * [misc]progress: [ 32 / 135 ] simplifiying candidate # 1536754424.706 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754424.707 * * [misc]simplify: iters left: 6 (13 enodes) 1536754424.712 * * [misc]simplify: iters left: 5 (16 enodes) 1536754424.720 * * [misc]simplify: iters left: 4 (19 enodes) 1536754424.726 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754424.726 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536754424.726 * * * * [misc]progress: [ 33 / 135 ] simplifiying candidate # 1536754424.727 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754424.728 * * [misc]simplify: iters left: 6 (13 enodes) 1536754424.733 * * [misc]simplify: iters left: 5 (16 enodes) 1536754424.738 * * [misc]simplify: iters left: 4 (19 enodes) 1536754424.745 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754424.746 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536754424.746 * * * * [misc]progress: [ 34 / 135 ] simplifiying candidate # 1536754424.746 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754424.747 * * [misc]simplify: iters left: 6 (12 enodes) 1536754424.751 * * [misc]simplify: iters left: 5 (15 enodes) 1536754424.757 * * [misc]simplify: iters left: 4 (18 enodes) 1536754424.763 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754424.763 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1536754424.763 * * * * [misc]progress: [ 35 / 135 ] simplifiying candidate # 1536754424.763 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754424.765 * * [misc]simplify: iters left: 6 (13 enodes) 1536754424.769 * * [misc]simplify: iters left: 5 (16 enodes) 1536754424.775 * * [misc]simplify: iters left: 4 (19 enodes) 1536754424.781 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754424.781 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536754424.781 * * * * [misc]progress: [ 36 / 135 ] simplifiying candidate # 1536754424.782 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754424.783 * * [misc]simplify: iters left: 6 (13 enodes) 1536754424.787 * * [misc]simplify: iters left: 5 (16 enodes) 1536754424.793 * * [misc]simplify: iters left: 4 (19 enodes) 1536754424.800 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754424.800 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536754424.800 * * * * [misc]progress: [ 37 / 135 ] simplifiying candidate # 1536754424.800 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754424.801 * * [misc]simplify: iters left: 6 (12 enodes) 1536754424.806 * * [misc]simplify: iters left: 5 (15 enodes) 1536754424.811 * * [misc]simplify: iters left: 4 (18 enodes) 1536754424.817 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754424.817 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1536754424.817 * * * * [misc]progress: [ 38 / 135 ] simplifiying candidate # 1536754424.818 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754424.819 * * [misc]simplify: iters left: 6 (12 enodes) 1536754424.823 * * [misc]simplify: iters left: 5 (15 enodes) 1536754424.828 * * [misc]simplify: iters left: 4 (18 enodes) 1536754424.834 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754424.834 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536754424.835 * * * * [misc]progress: [ 39 / 135 ] simplifiying candidate # 1536754424.835 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754424.836 * * [misc]simplify: iters left: 6 (12 enodes) 1536754424.840 * * [misc]simplify: iters left: 5 (15 enodes) 1536754424.843 * * [misc]simplify: iters left: 4 (18 enodes) 1536754424.846 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754424.846 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536754424.846 * * * * [misc]progress: [ 40 / 135 ] simplifiying candidate # 1536754424.846 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754424.847 * * [misc]simplify: iters left: 6 (11 enodes) 1536754424.850 * * [misc]simplify: iters left: 5 (14 enodes) 1536754424.853 * * [misc]simplify: iters left: 4 (17 enodes) 1536754424.856 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754424.856 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754424.856 * * * * [misc]progress: [ 41 / 135 ] simplifiying candidate # 1536754424.856 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754424.856 * * [misc]simplify: iters left: 6 (11 enodes) 1536754424.858 * * [misc]simplify: iters left: 5 (14 enodes) 1536754424.861 * * [misc]simplify: iters left: 4 (17 enodes) 1536754424.864 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754424.864 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754424.864 * * * * [misc]progress: [ 42 / 135 ] simplifiying candidate # 1536754424.864 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1536754424.864 * * [misc]simplify: iters left: 3 (4 enodes) 1536754424.865 * * [misc]simplify: iters left: 2 (6 enodes) 1536754424.866 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1536754424.866 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)))) 1536754424.866 * * * * [misc]progress: [ 43 / 135 ] simplifiying candidate # 1536754424.866 * [enter]simplify: Simplifying (pow 2 1/2) 1536754424.866 * * [misc]simplify: iters left: 1 (3 enodes) 1536754424.868 * [exit]simplify: Simplified to (sqrt 2) 1536754424.868 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536754424.868 * * * * [misc]progress: [ 44 / 135 ] simplifiying candidate # 1536754424.868 * [enter]simplify: Simplifying (pow 2 1/2) 1536754424.868 * * [misc]simplify: iters left: 1 (3 enodes) 1536754424.869 * [exit]simplify: Simplified to (sqrt 2) 1536754424.869 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536754424.869 * * * * [misc]progress: [ 45 / 135 ] simplifiying candidate # 1536754424.869 * [enter]simplify: Simplifying (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1536754424.870 * * [misc]simplify: iters left: 6 (8 enodes) 1536754424.871 * * [misc]simplify: iters left: 5 (10 enodes) 1536754424.873 * * [misc]simplify: iters left: 4 (13 enodes) 1536754424.875 * [exit]simplify: Simplified to (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1536754424.875 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536754424.876 * * * * [misc]progress: [ 46 / 135 ] simplifiying candidate # 1536754424.876 * [enter]simplify: Simplifying (sqrt (pow 2 (- 1/2 (/ k 2)))) 1536754424.876 * * [misc]simplify: iters left: 6 (7 enodes) 1536754424.879 * * [misc]simplify: iters left: 5 (9 enodes) 1536754424.882 * * [misc]simplify: iters left: 4 (12 enodes) 1536754424.886 * [exit]simplify: Simplified to (sqrt (pow 2 (- 1/2 (/ k 2)))) 1536754424.886 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536754424.886 * * * * [misc]progress: [ 47 / 135 ] simplifiying candidate # 1536754424.886 * * * * [misc]progress: [ 48 / 135 ] simplifiying candidate # 1536754424.887 * [enter]simplify: Simplifying (sqrt k) 1536754424.887 * * [misc]simplify: iters left: 1 (2 enodes) 1536754424.888 * [exit]simplify: Simplified to (sqrt k) 1536754424.888 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) 1536754424.888 * * * * [misc]progress: [ 49 / 135 ] simplifiying candidate # 1536754424.888 * [enter]simplify: Simplifying (* (pow 2 1/2) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536754424.889 * * [misc]simplify: iters left: 6 (13 enodes) 1536754424.896 * * [misc]simplify: iters left: 5 (20 enodes) 1536754424.905 * * [misc]simplify: iters left: 4 (27 enodes) 1536754424.913 * * [misc]simplify: iters left: 3 (29 enodes) 1536754424.919 * * [misc]simplify: iters left: 2 (31 enodes) 1536754424.924 * * [misc]simplify: iters left: 1 (32 enodes) 1536754424.930 * [exit]simplify: Simplified to (* (/ (sqrt 2) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1536754424.930 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (/ (sqrt 2) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) (pow 2 (/ k 2)))) 1536754424.930 * * * * [misc]progress: [ 50 / 135 ] simplifiying candidate # 1536754424.931 * * * * [misc]progress: [ 51 / 135 ] simplifiying candidate # 1536754424.931 * * * * [misc]progress: [ 52 / 135 ] simplifiying candidate # 1536754424.931 * * * * [misc]progress: [ 53 / 135 ] simplifiying candidate # 1536754424.931 * [enter]simplify: Simplifying (* (log (* n PI)) (- 1/2 (/ k 2))) 1536754424.931 * * [misc]simplify: iters left: 6 (10 enodes) 1536754424.933 * * [misc]simplify: iters left: 5 (17 enodes) 1536754424.937 * * [misc]simplify: iters left: 4 (33 enodes) 1536754424.949 * * [misc]simplify: iters left: 3 (73 enodes) 1536754424.995 * * [misc]simplify: iters left: 2 (196 enodes) 1536754425.108 * * [misc]simplify: iters left: 1 (420 enodes) 1536754425.355 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* n PI))) 1536754425.355 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) (sqrt k)))) 1536754425.355 * * * * [misc]progress: [ 54 / 135 ] simplifiying candidate # 1536754425.355 * * * * [misc]progress: [ 55 / 135 ] simplifiying candidate # 1536754425.355 * [enter]simplify: Simplifying (* n PI) 1536754425.355 * * [misc]simplify: iters left: 2 (3 enodes) 1536754425.356 * * [misc]simplify: iters left: 1 (4 enodes) 1536754425.357 * [exit]simplify: Simplified to (* n PI) 1536754425.357 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))) 1536754425.357 * * * * [misc]progress: [ 56 / 135 ] simplifiying candidate # 1536754425.357 * [enter]simplify: Simplifying (pow (* n PI) (/ k 2)) 1536754425.357 * * [misc]simplify: iters left: 3 (7 enodes) 1536754425.358 * * [misc]simplify: iters left: 2 (8 enodes) 1536754425.360 * [exit]simplify: Simplified to (pow (* n PI) (/ k 2)) 1536754425.360 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) 1/2) (pow (* n PI) (/ k 2))) (sqrt k)))) 1536754425.360 * * * * [misc]progress: [ 57 / 135 ] simplifiying candidate # 1536754425.360 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536754425.360 * * [misc]simplify: iters left: 5 (6 enodes) 1536754425.361 * * [misc]simplify: iters left: 4 (8 enodes) 1536754425.365 * * [misc]simplify: iters left: 3 (11 enodes) 1536754425.367 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536754425.367 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))) 1536754425.367 * * * * [misc]progress: [ 58 / 135 ] simplifiying candidate # 1536754425.367 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536754425.367 * * [misc]simplify: iters left: 5 (6 enodes) 1536754425.368 * * [misc]simplify: iters left: 4 (8 enodes) 1536754425.370 * * [misc]simplify: iters left: 3 (11 enodes) 1536754425.371 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536754425.371 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))) 1536754425.372 * * * * [misc]progress: [ 59 / 135 ] simplifiying candidate # 1536754425.372 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536754425.372 * * [misc]simplify: iters left: 4 (5 enodes) 1536754425.373 * * [misc]simplify: iters left: 3 (7 enodes) 1536754425.374 * * [misc]simplify: iters left: 2 (10 enodes) 1536754425.376 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536754425.376 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k)))) 1536754425.376 * * * * [misc]progress: [ 60 / 135 ] simplifiying candidate # 1536754425.376 * [enter]simplify: Simplifying (pow (* n PI) (- (/ k 2))) 1536754425.376 * * [misc]simplify: iters left: 5 (8 enodes) 1536754425.378 * * [misc]simplify: iters left: 4 (11 enodes) 1536754425.380 * [exit]simplify: Simplified to (pow (* n PI) (/ (- k) 2)) 1536754425.380 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (/ (- k) 2))) (sqrt k)))) 1536754425.380 * * * * [misc]progress: [ 61 / 135 ] simplifiying candidate # 1536754425.380 * [enter]simplify: Simplifying (pow (* n PI) (- (/ k 2))) 1536754425.380 * * [misc]simplify: iters left: 5 (8 enodes) 1536754425.382 * * [misc]simplify: iters left: 4 (11 enodes) 1536754425.384 * [exit]simplify: Simplified to (pow (* n PI) (/ (- k) 2)) 1536754425.384 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (/ (- k) 2))) (sqrt k)))) 1536754425.384 * * * * [misc]progress: [ 62 / 135 ] simplifiying candidate # 1536754425.384 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1536754425.384 * * [misc]simplify: iters left: 5 (7 enodes) 1536754425.386 * * [misc]simplify: iters left: 4 (9 enodes) 1536754425.388 * * [misc]simplify: iters left: 3 (12 enodes) 1536754425.390 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1536754425.390 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))) 1536754425.390 * * * * [misc]progress: [ 63 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 64 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 65 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 66 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 67 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 68 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 69 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 70 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 71 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 72 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 73 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 74 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 75 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 76 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 77 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 78 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 79 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 80 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 81 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 82 / 135 ] simplifiying candidate # 1536754425.390 * * * * [misc]progress: [ 83 / 135 ] simplifiying candidate # 1536754425.391 * [enter]simplify: Simplifying (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754425.391 * * [misc]simplify: iters left: 6 (13 enodes) 1536754425.394 * * [misc]simplify: iters left: 5 (23 enodes) 1536754425.399 * * [misc]simplify: iters left: 4 (41 enodes) 1536754425.412 * * [misc]simplify: iters left: 3 (105 enodes) 1536754425.475 * * [misc]simplify: iters left: 2 (334 enodes) 1536754425.765 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))) 1536754425.765 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))))) 1536754425.765 * * * * [misc]progress: [ 84 / 135 ] simplifiying candidate # 1536754425.765 * [enter]simplify: Simplifying (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754425.767 * * [misc]simplify: iters left: 6 (13 enodes) 1536754425.773 * * [misc]simplify: iters left: 5 (23 enodes) 1536754425.784 * * [misc]simplify: iters left: 4 (41 enodes) 1536754425.810 * * [misc]simplify: iters left: 3 (105 enodes) 1536754425.881 * * [misc]simplify: iters left: 2 (334 enodes) 1536754426.137 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))) 1536754426.137 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))))) 1536754426.137 * * * * [misc]progress: [ 85 / 135 ] simplifiying candidate # 1536754426.137 * [enter]simplify: Simplifying (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))) 1536754426.138 * * [misc]simplify: iters left: 6 (13 enodes) 1536754426.141 * * [misc]simplify: iters left: 5 (20 enodes) 1536754426.146 * * [misc]simplify: iters left: 4 (30 enodes) 1536754426.156 * * [misc]simplify: iters left: 3 (47 enodes) 1536754426.190 * * [misc]simplify: iters left: 2 (135 enodes) 1536754426.311 * * [misc]simplify: iters left: 1 (438 enodes) 1536754426.771 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))) 1536754426.771 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))))) 1536754426.772 * * * * [misc]progress: [ 86 / 135 ] simplifiying candidate # 1536754426.772 * * * * [misc]progress: [ 87 / 135 ] simplifiying candidate # 1536754426.772 * * * * [misc]progress: [ 88 / 135 ] simplifiying candidate # 1536754426.772 * [enter]simplify: Simplifying (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1536754426.774 * * [misc]simplify: iters left: 6 (15 enodes) 1536754426.782 * * [misc]simplify: iters left: 5 (27 enodes) 1536754426.795 * * [misc]simplify: iters left: 4 (56 enodes) 1536754426.820 * * [misc]simplify: iters left: 3 (104 enodes) 1536754426.845 * * [misc]simplify: iters left: 2 (175 enodes) 1536754426.912 * * [misc]simplify: iters left: 1 (287 enodes) 1536754427.120 * [exit]simplify: Simplified to (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ (* (sqrt k) k) (pow (* n PI) (- 1/2 (/ k 2))))) 1536754427.120 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ (* (sqrt k) k) (pow (* n PI) (- 1/2 (/ k 2)))))))) 1536754427.120 * * * * [misc]progress: [ 89 / 135 ] simplifiying candidate # 1536754427.120 * * * * [misc]progress: [ 90 / 135 ] simplifiying candidate # 1536754427.120 * * * * [misc]progress: [ 91 / 135 ] simplifiying candidate # 1536754427.121 * * * * [misc]progress: [ 92 / 135 ] simplifiying candidate # 1536754427.121 * * * * [misc]progress: [ 93 / 135 ] simplifiying candidate # 1536754427.121 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.122 * * [misc]simplify: iters left: 6 (10 enodes) 1536754427.126 * * [misc]simplify: iters left: 5 (14 enodes) 1536754427.131 * [exit]simplify: Simplified to (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.131 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536754427.132 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754427.133 * * [misc]simplify: iters left: 6 (11 enodes) 1536754427.137 * * [misc]simplify: iters left: 5 (14 enodes) 1536754427.142 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754427.142 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536754427.142 * * * * [misc]progress: [ 94 / 135 ] simplifiying candidate # 1536754427.142 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) 1536754427.143 * * [misc]simplify: iters left: 5 (9 enodes) 1536754427.146 * * [misc]simplify: iters left: 4 (11 enodes) 1536754427.150 * [exit]simplify: Simplified to (/ (sqrt (* n PI)) (sqrt (sqrt k))) 1536754427.150 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536754427.150 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754427.151 * * [misc]simplify: iters left: 6 (11 enodes) 1536754427.155 * * [misc]simplify: iters left: 5 (14 enodes) 1536754427.158 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754427.158 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536754427.158 * * * * [misc]progress: [ 95 / 135 ] simplifiying candidate # 1536754427.158 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) 1) 1536754427.158 * * [misc]simplify: iters left: 5 (7 enodes) 1536754427.160 * * [misc]simplify: iters left: 4 (11 enodes) 1536754427.164 * * [misc]simplify: iters left: 3 (13 enodes) 1536754427.166 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536754427.166 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))) 1536754427.166 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k)) 1536754427.166 * * [misc]simplify: iters left: 6 (10 enodes) 1536754427.168 * * [misc]simplify: iters left: 5 (13 enodes) 1536754427.170 * [exit]simplify: Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)) 1536754427.171 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))))) 1536754427.171 * * * * [misc]progress: [ 96 / 135 ] simplifiying candidate # 1536754427.171 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.171 * * [misc]simplify: iters left: 6 (10 enodes) 1536754427.173 * * [misc]simplify: iters left: 5 (14 enodes) 1536754427.176 * [exit]simplify: Simplified to (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.176 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536754427.176 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754427.177 * * [misc]simplify: iters left: 6 (11 enodes) 1536754427.178 * * [misc]simplify: iters left: 5 (14 enodes) 1536754427.181 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536754427.181 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536754427.181 * * * * [misc]progress: [ 97 / 135 ] simplifiying candidate # 1536754427.181 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) 1536754427.182 * * [misc]simplify: iters left: 5 (9 enodes) 1536754427.183 * * [misc]simplify: iters left: 4 (11 enodes) 1536754427.187 * [exit]simplify: Simplified to (/ (sqrt (* n PI)) (sqrt (sqrt k))) 1536754427.187 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536754427.187 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754427.188 * * [misc]simplify: iters left: 6 (11 enodes) 1536754427.192 * * [misc]simplify: iters left: 5 (14 enodes) 1536754427.197 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536754427.197 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536754427.197 * * * * [misc]progress: [ 98 / 135 ] simplifiying candidate # 1536754427.198 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) 1) 1536754427.198 * * [misc]simplify: iters left: 5 (7 enodes) 1536754427.201 * * [misc]simplify: iters left: 4 (11 enodes) 1536754427.205 * * [misc]simplify: iters left: 3 (13 enodes) 1536754427.208 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536754427.208 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))) 1536754427.208 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k)) 1536754427.208 * * [misc]simplify: iters left: 6 (10 enodes) 1536754427.210 * * [misc]simplify: iters left: 5 (13 enodes) 1536754427.213 * [exit]simplify: Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)) 1536754427.213 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))))) 1536754427.213 * * * * [misc]progress: [ 99 / 135 ] simplifiying candidate # 1536754427.213 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.213 * * [misc]simplify: iters left: 6 (11 enodes) 1536754427.215 * * [misc]simplify: iters left: 5 (15 enodes) 1536754427.218 * * [misc]simplify: iters left: 4 (18 enodes) 1536754427.221 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.221 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536754427.222 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754427.222 * * [misc]simplify: iters left: 6 (10 enodes) 1536754427.224 * * [misc]simplify: iters left: 5 (12 enodes) 1536754427.226 * * [misc]simplify: iters left: 4 (15 enodes) 1536754427.230 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754427.230 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536754427.231 * * * * [misc]progress: [ 100 / 135 ] simplifiying candidate # 1536754427.231 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754427.232 * * [misc]simplify: iters left: 6 (10 enodes) 1536754427.235 * * [misc]simplify: iters left: 5 (12 enodes) 1536754427.239 * * [misc]simplify: iters left: 4 (15 enodes) 1536754427.245 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754427.245 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536754427.245 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754427.246 * * [misc]simplify: iters left: 6 (10 enodes) 1536754427.249 * * [misc]simplify: iters left: 5 (12 enodes) 1536754427.254 * * [misc]simplify: iters left: 4 (15 enodes) 1536754427.259 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754427.259 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536754427.259 * * * * [misc]progress: [ 101 / 135 ] simplifiying candidate # 1536754427.259 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) 1) 1536754427.260 * * [misc]simplify: iters left: 6 (9 enodes) 1536754427.265 * * [misc]simplify: iters left: 5 (13 enodes) 1536754427.271 * * [misc]simplify: iters left: 4 (18 enodes) 1536754427.276 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1536754427.276 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754427.276 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754427.276 * * [misc]simplify: iters left: 6 (9 enodes) 1536754427.278 * * [misc]simplify: iters left: 5 (11 enodes) 1536754427.280 * * [misc]simplify: iters left: 4 (14 enodes) 1536754427.282 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754427.282 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754427.282 * * * * [misc]progress: [ 102 / 135 ] simplifiying candidate # 1536754427.282 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.283 * * [misc]simplify: iters left: 6 (15 enodes) 1536754427.286 * * [misc]simplify: iters left: 5 (24 enodes) 1536754427.291 * * [misc]simplify: iters left: 4 (36 enodes) 1536754427.297 * * [misc]simplify: iters left: 3 (39 enodes) 1536754427.303 * * [misc]simplify: iters left: 2 (42 enodes) 1536754427.311 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1536754427.311 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536754427.311 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754427.312 * * [misc]simplify: iters left: 6 (13 enodes) 1536754427.314 * * [misc]simplify: iters left: 5 (16 enodes) 1536754427.317 * * [misc]simplify: iters left: 4 (19 enodes) 1536754427.320 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754427.320 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536754427.320 * * * * [misc]progress: [ 103 / 135 ] simplifiying candidate # 1536754427.320 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536754427.321 * * [misc]simplify: iters left: 6 (14 enodes) 1536754427.324 * * [misc]simplify: iters left: 5 (19 enodes) 1536754427.327 * * [misc]simplify: iters left: 4 (24 enodes) 1536754427.331 * * [misc]simplify: iters left: 3 (25 enodes) 1536754427.336 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1536754427.336 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536754427.337 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754427.338 * * [misc]simplify: iters left: 6 (13 enodes) 1536754427.345 * * [misc]simplify: iters left: 5 (16 enodes) 1536754427.350 * * [misc]simplify: iters left: 4 (19 enodes) 1536754427.357 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754427.357 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536754427.358 * * * * [misc]progress: [ 104 / 135 ] simplifiying candidate # 1536754427.358 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1) 1536754427.359 * * [misc]simplify: iters left: 6 (13 enodes) 1536754427.364 * * [misc]simplify: iters left: 5 (20 enodes) 1536754427.373 * * [misc]simplify: iters left: 4 (29 enodes) 1536754427.381 * * [misc]simplify: iters left: 3 (31 enodes) 1536754427.390 * * [misc]simplify: iters left: 2 (36 enodes) 1536754427.401 * [exit]simplify: Simplified to (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1536754427.401 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1536754427.402 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754427.403 * * [misc]simplify: iters left: 6 (12 enodes) 1536754427.407 * * [misc]simplify: iters left: 5 (15 enodes) 1536754427.412 * * [misc]simplify: iters left: 4 (18 enodes) 1536754427.418 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754427.419 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1536754427.419 * * * * [misc]progress: [ 105 / 135 ] simplifiying candidate # 1536754427.419 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.420 * * [misc]simplify: iters left: 6 (14 enodes) 1536754427.426 * * [misc]simplify: iters left: 5 (19 enodes) 1536754427.432 * * [misc]simplify: iters left: 4 (22 enodes) 1536754427.440 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.441 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536754427.441 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754427.442 * * [misc]simplify: iters left: 6 (13 enodes) 1536754427.447 * * [misc]simplify: iters left: 5 (16 enodes) 1536754427.453 * * [misc]simplify: iters left: 4 (19 enodes) 1536754427.460 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754427.460 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536754427.460 * * * * [misc]progress: [ 106 / 135 ] simplifiying candidate # 1536754427.460 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754427.461 * * [misc]simplify: iters left: 6 (13 enodes) 1536754427.466 * * [misc]simplify: iters left: 5 (16 enodes) 1536754427.471 * * [misc]simplify: iters left: 4 (19 enodes) 1536754427.479 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754427.479 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536754427.479 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754427.480 * * [misc]simplify: iters left: 6 (13 enodes) 1536754427.487 * * [misc]simplify: iters left: 5 (16 enodes) 1536754427.493 * * [misc]simplify: iters left: 4 (19 enodes) 1536754427.500 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754427.500 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536754427.500 * * * * [misc]progress: [ 107 / 135 ] simplifiying candidate # 1536754427.500 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1) 1536754427.501 * * [misc]simplify: iters left: 6 (12 enodes) 1536754427.506 * * [misc]simplify: iters left: 5 (17 enodes) 1536754427.510 * * [misc]simplify: iters left: 4 (22 enodes) 1536754427.513 * [exit]simplify: Simplified to (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1536754427.513 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1536754427.514 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754427.514 * * [misc]simplify: iters left: 6 (12 enodes) 1536754427.516 * * [misc]simplify: iters left: 5 (15 enodes) 1536754427.519 * * [misc]simplify: iters left: 4 (18 enodes) 1536754427.522 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536754427.522 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1536754427.522 * * * * [misc]progress: [ 108 / 135 ] simplifiying candidate # 1536754427.522 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754427.523 * * [misc]simplify: iters left: 6 (6 enodes) 1536754427.524 * * [misc]simplify: iters left: 5 (10 enodes) 1536754427.526 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536754427.526 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536754427.526 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754427.527 * * [misc]simplify: iters left: 6 (12 enodes) 1536754427.529 * * [misc]simplify: iters left: 5 (15 enodes) 1536754427.532 * * [misc]simplify: iters left: 4 (18 enodes) 1536754427.535 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754427.535 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536754427.535 * * * * [misc]progress: [ 109 / 135 ] simplifiying candidate # 1536754427.535 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536754427.535 * * [misc]simplify: iters left: 4 (5 enodes) 1536754427.536 * * [misc]simplify: iters left: 3 (7 enodes) 1536754427.537 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536754427.537 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536754427.537 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754427.538 * * [misc]simplify: iters left: 6 (12 enodes) 1536754427.540 * * [misc]simplify: iters left: 5 (15 enodes) 1536754427.542 * * [misc]simplify: iters left: 4 (18 enodes) 1536754427.545 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754427.545 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536754427.545 * * * * [misc]progress: [ 110 / 135 ] simplifiying candidate # 1536754427.546 * [enter]simplify: Simplifying (/ 1 1) 1536754427.546 * * [misc]simplify: iters left: 2 (2 enodes) 1536754427.546 * * [misc]simplify: iters left: 1 (4 enodes) 1536754427.547 * [exit]simplify: Simplified to 1 1536754427.547 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536754427.547 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754427.547 * * [misc]simplify: iters left: 6 (11 enodes) 1536754427.551 * * [misc]simplify: iters left: 5 (14 enodes) 1536754427.556 * * [misc]simplify: iters left: 4 (17 enodes) 1536754427.562 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536754427.562 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536754427.562 * * * * [misc]progress: [ 111 / 135 ] simplifiying candidate # 1536754427.562 * * * * [misc]progress: [ 112 / 135 ] simplifiying candidate # 1536754427.562 * * * * [misc]progress: [ 113 / 135 ] simplifiying candidate # 1536754427.562 * * * * [misc]progress: [ 114 / 135 ] simplifiying candidate # 1536754427.562 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536754427.563 * * [misc]simplify: iters left: 2 (3 enodes) 1536754427.564 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536754427.564 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))) 1536754427.564 * * * * [misc]progress: [ 115 / 135 ] simplifiying candidate # 1536754427.564 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536754427.564 * * [misc]simplify: iters left: 2 (3 enodes) 1536754427.565 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536754427.565 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))) 1536754427.565 * * * * [misc]progress: [ 116 / 135 ] simplifiying candidate # 1536754427.566 * [enter]simplify: Simplifying (sqrt k) 1536754427.566 * * [misc]simplify: iters left: 1 (2 enodes) 1536754427.567 * [exit]simplify: Simplified to (sqrt k) 1536754427.567 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) 1) (sqrt k)))) 1536754427.567 * * * * [misc]progress: [ 117 / 135 ] simplifiying candidate # 1536754427.567 * [enter]simplify: Simplifying (pow (* n PI) 1/2) 1536754427.567 * * [misc]simplify: iters left: 3 (5 enodes) 1536754427.569 * * [misc]simplify: iters left: 2 (7 enodes) 1536754427.572 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536754427.572 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (/ (sqrt k) (pow (* n PI) (- (/ k 2))))))) 1536754427.572 * * * * [misc]progress: [ 118 / 135 ] simplifiying candidate # 1536754427.572 * [enter]simplify: Simplifying (pow (* n PI) 1/2) 1536754427.572 * * [misc]simplify: iters left: 3 (5 enodes) 1536754427.574 * * [misc]simplify: iters left: 2 (7 enodes) 1536754427.577 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536754427.577 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (/ (sqrt k) (pow (* n PI) (- (/ k 2))))))) 1536754427.577 * * * * [misc]progress: [ 119 / 135 ] simplifiying candidate # 1536754427.577 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1536754427.577 * * [misc]simplify: iters left: 5 (7 enodes) 1536754427.580 * * [misc]simplify: iters left: 4 (9 enodes) 1536754427.584 * * [misc]simplify: iters left: 3 (12 enodes) 1536754427.588 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1536754427.588 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))) 1536754427.588 * * * * [misc]progress: [ 120 / 135 ] simplifiying candidate # 1536754427.588 * [enter]simplify: Simplifying (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1536754427.591 * * [misc]simplify: iters left: 6 (11 enodes) 1536754427.595 * * [misc]simplify: iters left: 5 (14 enodes) 1536754427.600 * * [misc]simplify: iters left: 4 (17 enodes) 1536754427.603 * [exit]simplify: Simplified to (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1536754427.603 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))))) 1536754427.603 * * * * [misc]progress: [ 121 / 135 ] simplifiying candidate # 1536754427.603 * [enter]simplify: Simplifying (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1536754427.604 * * [misc]simplify: iters left: 6 (10 enodes) 1536754427.606 * * [misc]simplify: iters left: 5 (13 enodes) 1536754427.608 * * [misc]simplify: iters left: 4 (16 enodes) 1536754427.610 * [exit]simplify: Simplified to (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1536754427.610 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))))) 1536754427.610 * * * * [misc]progress: [ 122 / 135 ] simplifiying candidate # 1536754427.610 * * * * [misc]progress: [ 123 / 135 ] simplifiying candidate # 1536754427.611 * [enter]simplify: Simplifying (pow (* n PI) 1/2) 1536754427.611 * * [misc]simplify: iters left: 3 (5 enodes) 1536754427.612 * * [misc]simplify: iters left: 2 (7 enodes) 1536754427.613 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536754427.613 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (* (sqrt k) (pow (* n PI) (/ k 2)))))) 1536754427.613 * * * * [misc]progress: [ 124 / 135 ] simplifiying candidate # 1536754427.613 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1536754427.613 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754427.613 * * * * [misc]progress: [ 125 / 135 ] simplifiying candidate # 1536754427.613 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1536754427.613 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754427.613 * * * * [misc]progress: [ 126 / 135 ] simplifiying candidate # 1536754427.614 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))))) 1536754427.614 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754427.614 * * * * [misc]progress: [ 127 / 135 ] simplifiying candidate # 1536754427.614 * [enter]simplify: Simplifying (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))))) 1536754427.616 * * [misc]simplify: iters left: 6 (36 enodes) 1536754427.629 * * [misc]simplify: iters left: 5 (104 enodes) 1536754427.673 * * [misc]simplify: iters left: 4 (331 enodes) 1536754428.301 * [exit]simplify: Simplified to (+ (fma (* (* (* k k) (log PI)) (log PI)) (* 1/8 (* (pow PI 1/2) (pow n 1/2))) (fma (* 1/8 (* (pow PI 1/2) (pow n 1/2))) (* (* (log n) k) (* (log n) k)) (* (pow PI 1/2) (pow n 1/2)))) (- (* (* (* (pow PI 1/2) (pow n 1/2)) (* 1/4 (log PI))) (* (* k k) (log n))) (* (* k 1/2) (* (* (pow PI 1/2) (pow n 1/2)) (+ (log PI) (log n)))))) 1536754428.301 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (+ (fma (* (* (* k k) (log PI)) (log PI)) (* 1/8 (* (pow PI 1/2) (pow n 1/2))) (fma (* 1/8 (* (pow PI 1/2) (pow n 1/2))) (* (* (log n) k) (* (log n) k)) (* (pow PI 1/2) (pow n 1/2)))) (- (* (* (* (pow PI 1/2) (pow n 1/2)) (* 1/4 (log PI))) (* (* k k) (log n))) (* (* k 1/2) (* (* (pow PI 1/2) (pow n 1/2)) (+ (log PI) (log n)))))) (sqrt k)))) 1536754428.301 * * * * [misc]progress: [ 128 / 135 ] simplifiying candidate # 1536754428.302 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) 1536754428.303 * * [misc]simplify: iters left: 6 (13 enodes) 1536754428.311 * * [misc]simplify: iters left: 5 (27 enodes) 1536754428.324 * * [misc]simplify: iters left: 4 (53 enodes) 1536754428.353 * * [misc]simplify: iters left: 3 (128 enodes) 1536754428.413 * * [misc]simplify: iters left: 2 (409 enodes) 1536754428.964 * [exit]simplify: Simplified to (pow (* n PI) (fma k -1/2 1/2)) 1536754428.964 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (fma k -1/2 1/2)) (sqrt k)))) 1536754428.964 * * * * [misc]progress: [ 129 / 135 ] simplifiying candidate # 1536754428.964 * [enter]simplify: Simplifying (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) 1536754428.965 * * [misc]simplify: iters left: 6 (14 enodes) 1536754428.969 * * [misc]simplify: iters left: 5 (29 enodes) 1536754428.982 * * [misc]simplify: iters left: 4 (64 enodes) 1536754429.012 * * [misc]simplify: iters left: 3 (212 enodes) 1536754429.246 * [exit]simplify: Simplified to (pow (* (* PI 1) n) (fma k -1/2 1/2)) 1536754429.246 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* (* PI 1) n) (fma k -1/2 1/2)) (sqrt k)))) 1536754429.246 * * * * [misc]progress: [ 130 / 135 ] simplifiying candidate # 1536754429.246 * [enter]simplify: Simplifying (* n PI) 1536754429.252 * * [misc]simplify: iters left: 2 (3 enodes) 1536754429.253 * * [misc]simplify: iters left: 1 (4 enodes) 1536754429.255 * [exit]simplify: Simplified to (* n PI) 1536754429.255 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754429.255 * * * * [misc]progress: [ 131 / 135 ] simplifiying candidate # 1536754429.255 * [enter]simplify: Simplifying (* n PI) 1536754429.255 * * [misc]simplify: iters left: 2 (3 enodes) 1536754429.257 * * [misc]simplify: iters left: 1 (4 enodes) 1536754429.258 * [exit]simplify: Simplified to (* n PI) 1536754429.258 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754429.258 * * * * [misc]progress: [ 132 / 135 ] simplifiying candidate # 1536754429.258 * [enter]simplify: Simplifying (* n PI) 1536754429.259 * * [misc]simplify: iters left: 2 (3 enodes) 1536754429.260 * * [misc]simplify: iters left: 1 (4 enodes) 1536754429.261 * [exit]simplify: Simplified to (* n PI) 1536754429.261 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536754429.262 * * * * [misc]progress: [ 133 / 135 ] simplifiying candidate # 1536754429.262 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2))))))))))))))))))))))) 1536754429.262 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536754429.262 * * * * [misc]progress: [ 134 / 135 ] simplifiying candidate # 1536754429.262 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3)))))))) 1536754429.262 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536754429.263 * * * * [misc]progress: [ 135 / 135 ] simplifiying candidate # 1536754429.263 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))))))))) 1536754429.263 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536754429.263 * * * [misc]progress: adding candidates to table 1536754432.021 * * [misc]progress: iteration 4 / 4 1536754432.021 * * * [misc]progress: picking best candidate 1536754432.121 * * * * [misc]pick: Picked # 1536754432.121 * * * [misc]progress: localizing error 1536754432.156 * * * [misc]progress: generating rewritten candidates 1536754432.156 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 1) 1536754432.168 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2) 1536754432.306 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1536754432.362 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 2) 1536754432.394 * * * [misc]progress: generating series expansions 1536754432.394 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 1) 1536754432.395 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 1536754432.395 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 1536754432.395 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536754432.395 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536754432.395 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536754432.395 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.395 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.395 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.395 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.395 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.395 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.395 * [misc]taylor: Taking taylor expansion of k in k 1536754432.395 * [misc]backup-simplify: Simplify 0 into 0 1536754432.395 * [misc]backup-simplify: Simplify 1 into 1 1536754432.395 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.395 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.395 * [misc]backup-simplify: Simplify PI into PI 1536754432.395 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.395 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.396 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.396 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.396 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.396 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536754432.396 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536754432.397 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536754432.397 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536754432.397 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.397 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.397 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.397 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.397 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.397 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.397 * [misc]taylor: Taking taylor expansion of k in k 1536754432.397 * [misc]backup-simplify: Simplify 0 into 0 1536754432.397 * [misc]backup-simplify: Simplify 1 into 1 1536754432.397 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.397 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.397 * [misc]backup-simplify: Simplify PI into PI 1536754432.397 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.397 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.397 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.397 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.398 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.398 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536754432.398 * [misc]backup-simplify: Simplify (pow PI 1/2) into (pow PI 1/2) 1536754432.400 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754432.401 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754432.401 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.401 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.402 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1536754432.406 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1536754432.407 * [misc]backup-simplify: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 1536754432.413 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754432.413 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754432.413 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.413 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.415 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1536754432.420 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536754432.422 * [misc]backup-simplify: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536754432.427 * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1536754432.427 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.427 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 1536754432.427 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754432.427 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536754432.427 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536754432.427 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754432.427 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.427 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.427 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.427 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.427 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.427 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.427 * [misc]taylor: Taking taylor expansion of k in k 1536754432.427 * [misc]backup-simplify: Simplify 0 into 0 1536754432.427 * [misc]backup-simplify: Simplify 1 into 1 1536754432.427 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.428 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.428 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.428 * [misc]backup-simplify: Simplify PI into PI 1536754432.428 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.428 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.428 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.428 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.429 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536754432.429 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.429 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754432.429 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536754432.429 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536754432.429 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754432.430 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.430 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.430 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.430 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.430 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.430 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.430 * [misc]taylor: Taking taylor expansion of k in k 1536754432.430 * [misc]backup-simplify: Simplify 0 into 0 1536754432.430 * [misc]backup-simplify: Simplify 1 into 1 1536754432.430 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.430 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.430 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.430 * [misc]backup-simplify: Simplify PI into PI 1536754432.430 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.430 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.431 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.431 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.431 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536754432.432 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.432 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.432 * [misc]backup-simplify: Simplify 0 into 0 1536754432.432 * [misc]backup-simplify: Simplify 0 into 0 1536754432.432 * [misc]backup-simplify: Simplify 0 into 0 1536754432.432 * [misc]backup-simplify: Simplify 0 into 0 1536754432.432 * [misc]backup-simplify: Simplify 0 into 0 1536754432.432 * [misc]backup-simplify: Simplify 0 into 0 1536754432.433 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 1536754432.433 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.433 * [misc]approximate: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 1536754432.433 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754432.433 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536754432.433 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536754432.433 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754432.433 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.433 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.433 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.433 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.433 * [misc]taylor: Taking taylor expansion of k in k 1536754432.433 * [misc]backup-simplify: Simplify 0 into 0 1536754432.433 * [misc]backup-simplify: Simplify 1 into 1 1536754432.433 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.433 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.433 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.433 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.434 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.434 * [misc]backup-simplify: Simplify PI into PI 1536754432.434 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.434 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.434 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.435 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.435 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.435 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754432.435 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536754432.435 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536754432.435 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754432.435 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.435 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.435 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.435 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.435 * [misc]taylor: Taking taylor expansion of k in k 1536754432.435 * [misc]backup-simplify: Simplify 0 into 0 1536754432.435 * [misc]backup-simplify: Simplify 1 into 1 1536754432.436 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.436 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.436 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.436 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.436 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.436 * [misc]backup-simplify: Simplify PI into PI 1536754432.436 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.436 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.436 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.437 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.437 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.437 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.438 * [misc]backup-simplify: Simplify 0 into 0 1536754432.438 * [misc]backup-simplify: Simplify 0 into 0 1536754432.438 * [misc]backup-simplify: Simplify 0 into 0 1536754432.438 * [misc]backup-simplify: Simplify 0 into 0 1536754432.438 * [misc]backup-simplify: Simplify 0 into 0 1536754432.438 * [misc]backup-simplify: Simplify 0 into 0 1536754432.438 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 1536754432.438 * * * * [misc]progress: [ 2 / 4 ] generating series at (2) 1536754432.439 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) into (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) 1536754432.439 * [misc]approximate: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in (k n) around 0 1536754432.439 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in n 1536754432.439 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in n 1536754432.439 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 1536754432.439 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 1536754432.439 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 1536754432.439 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754432.439 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.439 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.439 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754432.439 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.439 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.439 * [misc]taylor: Taking taylor expansion of k in n 1536754432.439 * [misc]backup-simplify: Simplify k into k 1536754432.439 * [misc]taylor: Taking taylor expansion of (log n) in n 1536754432.439 * [misc]taylor: Taking taylor expansion of n in n 1536754432.439 * [misc]backup-simplify: Simplify 0 into 0 1536754432.439 * [misc]backup-simplify: Simplify 1 into 1 1536754432.439 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.440 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754432.440 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754432.440 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754432.440 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.440 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 1536754432.440 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 1536754432.440 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1536754432.440 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n 1536754432.440 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n 1536754432.440 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n 1536754432.440 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754432.440 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.440 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.441 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754432.441 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.441 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.441 * [misc]taylor: Taking taylor expansion of k in n 1536754432.441 * [misc]backup-simplify: Simplify k into k 1536754432.441 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.441 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.441 * [misc]backup-simplify: Simplify 2 into 2 1536754432.441 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.441 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754432.441 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754432.441 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754432.441 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k))) 1536754432.442 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k)))) 1536754432.442 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1536754432.442 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1536754432.442 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1536754432.442 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754432.442 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.442 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.442 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754432.442 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.442 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.442 * [misc]taylor: Taking taylor expansion of k in n 1536754432.442 * [misc]backup-simplify: Simplify k into k 1536754432.442 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.442 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.442 * [misc]backup-simplify: Simplify PI into PI 1536754432.442 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.442 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754432.442 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754432.443 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754432.443 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1536754432.443 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1536754432.443 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754432.444 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.444 * [misc]taylor: Taking taylor expansion of k in n 1536754432.444 * [misc]backup-simplify: Simplify k into k 1536754432.444 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.444 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754432.444 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754432.444 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754432.444 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in k 1536754432.444 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 1536754432.444 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 1536754432.444 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 1536754432.444 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 1536754432.444 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.444 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.444 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.444 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.444 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.444 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.444 * [misc]taylor: Taking taylor expansion of k in k 1536754432.444 * [misc]backup-simplify: Simplify 0 into 0 1536754432.444 * [misc]backup-simplify: Simplify 1 into 1 1536754432.444 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754432.444 * [misc]taylor: Taking taylor expansion of n in k 1536754432.444 * [misc]backup-simplify: Simplify n into n 1536754432.445 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754432.445 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.445 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.445 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.445 * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 1536754432.445 * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 1536754432.445 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1536754432.445 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 1536754432.445 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 1536754432.445 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 1536754432.445 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.445 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.445 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.445 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.445 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.446 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.446 * [misc]taylor: Taking taylor expansion of k in k 1536754432.446 * [misc]backup-simplify: Simplify 0 into 0 1536754432.446 * [misc]backup-simplify: Simplify 1 into 1 1536754432.446 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754432.446 * [misc]taylor: Taking taylor expansion of 2 in k 1536754432.446 * [misc]backup-simplify: Simplify 2 into 2 1536754432.446 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.446 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.446 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.446 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.447 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536754432.447 * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 1536754432.447 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536754432.447 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536754432.447 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536754432.447 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.447 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.447 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.448 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.448 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.448 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.448 * [misc]taylor: Taking taylor expansion of k in k 1536754432.448 * [misc]backup-simplify: Simplify 0 into 0 1536754432.448 * [misc]backup-simplify: Simplify 1 into 1 1536754432.448 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.448 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.448 * [misc]backup-simplify: Simplify PI into PI 1536754432.448 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.448 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.448 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.449 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.449 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.450 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536754432.450 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754432.450 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.450 * [misc]taylor: Taking taylor expansion of k in k 1536754432.450 * [misc]backup-simplify: Simplify 0 into 0 1536754432.450 * [misc]backup-simplify: Simplify 1 into 1 1536754432.450 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.450 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.451 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754432.451 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in k 1536754432.451 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 1536754432.451 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 1536754432.451 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 1536754432.451 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 1536754432.451 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.451 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.451 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.451 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.451 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.451 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.451 * [misc]taylor: Taking taylor expansion of k in k 1536754432.451 * [misc]backup-simplify: Simplify 0 into 0 1536754432.451 * [misc]backup-simplify: Simplify 1 into 1 1536754432.451 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754432.451 * [misc]taylor: Taking taylor expansion of n in k 1536754432.451 * [misc]backup-simplify: Simplify n into n 1536754432.452 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754432.452 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.452 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.452 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.452 * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 1536754432.452 * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 1536754432.452 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1536754432.452 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 1536754432.452 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 1536754432.452 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 1536754432.452 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.452 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.452 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.452 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.452 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.452 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.453 * [misc]taylor: Taking taylor expansion of k in k 1536754432.453 * [misc]backup-simplify: Simplify 0 into 0 1536754432.453 * [misc]backup-simplify: Simplify 1 into 1 1536754432.453 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754432.453 * [misc]taylor: Taking taylor expansion of 2 in k 1536754432.453 * [misc]backup-simplify: Simplify 2 into 2 1536754432.453 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.453 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.453 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.453 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.454 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536754432.454 * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 1536754432.454 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536754432.454 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536754432.454 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536754432.454 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.454 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.454 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.454 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.454 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.454 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.454 * [misc]taylor: Taking taylor expansion of k in k 1536754432.454 * [misc]backup-simplify: Simplify 0 into 0 1536754432.455 * [misc]backup-simplify: Simplify 1 into 1 1536754432.455 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.455 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.455 * [misc]backup-simplify: Simplify PI into PI 1536754432.455 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.455 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.455 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.455 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.456 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.456 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536754432.456 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754432.456 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.456 * [misc]taylor: Taking taylor expansion of k in k 1536754432.456 * [misc]backup-simplify: Simplify 0 into 0 1536754432.456 * [misc]backup-simplify: Simplify 1 into 1 1536754432.456 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.456 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.457 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754432.457 * [misc]backup-simplify: Simplify (* (pow 2 1/2) (pow PI 1/2)) into (sqrt (* PI 2)) 1536754432.458 * [misc]backup-simplify: Simplify (* (pow n 1/2) (sqrt (* PI 2))) into (* (sqrt 2) (sqrt (* n PI))) 1536754432.458 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (sqrt (* n PI))) 0) into 0 1536754432.458 * [misc]taylor: Taking taylor expansion of 0 in n 1536754432.458 * [misc]backup-simplify: Simplify 0 into 0 1536754432.458 * [misc]backup-simplify: Simplify 0 into 0 1536754432.460 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754432.460 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754432.460 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.460 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.461 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1536754432.466 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1536754432.468 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536754432.468 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754432.468 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.468 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.469 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2))) 1536754432.471 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2))) 1536754432.473 * [misc]backup-simplify: Simplify (+ (* (pow 2 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (log 2) (sqrt 2))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI))))) 1536754432.474 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536754432.474 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754432.474 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.474 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.474 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 1536754432.474 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 1536754432.478 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* -1/2 (* (sqrt n) (log n))) (sqrt (* PI 2)))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) 1536754432.479 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1536754432.479 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1536754432.479 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536754432.479 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.479 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.479 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536754432.479 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.479 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.479 * [misc]backup-simplify: Simplify 2 into 2 1536754432.480 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.480 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.480 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.480 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.480 * [misc]taylor: Taking taylor expansion of n in n 1536754432.480 * [misc]backup-simplify: Simplify 0 into 0 1536754432.480 * [misc]backup-simplify: Simplify 1 into 1 1536754432.480 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.480 * [misc]backup-simplify: Simplify PI into PI 1536754432.480 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.480 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.481 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.481 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.481 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536754432.481 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.481 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.481 * [misc]backup-simplify: Simplify 0 into 0 1536754432.481 * [misc]backup-simplify: Simplify 0 into 0 1536754432.481 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754432.482 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754432.485 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754432.485 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754432.485 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.485 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.486 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1536754432.490 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536754432.492 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1536754432.492 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754432.492 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.493 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.493 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0 1536754432.495 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) 1536754432.502 * [misc]backup-simplify: Simplify (+ (* (pow 2 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI))))) 1536754432.503 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536754432.503 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754432.503 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.503 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.503 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 1536754432.504 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 1536754432.517 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (sqrt (* PI 2))))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) 1536754432.527 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) 1536754432.527 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.527 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.527 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.527 * [misc]backup-simplify: Simplify 2 into 2 1536754432.527 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.527 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.527 * [misc]backup-simplify: Simplify 2 into 2 1536754432.527 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.527 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.527 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.527 * [misc]taylor: Taking taylor expansion of n in n 1536754432.527 * [misc]backup-simplify: Simplify 0 into 0 1536754432.527 * [misc]backup-simplify: Simplify 1 into 1 1536754432.527 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.528 * [misc]backup-simplify: Simplify PI into PI 1536754432.528 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.528 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.528 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.529 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.529 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.529 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.529 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.529 * [misc]backup-simplify: Simplify 2 into 2 1536754432.529 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.529 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.529 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.529 * [misc]backup-simplify: Simplify PI into PI 1536754432.529 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.529 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536754432.529 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.529 * [misc]backup-simplify: Simplify PI into PI 1536754432.529 * [misc]taylor: Taking taylor expansion of n in n 1536754432.529 * [misc]backup-simplify: Simplify 0 into 0 1536754432.529 * [misc]backup-simplify: Simplify 1 into 1 1536754432.530 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536754432.530 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536754432.530 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.530 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.531 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) in n 1536754432.531 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) in n 1536754432.531 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536754432.531 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.531 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.531 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536754432.531 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.531 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.531 * [misc]backup-simplify: Simplify 2 into 2 1536754432.531 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.531 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.531 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.531 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.531 * [misc]taylor: Taking taylor expansion of n in n 1536754432.531 * [misc]backup-simplify: Simplify 0 into 0 1536754432.531 * [misc]backup-simplify: Simplify 1 into 1 1536754432.531 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.531 * [misc]backup-simplify: Simplify PI into PI 1536754432.531 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.532 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.532 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.532 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.532 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))) in n 1536754432.532 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) in n 1536754432.532 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.532 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.532 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log n)) (sqrt (* n PI))) in n 1536754432.532 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) in n 1536754432.532 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.532 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.532 * [misc]backup-simplify: Simplify 2 into 2 1536754432.532 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.532 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.533 * [misc]taylor: Taking taylor expansion of (log n) in n 1536754432.533 * [misc]taylor: Taking taylor expansion of n in n 1536754432.533 * [misc]backup-simplify: Simplify 0 into 0 1536754432.533 * [misc]backup-simplify: Simplify 1 into 1 1536754432.533 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.533 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.533 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.533 * [misc]taylor: Taking taylor expansion of n in n 1536754432.533 * [misc]backup-simplify: Simplify 0 into 0 1536754432.533 * [misc]backup-simplify: Simplify 1 into 1 1536754432.533 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.533 * [misc]backup-simplify: Simplify PI into PI 1536754432.533 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.533 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.533 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.534 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.534 * [misc]backup-simplify: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 1536754432.534 * [misc]backup-simplify: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 1536754432.534 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.535 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1536754432.535 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1536754432.536 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.536 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536754432.536 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.536 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.536 * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 1536754432.536 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log n)) 0) into 0 1536754432.536 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.536 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.536 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.537 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.537 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.537 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.537 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.537 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.537 * [misc]backup-simplify: Simplify 0 into 0 1536754432.538 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754432.539 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754432.540 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754432.541 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754432.541 * [misc]backup-simplify: Simplify 0 into 0 1536754432.541 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754432.542 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754432.546 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754432.547 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754432.547 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.547 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.549 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536754432.561 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1536754432.570 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1536754432.571 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754432.571 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.571 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.571 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0 1536754432.579 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2))) 1536754432.591 * [misc]backup-simplify: Simplify (+ (* (pow 2 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (pow (log 2) 3) (sqrt 2))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))) (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI))))))) 1536754432.593 * [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 1536754432.593 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754432.593 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.593 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.594 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 1536754432.595 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) 1536754432.635 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))) (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI)))))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (sqrt (* PI 2)))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))))))))))))) 1536754432.718 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) +nan.0) (* (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))))))))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) 1536754432.718 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) in n 1536754432.719 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))))) in n 1536754432.719 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) in n 1536754432.719 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.719 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.719 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI))) in n 1536754432.719 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log n) 2)) in n 1536754432.719 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.719 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.719 * [misc]backup-simplify: Simplify 2 into 2 1536754432.719 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.720 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.720 * [misc]taylor: Taking taylor expansion of (pow (log n) 2) in n 1536754432.720 * [misc]taylor: Taking taylor expansion of (log n) in n 1536754432.720 * [misc]taylor: Taking taylor expansion of n in n 1536754432.720 * [misc]backup-simplify: Simplify 0 into 0 1536754432.720 * [misc]backup-simplify: Simplify 1 into 1 1536754432.720 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.720 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.720 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.720 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.721 * [misc]taylor: Taking taylor expansion of n in n 1536754432.721 * [misc]backup-simplify: Simplify 0 into 0 1536754432.721 * [misc]backup-simplify: Simplify 1 into 1 1536754432.721 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.721 * [misc]backup-simplify: Simplify PI into PI 1536754432.721 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.722 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.722 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.723 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.723 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))) in n 1536754432.723 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))) in n 1536754432.723 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) in n 1536754432.723 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.723 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.723 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n))) in n 1536754432.723 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log PI) 2)) in n 1536754432.723 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.723 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.723 * [misc]backup-simplify: Simplify 2 into 2 1536754432.723 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.723 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.724 * [misc]taylor: Taking taylor expansion of (pow (log PI) 2) in n 1536754432.724 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.724 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.724 * [misc]backup-simplify: Simplify PI into PI 1536754432.724 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.724 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536754432.724 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536754432.724 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.724 * [misc]backup-simplify: Simplify PI into PI 1536754432.724 * [misc]taylor: Taking taylor expansion of n in n 1536754432.724 * [misc]backup-simplify: Simplify 0 into 0 1536754432.724 * [misc]backup-simplify: Simplify 1 into 1 1536754432.724 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536754432.725 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536754432.725 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.726 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.726 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))) in n 1536754432.726 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))) in n 1536754432.726 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536754432.726 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.726 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.726 * [misc]taylor: Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n 1536754432.726 * [misc]taylor: Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n 1536754432.726 * [misc]taylor: Taking taylor expansion of (pow (log 2) 2) in n 1536754432.726 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.726 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.726 * [misc]backup-simplify: Simplify 2 into 2 1536754432.726 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.727 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.727 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.727 * [misc]backup-simplify: Simplify 2 into 2 1536754432.727 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.727 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.727 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.727 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.727 * [misc]taylor: Taking taylor expansion of n in n 1536754432.727 * [misc]backup-simplify: Simplify 0 into 0 1536754432.727 * [misc]backup-simplify: Simplify 1 into 1 1536754432.727 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.727 * [misc]backup-simplify: Simplify PI into PI 1536754432.728 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.728 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.728 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.729 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.729 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))) in n 1536754432.729 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))) in n 1536754432.729 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536754432.729 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.729 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.729 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536754432.729 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.729 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.729 * [misc]backup-simplify: Simplify 2 into 2 1536754432.729 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.730 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.730 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.730 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.730 * [misc]taylor: Taking taylor expansion of n in n 1536754432.730 * [misc]backup-simplify: Simplify 0 into 0 1536754432.730 * [misc]backup-simplify: Simplify 1 into 1 1536754432.730 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.730 * [misc]backup-simplify: Simplify PI into PI 1536754432.730 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.731 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.731 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.732 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.732 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))) in n 1536754432.732 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))) in n 1536754432.732 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) in n 1536754432.732 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.732 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.732 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log n)) (sqrt (* n PI))) in n 1536754432.732 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) in n 1536754432.732 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.732 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.732 * [misc]backup-simplify: Simplify 2 into 2 1536754432.732 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.733 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.733 * [misc]taylor: Taking taylor expansion of (log n) in n 1536754432.733 * [misc]taylor: Taking taylor expansion of n in n 1536754432.733 * [misc]backup-simplify: Simplify 0 into 0 1536754432.733 * [misc]backup-simplify: Simplify 1 into 1 1536754432.733 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.733 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.733 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.733 * [misc]taylor: Taking taylor expansion of n in n 1536754432.733 * [misc]backup-simplify: Simplify 0 into 0 1536754432.733 * [misc]backup-simplify: Simplify 1 into 1 1536754432.733 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.733 * [misc]backup-simplify: Simplify PI into PI 1536754432.733 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.734 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.734 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.735 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.735 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))) in n 1536754432.735 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))) in n 1536754432.735 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1536754432.735 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.735 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.735 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1536754432.735 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1536754432.735 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.735 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.735 * [misc]backup-simplify: Simplify 2 into 2 1536754432.735 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.735 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.735 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.735 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.735 * [misc]backup-simplify: Simplify PI into PI 1536754432.736 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.736 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536754432.736 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536754432.736 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.736 * [misc]backup-simplify: Simplify PI into PI 1536754432.736 * [misc]taylor: Taking taylor expansion of n in n 1536754432.736 * [misc]backup-simplify: Simplify 0 into 0 1536754432.736 * [misc]backup-simplify: Simplify 1 into 1 1536754432.736 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536754432.737 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536754432.737 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.737 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.737 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))) in n 1536754432.737 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))) in n 1536754432.737 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) in n 1536754432.737 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.737 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.737 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))) in n 1536754432.737 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log PI) (log n))) in n 1536754432.737 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.737 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.737 * [misc]backup-simplify: Simplify 2 into 2 1536754432.737 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.737 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.737 * [misc]taylor: Taking taylor expansion of (* (log PI) (log n)) in n 1536754432.737 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.737 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.737 * [misc]backup-simplify: Simplify PI into PI 1536754432.738 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.738 * [misc]taylor: Taking taylor expansion of (log n) in n 1536754432.738 * [misc]taylor: Taking taylor expansion of n in n 1536754432.738 * [misc]backup-simplify: Simplify 0 into 0 1536754432.738 * [misc]backup-simplify: Simplify 1 into 1 1536754432.738 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.738 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536754432.738 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536754432.738 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.738 * [misc]backup-simplify: Simplify PI into PI 1536754432.738 * [misc]taylor: Taking taylor expansion of n in n 1536754432.738 * [misc]backup-simplify: Simplify 0 into 0 1536754432.738 * [misc]backup-simplify: Simplify 1 into 1 1536754432.738 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536754432.739 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536754432.739 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.739 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.739 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))) in n 1536754432.739 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))) in n 1536754432.739 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) in n 1536754432.739 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.739 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.739 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI))) in n 1536754432.739 * [misc]taylor: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log n))) in n 1536754432.739 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.739 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.739 * [misc]backup-simplify: Simplify 2 into 2 1536754432.739 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.739 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) in n 1536754432.739 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.739 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.739 * [misc]backup-simplify: Simplify 2 into 2 1536754432.739 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.740 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.740 * [misc]taylor: Taking taylor expansion of (log n) in n 1536754432.740 * [misc]taylor: Taking taylor expansion of n in n 1536754432.740 * [misc]backup-simplify: Simplify 0 into 0 1536754432.740 * [misc]backup-simplify: Simplify 1 into 1 1536754432.740 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.740 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.740 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.740 * [misc]taylor: Taking taylor expansion of n in n 1536754432.740 * [misc]backup-simplify: Simplify 0 into 0 1536754432.740 * [misc]backup-simplify: Simplify 1 into 1 1536754432.740 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.740 * [misc]backup-simplify: Simplify PI into PI 1536754432.740 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.740 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.741 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.741 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.741 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))) in n 1536754432.741 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))) in n 1536754432.741 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) in n 1536754432.741 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.741 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.741 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n))) in n 1536754432.741 * [misc]taylor: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log PI))) in n 1536754432.741 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.741 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.741 * [misc]backup-simplify: Simplify 2 into 2 1536754432.741 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.741 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1536754432.741 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.741 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.741 * [misc]backup-simplify: Simplify 2 into 2 1536754432.741 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.742 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.742 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.742 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.742 * [misc]backup-simplify: Simplify PI into PI 1536754432.742 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.742 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536754432.742 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536754432.742 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.742 * [misc]backup-simplify: Simplify PI into PI 1536754432.742 * [misc]taylor: Taking taylor expansion of n in n 1536754432.742 * [misc]backup-simplify: Simplify 0 into 0 1536754432.742 * [misc]backup-simplify: Simplify 1 into 1 1536754432.742 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536754432.743 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536754432.743 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.743 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.743 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))) in n 1536754432.743 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536754432.743 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.743 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.743 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 1536754432.743 * [misc]taylor: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 1536754432.743 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.743 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.743 * [misc]backup-simplify: Simplify 2 into 2 1536754432.743 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.743 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536754432.743 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.744 * [misc]backup-simplify: Simplify 2 into 2 1536754432.744 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536754432.744 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536754432.744 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536754432.744 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536754432.744 * [misc]taylor: Taking taylor expansion of n in n 1536754432.744 * [misc]backup-simplify: Simplify 0 into 0 1536754432.744 * [misc]backup-simplify: Simplify 1 into 1 1536754432.744 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.744 * [misc]backup-simplify: Simplify PI into PI 1536754432.744 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536754432.744 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536754432.745 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.745 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536754432.745 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.745 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.745 * [misc]backup-simplify: Simplify (* (log n) (log n)) into (pow (log n) 2) 1536754432.746 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log n) 2)) into (* (sqrt 2) (pow (log n) 2)) 1536754432.746 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log n) 2)) 0) into 0 1536754432.746 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.747 * [misc]backup-simplify: Simplify (* (log PI) (log PI)) into (pow (log PI) 2) 1536754432.748 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log PI) 2)) into (* (sqrt 2) (pow (log PI) 2)) 1536754432.749 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log PI) 2)) 0) into 0 1536754432.749 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.749 * [misc]backup-simplify: Simplify (* (log 2) (log 2)) into (pow (log 2) 2) 1536754432.750 * [misc]backup-simplify: Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2)) 1536754432.751 * [misc]backup-simplify: Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0 1536754432.751 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.751 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536754432.751 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.751 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.751 * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 1536754432.751 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log n)) 0) into 0 1536754432.752 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.752 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1536754432.753 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1536754432.753 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.753 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.753 * [misc]backup-simplify: Simplify (* (log PI) (log n)) into (* (log PI) (log n)) 1536754432.754 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (log PI) (log n))) into (* (sqrt 2) (* (log PI) (log n))) 1536754432.754 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (log PI) (log n))) 0) into 0 1536754432.754 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.754 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.754 * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 1536754432.754 * [misc]backup-simplify: Simplify (* (log 2) (* (sqrt 2) (log n))) into (* (log 2) (* (sqrt 2) (log n))) 1536754432.755 * [misc]backup-simplify: Simplify (* (* (log 2) (* (sqrt 2) (log n))) 0) into 0 1536754432.755 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.755 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1536754432.756 * [misc]backup-simplify: Simplify (* (log 2) (* (sqrt 2) (log PI))) into (* (log 2) (* (sqrt 2) (log PI))) 1536754432.757 * [misc]backup-simplify: Simplify (* (* (log 2) (* (sqrt 2) (log PI))) 0) into 0 1536754432.757 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.757 * [misc]backup-simplify: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 1536754432.757 * [misc]backup-simplify: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 1536754432.757 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.758 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.759 * [misc]backup-simplify: Simplify 0 into 0 1536754432.761 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536754432.761 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0 1536754432.762 * [misc]backup-simplify: Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 1536754432.764 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 1536754432.765 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754432.766 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log PI))) into 0 1536754432.767 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log PI)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1536754432.769 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1536754432.770 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754432.771 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536754432.772 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1536754432.772 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.773 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log n))) into 0 1536754432.773 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log n)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 1536754432.774 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 1536754432.774 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 1536754432.775 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) 1536754432.776 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) 1536754432.778 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536754432.781 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536754432.784 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536754432.790 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536754432.799 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536754432.802 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536754432.803 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536754432.804 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536754432.806 * [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)))) 1536754432.809 * [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)))) 1536754432.810 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536754432.811 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536754432.819 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1536754432.819 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) into (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) 1536754432.819 * [misc]approximate: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in (k n) around 0 1536754432.819 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.819 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.819 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.819 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.819 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of k in n 1536754432.819 * [misc]backup-simplify: Simplify k into k 1536754432.819 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.819 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.819 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.819 * [misc]backup-simplify: Simplify 2 into 2 1536754432.820 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.820 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.820 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.820 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.820 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.820 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.820 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754432.820 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.820 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536754432.820 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536754432.820 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.820 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.820 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.820 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.820 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.820 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.820 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.820 * [misc]taylor: Taking taylor expansion of k in n 1536754432.820 * [misc]backup-simplify: Simplify k into k 1536754432.820 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.820 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.820 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.821 * [misc]backup-simplify: Simplify PI into PI 1536754432.821 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.821 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.821 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.821 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.821 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536754432.821 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.821 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.821 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536754432.822 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536754432.822 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.822 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.822 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.822 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.822 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.822 * [misc]taylor: Taking taylor expansion of k in n 1536754432.822 * [misc]backup-simplify: Simplify k into k 1536754432.822 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.822 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536754432.822 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536754432.822 * [misc]taylor: Taking taylor expansion of n in n 1536754432.822 * [misc]backup-simplify: Simplify 0 into 0 1536754432.822 * [misc]backup-simplify: Simplify 1 into 1 1536754432.822 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.822 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.822 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.822 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.822 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.822 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754432.822 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536754432.823 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536754432.823 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754432.823 * [misc]taylor: Taking taylor expansion of k in n 1536754432.823 * [misc]backup-simplify: Simplify k into k 1536754432.823 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754432.823 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754432.823 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.823 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.823 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.823 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.823 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of k in k 1536754432.823 * [misc]backup-simplify: Simplify 0 into 0 1536754432.823 * [misc]backup-simplify: Simplify 1 into 1 1536754432.823 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.823 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754432.823 * [misc]taylor: Taking taylor expansion of 2 in k 1536754432.823 * [misc]backup-simplify: Simplify 2 into 2 1536754432.823 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.823 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.823 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.824 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.824 * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 1536754432.824 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.824 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754432.824 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754432.824 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536754432.824 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536754432.824 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754432.824 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.824 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.824 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.824 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.824 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.824 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.824 * [misc]taylor: Taking taylor expansion of k in k 1536754432.824 * [misc]backup-simplify: Simplify 0 into 0 1536754432.824 * [misc]backup-simplify: Simplify 1 into 1 1536754432.824 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.824 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.824 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.824 * [misc]backup-simplify: Simplify PI into PI 1536754432.825 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.825 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.825 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.825 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.825 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536754432.826 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.826 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754432.826 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 1536754432.826 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 1536754432.826 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754432.826 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.826 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.826 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.826 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.826 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.826 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.826 * [misc]taylor: Taking taylor expansion of k in k 1536754432.826 * [misc]backup-simplify: Simplify 0 into 0 1536754432.826 * [misc]backup-simplify: Simplify 1 into 1 1536754432.826 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.826 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in k 1536754432.826 * [misc]taylor: Taking taylor expansion of (/ 1 n) in k 1536754432.826 * [misc]taylor: Taking taylor expansion of n in k 1536754432.826 * [misc]backup-simplify: Simplify n into n 1536754432.826 * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) 1536754432.826 * [misc]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) 1536754432.826 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.826 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.827 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.827 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 1536754432.827 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.827 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of k in k 1536754432.827 * [misc]backup-simplify: Simplify 0 into 0 1536754432.827 * [misc]backup-simplify: Simplify 1 into 1 1536754432.827 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.827 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754432.827 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.827 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.827 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.827 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.827 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.827 * [misc]taylor: Taking taylor expansion of k in k 1536754432.827 * [misc]backup-simplify: Simplify 0 into 0 1536754432.827 * [misc]backup-simplify: Simplify 1 into 1 1536754432.828 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.828 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754432.828 * [misc]taylor: Taking taylor expansion of 2 in k 1536754432.828 * [misc]backup-simplify: Simplify 2 into 2 1536754432.828 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.828 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.828 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.828 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.828 * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 1536754432.828 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.828 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754432.828 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754432.828 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536754432.828 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536754432.828 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754432.828 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.829 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.829 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.829 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.829 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.829 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.829 * [misc]taylor: Taking taylor expansion of k in k 1536754432.829 * [misc]backup-simplify: Simplify 0 into 0 1536754432.829 * [misc]backup-simplify: Simplify 1 into 1 1536754432.829 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.829 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.829 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.829 * [misc]backup-simplify: Simplify PI into PI 1536754432.829 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.829 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.829 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.829 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.830 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536754432.830 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.830 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754432.830 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 1536754432.830 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 1536754432.830 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754432.830 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.830 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.830 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.830 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.830 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.830 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.830 * [misc]taylor: Taking taylor expansion of k in k 1536754432.830 * [misc]backup-simplify: Simplify 0 into 0 1536754432.830 * [misc]backup-simplify: Simplify 1 into 1 1536754432.830 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.830 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in k 1536754432.830 * [misc]taylor: Taking taylor expansion of (/ 1 n) in k 1536754432.830 * [misc]taylor: Taking taylor expansion of n in k 1536754432.830 * [misc]backup-simplify: Simplify n into n 1536754432.830 * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) 1536754432.830 * [misc]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) 1536754432.830 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.831 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754432.831 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754432.831 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 1536754432.831 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.831 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754432.831 * [misc]taylor: Taking taylor expansion of k in k 1536754432.831 * [misc]backup-simplify: Simplify 0 into 0 1536754432.831 * [misc]backup-simplify: Simplify 1 into 1 1536754432.831 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.831 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754432.832 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.832 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) 1536754432.832 * [misc]backup-simplify: Simplify (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) 0) into 0 1536754432.832 * [misc]taylor: Taking taylor expansion of 0 in n 1536754432.832 * [misc]backup-simplify: Simplify 0 into 0 1536754432.832 * [misc]backup-simplify: Simplify 0 into 0 1536754432.833 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1536754432.833 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536754432.834 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.834 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.834 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.834 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.834 * [misc]backup-simplify: Simplify 2 into 2 1536754432.834 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.834 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.834 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.834 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.834 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.834 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.834 * [misc]taylor: Taking taylor expansion of k in n 1536754432.834 * [misc]backup-simplify: Simplify k into k 1536754432.834 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.834 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.834 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.834 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.834 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.835 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.835 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754432.835 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.835 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536754432.835 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536754432.835 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.835 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.835 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.835 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.835 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.835 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.835 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.835 * [misc]taylor: Taking taylor expansion of k in n 1536754432.835 * [misc]backup-simplify: Simplify k into k 1536754432.835 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.835 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.835 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.835 * [misc]backup-simplify: Simplify PI into PI 1536754432.835 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.835 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.835 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.835 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.836 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536754432.836 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.836 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.836 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536754432.836 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536754432.836 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.836 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.836 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.836 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.836 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.836 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.836 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.836 * [misc]taylor: Taking taylor expansion of k in n 1536754432.836 * [misc]backup-simplify: Simplify k into k 1536754432.836 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.836 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536754432.836 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536754432.836 * [misc]taylor: Taking taylor expansion of n in n 1536754432.836 * [misc]backup-simplify: Simplify 0 into 0 1536754432.836 * [misc]backup-simplify: Simplify 1 into 1 1536754432.836 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.836 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.837 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.837 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.837 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.837 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754432.837 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536754432.837 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536754432.837 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.838 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754432.838 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754432.838 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.839 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.839 * [misc]backup-simplify: Simplify 0 into 0 1536754432.840 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754432.840 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536754432.841 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536754432.841 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.841 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 1536754432.841 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536754432.841 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.841 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.841 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536754432.841 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754432.841 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.841 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.841 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.841 * [misc]backup-simplify: Simplify 2 into 2 1536754432.841 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.841 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.841 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.841 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.841 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.841 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.842 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.842 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of k in n 1536754432.842 * [misc]backup-simplify: Simplify k into k 1536754432.842 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.842 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.842 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.842 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.842 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.842 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.842 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.842 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.842 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.842 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.842 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of k in n 1536754432.842 * [misc]backup-simplify: Simplify k into k 1536754432.842 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.842 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.842 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.842 * [misc]backup-simplify: Simplify PI into PI 1536754432.843 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.843 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.843 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.843 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.843 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536754432.843 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.844 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.844 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536754432.844 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536754432.844 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.844 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.844 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.844 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.844 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.844 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.844 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.844 * [misc]taylor: Taking taylor expansion of k in n 1536754432.844 * [misc]backup-simplify: Simplify k into k 1536754432.844 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.844 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536754432.844 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536754432.844 * [misc]taylor: Taking taylor expansion of n in n 1536754432.844 * [misc]backup-simplify: Simplify 0 into 0 1536754432.844 * [misc]backup-simplify: Simplify 1 into 1 1536754432.844 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.845 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.845 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.845 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.845 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.845 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754432.845 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536754432.845 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536754432.846 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.846 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754432.847 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754432.848 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.849 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.849 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754432.852 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1536754432.852 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754432.852 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754432.852 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.852 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.853 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754432.853 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 1536754432.854 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754432.857 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754432.857 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754432.857 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754432.857 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.857 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.858 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 1536754432.860 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754432.860 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 1536754432.860 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754432.861 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754432.861 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.861 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.864 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536754432.864 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 1536754432.865 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754432.866 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536754432.867 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536754432.867 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.867 * [misc]backup-simplify: Simplify 0 into 0 1536754432.867 * [misc]backup-simplify: Simplify 0 into 0 1536754432.868 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754432.869 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536754432.869 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 1536754432.870 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.870 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.871 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.871 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.871 * [misc]backup-simplify: Simplify 2 into 2 1536754432.871 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.871 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.871 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.871 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.871 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.871 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.871 * [misc]taylor: Taking taylor expansion of k in n 1536754432.871 * [misc]backup-simplify: Simplify k into k 1536754432.871 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.871 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.871 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.871 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.872 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.872 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.872 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754432.872 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.872 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536754432.872 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536754432.872 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.872 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.872 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.872 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.872 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.872 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.872 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.872 * [misc]taylor: Taking taylor expansion of k in n 1536754432.872 * [misc]backup-simplify: Simplify k into k 1536754432.872 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.872 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.872 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.873 * [misc]backup-simplify: Simplify PI into PI 1536754432.873 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.873 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.873 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.873 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.873 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536754432.874 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754432.874 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754432.874 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536754432.874 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536754432.874 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754432.874 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.874 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.874 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.874 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.874 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.874 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.874 * [misc]taylor: Taking taylor expansion of k in n 1536754432.874 * [misc]backup-simplify: Simplify k into k 1536754432.874 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.874 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536754432.874 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536754432.874 * [misc]taylor: Taking taylor expansion of n in n 1536754432.874 * [misc]backup-simplify: Simplify 0 into 0 1536754432.874 * [misc]backup-simplify: Simplify 1 into 1 1536754432.875 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.875 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.875 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.875 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754432.875 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754432.875 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754432.875 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536754432.876 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536754432.876 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536754432.876 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754432.877 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754432.878 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.879 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536754432.884 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2)))))))) 1536754432.884 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) into (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) 1536754432.885 * [misc]approximate: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in (k n) around 0 1536754432.885 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.885 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.885 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of k in n 1536754432.885 * [misc]backup-simplify: Simplify k into k 1536754432.885 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.885 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.885 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.885 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536754432.885 * [misc]taylor: Taking taylor expansion of -1 in n 1536754432.885 * [misc]backup-simplify: Simplify -1 into -1 1536754432.885 * [misc]taylor: Taking taylor expansion of n in n 1536754432.885 * [misc]backup-simplify: Simplify 0 into 0 1536754432.885 * [misc]backup-simplify: Simplify 1 into 1 1536754432.886 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754432.886 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536754432.886 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.886 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.886 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754432.887 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536754432.887 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536754432.887 * [misc]taylor: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.887 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.887 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n 1536754432.887 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n 1536754432.887 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.887 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.887 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.887 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.887 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.887 * [misc]taylor: Taking taylor expansion of k in n 1536754432.888 * [misc]backup-simplify: Simplify k into k 1536754432.888 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.888 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.888 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.888 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.888 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.888 * [misc]backup-simplify: Simplify 2 into 2 1536754432.888 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.888 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.888 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.888 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.889 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.889 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.889 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536754432.889 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536754432.889 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.889 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.889 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.889 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.889 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.889 * [misc]taylor: Taking taylor expansion of k in n 1536754432.889 * [misc]backup-simplify: Simplify k into k 1536754432.889 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.889 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.889 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.889 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.889 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.889 * [misc]backup-simplify: Simplify PI into PI 1536754432.890 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.890 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.890 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.890 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536754432.891 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.891 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754432.891 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754432.891 * [misc]taylor: Taking taylor expansion of -1 in n 1536754432.891 * [misc]backup-simplify: Simplify -1 into -1 1536754432.891 * [misc]taylor: Taking taylor expansion of k in n 1536754432.891 * [misc]backup-simplify: Simplify k into k 1536754432.891 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754432.891 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754432.891 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754432.891 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754432.892 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.893 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754432.894 * [misc]backup-simplify: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) into (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) 1536754432.894 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.894 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.894 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of k in k 1536754432.894 * [misc]backup-simplify: Simplify 0 into 0 1536754432.894 * [misc]backup-simplify: Simplify 1 into 1 1536754432.894 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.894 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.894 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.894 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of (/ -1 n) in k 1536754432.894 * [misc]taylor: Taking taylor expansion of -1 in k 1536754432.894 * [misc]backup-simplify: Simplify -1 into -1 1536754432.894 * [misc]taylor: Taking taylor expansion of n in k 1536754432.894 * [misc]backup-simplify: Simplify n into n 1536754432.894 * [misc]backup-simplify: Simplify (/ -1 n) into (/ -1 n) 1536754432.895 * [misc]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) 1536754432.895 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.895 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.895 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 1536754432.895 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.895 * [misc]taylor: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536754432.895 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754432.895 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 1536754432.895 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 1536754432.895 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754432.895 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.895 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.895 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.895 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.895 * [misc]taylor: Taking taylor expansion of k in k 1536754432.896 * [misc]backup-simplify: Simplify 0 into 0 1536754432.896 * [misc]backup-simplify: Simplify 1 into 1 1536754432.896 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.896 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.896 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.896 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754432.896 * [misc]taylor: Taking taylor expansion of 2 in k 1536754432.896 * [misc]backup-simplify: Simplify 2 into 2 1536754432.896 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.896 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.896 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.897 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536754432.897 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.897 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754432.897 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536754432.897 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536754432.897 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754432.897 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.897 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.897 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.897 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.897 * [misc]taylor: Taking taylor expansion of k in k 1536754432.897 * [misc]backup-simplify: Simplify 0 into 0 1536754432.897 * [misc]backup-simplify: Simplify 1 into 1 1536754432.897 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.898 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.898 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.898 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.898 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.898 * [misc]backup-simplify: Simplify PI into PI 1536754432.898 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.898 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.898 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.899 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.899 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.899 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754432.899 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754432.899 * [misc]taylor: Taking taylor expansion of -1 in k 1536754432.899 * [misc]backup-simplify: Simplify -1 into -1 1536754432.899 * [misc]taylor: Taking taylor expansion of k in k 1536754432.899 * [misc]backup-simplify: Simplify 0 into 0 1536754432.899 * [misc]backup-simplify: Simplify 1 into 1 1536754432.900 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754432.900 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.900 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754432.901 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.901 * [misc]backup-simplify: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754432.902 * [misc]backup-simplify: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754432.902 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in k 1536754432.902 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 1536754432.902 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754432.902 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 1536754432.902 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 1536754432.902 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754432.902 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.902 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.902 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.902 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.903 * [misc]taylor: Taking taylor expansion of k in k 1536754432.903 * [misc]backup-simplify: Simplify 0 into 0 1536754432.903 * [misc]backup-simplify: Simplify 1 into 1 1536754432.903 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.903 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.903 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.903 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in k 1536754432.903 * [misc]taylor: Taking taylor expansion of (/ -1 n) in k 1536754432.903 * [misc]taylor: Taking taylor expansion of -1 in k 1536754432.903 * [misc]backup-simplify: Simplify -1 into -1 1536754432.903 * [misc]taylor: Taking taylor expansion of n in k 1536754432.903 * [misc]backup-simplify: Simplify n into n 1536754432.903 * [misc]backup-simplify: Simplify (/ -1 n) into (/ -1 n) 1536754432.903 * [misc]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) 1536754432.903 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.903 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.904 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 1536754432.904 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.904 * [misc]taylor: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536754432.904 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754432.904 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 1536754432.904 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 1536754432.904 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754432.904 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.904 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.904 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.904 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.904 * [misc]taylor: Taking taylor expansion of k in k 1536754432.904 * [misc]backup-simplify: Simplify 0 into 0 1536754432.904 * [misc]backup-simplify: Simplify 1 into 1 1536754432.904 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.904 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.904 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.904 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536754432.904 * [misc]taylor: Taking taylor expansion of 2 in k 1536754432.904 * [misc]backup-simplify: Simplify 2 into 2 1536754432.905 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.905 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.905 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.905 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536754432.906 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.906 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754432.906 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536754432.906 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536754432.906 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754432.906 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754432.906 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.906 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.906 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.906 * [misc]taylor: Taking taylor expansion of k in k 1536754432.906 * [misc]backup-simplify: Simplify 0 into 0 1536754432.906 * [misc]backup-simplify: Simplify 1 into 1 1536754432.906 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.906 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.906 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.906 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.906 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.906 * [misc]backup-simplify: Simplify PI into PI 1536754432.907 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.907 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754432.907 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.908 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.908 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.908 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754432.908 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754432.908 * [misc]taylor: Taking taylor expansion of -1 in k 1536754432.908 * [misc]backup-simplify: Simplify -1 into -1 1536754432.908 * [misc]taylor: Taking taylor expansion of k in k 1536754432.908 * [misc]backup-simplify: Simplify 0 into 0 1536754432.908 * [misc]backup-simplify: Simplify 1 into 1 1536754432.908 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754432.909 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.909 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754432.910 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.910 * [misc]backup-simplify: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754432.911 * [misc]backup-simplify: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754432.911 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536754432.911 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.911 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.911 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536754432.911 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.911 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.911 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.911 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.911 * [misc]backup-simplify: Simplify 2 into 2 1536754432.912 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.912 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.912 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.912 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.912 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.912 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.912 * [misc]taylor: Taking taylor expansion of k in n 1536754432.912 * [misc]backup-simplify: Simplify k into k 1536754432.912 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.912 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.912 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.912 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.912 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.912 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.913 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.913 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.913 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.913 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of k in n 1536754432.913 * [misc]backup-simplify: Simplify k into k 1536754432.913 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.913 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.913 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.913 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536754432.913 * [misc]taylor: Taking taylor expansion of -1 in n 1536754432.913 * [misc]backup-simplify: Simplify -1 into -1 1536754432.913 * [misc]taylor: Taking taylor expansion of n in n 1536754432.913 * [misc]backup-simplify: Simplify 0 into 0 1536754432.913 * [misc]backup-simplify: Simplify 1 into 1 1536754432.914 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754432.914 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536754432.914 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.914 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.914 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754432.915 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536754432.915 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536754432.915 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.915 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536754432.915 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536754432.915 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.915 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.915 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.915 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.915 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.915 * [misc]taylor: Taking taylor expansion of k in n 1536754432.915 * [misc]backup-simplify: Simplify k into k 1536754432.915 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.915 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.915 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.915 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.916 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.916 * [misc]backup-simplify: Simplify PI into PI 1536754432.916 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.916 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.916 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.916 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536754432.917 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.917 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.918 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754432.919 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754432.920 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754432.921 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1536754432.921 * [misc]backup-simplify: Simplify (+ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536754432.922 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754432.923 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754432.924 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754432.924 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1536754432.924 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536754432.924 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.924 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.924 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536754432.924 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.924 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536754432.925 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536754432.925 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.925 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.925 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.925 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.925 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.925 * [misc]taylor: Taking taylor expansion of k in n 1536754432.925 * [misc]backup-simplify: Simplify k into k 1536754432.925 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.925 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.925 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.925 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536754432.925 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536754432.925 * [misc]taylor: Taking taylor expansion of -1 in n 1536754432.925 * [misc]backup-simplify: Simplify -1 into -1 1536754432.925 * [misc]taylor: Taking taylor expansion of n in n 1536754432.925 * [misc]backup-simplify: Simplify 0 into 0 1536754432.925 * [misc]backup-simplify: Simplify 1 into 1 1536754432.925 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754432.925 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536754432.925 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.926 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.926 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754432.926 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536754432.927 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536754432.927 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.927 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.927 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.927 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.927 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.927 * [misc]backup-simplify: Simplify 2 into 2 1536754432.927 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.927 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.927 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.927 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.927 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.927 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.927 * [misc]taylor: Taking taylor expansion of k in n 1536754432.927 * [misc]backup-simplify: Simplify k into k 1536754432.927 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.927 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.927 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.927 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.928 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.928 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.928 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.928 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.928 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536754432.928 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536754432.928 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.928 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.928 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.928 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.928 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.928 * [misc]taylor: Taking taylor expansion of k in n 1536754432.928 * [misc]backup-simplify: Simplify k into k 1536754432.928 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.929 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.929 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.929 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.929 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.929 * [misc]backup-simplify: Simplify PI into PI 1536754432.929 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.929 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.929 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.930 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536754432.930 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.930 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.931 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754432.935 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754432.936 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754432.937 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754432.940 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754432.940 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754432.940 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754432.940 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.941 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 1536754432.942 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754432.943 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754432.946 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 1536754432.946 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754432.946 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754432.946 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.947 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754432.947 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 1536754432.948 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754432.949 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1536754432.949 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754432.949 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754432.949 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754432.952 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536754432.952 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1536754432.954 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754432.955 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536754432.956 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 1536754432.956 * [misc]backup-simplify: Simplify 0 into 0 1536754432.957 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536754432.957 * [misc]backup-simplify: Simplify (+ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 1536754432.958 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754432.959 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754432.961 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) 1536754432.961 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.962 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.962 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.962 * [misc]backup-simplify: Simplify 2 into 2 1536754432.962 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.962 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.962 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.962 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.962 * [misc]taylor: Taking taylor expansion of k in n 1536754432.962 * [misc]backup-simplify: Simplify k into k 1536754432.962 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.962 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.962 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.963 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.963 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.963 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.963 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.963 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.963 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.963 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536754432.963 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536754432.963 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.963 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.963 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.964 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.964 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.964 * [misc]taylor: Taking taylor expansion of k in n 1536754432.964 * [misc]backup-simplify: Simplify k into k 1536754432.964 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.964 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.964 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.964 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536754432.964 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536754432.964 * [misc]taylor: Taking taylor expansion of -1 in n 1536754432.964 * [misc]backup-simplify: Simplify -1 into -1 1536754432.964 * [misc]taylor: Taking taylor expansion of n in n 1536754432.964 * [misc]backup-simplify: Simplify 0 into 0 1536754432.964 * [misc]backup-simplify: Simplify 1 into 1 1536754432.964 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754432.964 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536754432.964 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.964 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.965 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754432.965 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536754432.965 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536754432.966 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.966 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536754432.966 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536754432.966 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.966 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.966 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.966 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.966 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.966 * [misc]taylor: Taking taylor expansion of k in n 1536754432.966 * [misc]backup-simplify: Simplify k into k 1536754432.966 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.966 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.966 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.966 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.966 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.966 * [misc]backup-simplify: Simplify PI into PI 1536754432.966 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.966 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.967 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.967 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536754432.967 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.967 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536754432.968 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536754432.968 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.968 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.968 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of k in n 1536754432.968 * [misc]backup-simplify: Simplify k into k 1536754432.968 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.968 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.968 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.968 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536754432.968 * [misc]taylor: Taking taylor expansion of -1 in n 1536754432.968 * [misc]backup-simplify: Simplify -1 into -1 1536754432.968 * [misc]taylor: Taking taylor expansion of n in n 1536754432.968 * [misc]backup-simplify: Simplify 0 into 0 1536754432.968 * [misc]backup-simplify: Simplify 1 into 1 1536754432.968 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754432.969 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536754432.969 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.969 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.969 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754432.969 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536754432.970 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536754432.970 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.970 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754432.970 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.970 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536754432.970 * [misc]taylor: Taking taylor expansion of 2 in n 1536754432.970 * [misc]backup-simplify: Simplify 2 into 2 1536754432.970 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536754432.970 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.970 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.970 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.970 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.970 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.970 * [misc]taylor: Taking taylor expansion of k in n 1536754432.970 * [misc]backup-simplify: Simplify k into k 1536754432.970 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.970 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.970 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.970 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.970 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.971 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.971 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.971 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754432.971 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536754432.971 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536754432.971 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754432.971 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754432.971 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.971 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.971 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.971 * [misc]taylor: Taking taylor expansion of k in n 1536754432.971 * [misc]backup-simplify: Simplify k into k 1536754432.971 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.971 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.971 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.971 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.971 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.972 * [misc]backup-simplify: Simplify PI into PI 1536754432.972 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.972 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754432.972 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754432.972 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536754432.973 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754432.973 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.974 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754432.975 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754432.975 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754432.976 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754432.977 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754432.978 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754432.980 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754432.981 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754432.982 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536754432.986 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k))))))) 1536754432.986 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1536754432.987 * [misc]backup-simplify: Simplify (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1536754432.987 * [misc]approximate: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (n k) around 0 1536754432.987 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1536754432.987 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1536754432.987 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 1536754432.987 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 1536754432.987 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 1536754432.987 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.987 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.987 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.987 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.987 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.987 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.987 * [misc]taylor: Taking taylor expansion of k in k 1536754432.987 * [misc]backup-simplify: Simplify 0 into 0 1536754432.987 * [misc]backup-simplify: Simplify 1 into 1 1536754432.987 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754432.987 * [misc]taylor: Taking taylor expansion of n in k 1536754432.987 * [misc]backup-simplify: Simplify n into n 1536754432.987 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754432.988 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.988 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.988 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.988 * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 1536754432.988 * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 1536754432.988 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536754432.988 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536754432.988 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536754432.988 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754432.988 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.988 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.988 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754432.988 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754432.988 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.988 * [misc]taylor: Taking taylor expansion of k in k 1536754432.988 * [misc]backup-simplify: Simplify 0 into 0 1536754432.989 * [misc]backup-simplify: Simplify 1 into 1 1536754432.989 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754432.989 * [misc]taylor: Taking taylor expansion of PI in k 1536754432.989 * [misc]backup-simplify: Simplify PI into PI 1536754432.989 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.989 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754432.989 * [misc]backup-simplify: Simplify (- 0) into 0 1536754432.989 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754432.990 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754432.991 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536754432.991 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754432.991 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754432.991 * [misc]taylor: Taking taylor expansion of k in k 1536754432.991 * [misc]backup-simplify: Simplify 0 into 0 1536754432.991 * [misc]backup-simplify: Simplify 1 into 1 1536754432.991 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754432.991 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754432.992 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754432.992 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1536754432.992 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1536754432.992 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 1536754432.992 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 1536754432.992 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 1536754432.992 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754432.992 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.992 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.992 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754432.992 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.992 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.992 * [misc]taylor: Taking taylor expansion of k in n 1536754432.992 * [misc]backup-simplify: Simplify k into k 1536754432.992 * [misc]taylor: Taking taylor expansion of (log n) in n 1536754432.992 * [misc]taylor: Taking taylor expansion of n in n 1536754432.992 * [misc]backup-simplify: Simplify 0 into 0 1536754432.992 * [misc]backup-simplify: Simplify 1 into 1 1536754432.992 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.992 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754432.993 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754432.993 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754432.993 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.993 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 1536754432.993 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 1536754432.993 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1536754432.993 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1536754432.993 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1536754432.993 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754432.993 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.993 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.993 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754432.994 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.994 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.994 * [misc]taylor: Taking taylor expansion of k in n 1536754432.994 * [misc]backup-simplify: Simplify k into k 1536754432.994 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.994 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.994 * [misc]backup-simplify: Simplify PI into PI 1536754432.994 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.995 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754432.995 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754432.995 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754432.995 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1536754432.996 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1536754432.996 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754432.996 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754432.996 * [misc]taylor: Taking taylor expansion of k in n 1536754432.996 * [misc]backup-simplify: Simplify k into k 1536754432.996 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754432.996 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754432.996 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754432.996 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754432.996 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1536754432.996 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1536754432.996 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 1536754432.996 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 1536754432.996 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 1536754432.996 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754432.997 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.997 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.997 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754432.997 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.997 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.997 * [misc]taylor: Taking taylor expansion of k in n 1536754432.997 * [misc]backup-simplify: Simplify k into k 1536754432.997 * [misc]taylor: Taking taylor expansion of (log n) in n 1536754432.997 * [misc]taylor: Taking taylor expansion of n in n 1536754432.997 * [misc]backup-simplify: Simplify 0 into 0 1536754432.997 * [misc]backup-simplify: Simplify 1 into 1 1536754432.997 * [misc]backup-simplify: Simplify (log 1) into 0 1536754432.997 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754432.997 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754432.997 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754432.998 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754432.998 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 1536754432.998 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 1536754432.998 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1536754432.998 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1536754432.998 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1536754432.998 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536754432.998 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.998 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.998 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536754432.998 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754432.998 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754432.998 * [misc]taylor: Taking taylor expansion of k in n 1536754432.998 * [misc]backup-simplify: Simplify k into k 1536754432.998 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754432.998 * [misc]taylor: Taking taylor expansion of PI in n 1536754432.998 * [misc]backup-simplify: Simplify PI into PI 1536754432.999 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754432.999 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536754432.999 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536754432.999 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536754432.999 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1536754433.000 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1536754433.000 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536754433.000 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.000 * [misc]taylor: Taking taylor expansion of k in n 1536754433.000 * [misc]backup-simplify: Simplify k into k 1536754433.000 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.000 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536754433.000 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754433.000 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536754433.001 * [misc]backup-simplify: Simplify (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) into (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 1536754433.001 * [misc]backup-simplify: Simplify (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1536754433.001 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1536754433.001 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1536754433.001 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 1536754433.001 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 1536754433.001 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 1536754433.001 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754433.001 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.001 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.001 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754433.001 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.001 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.001 * [misc]taylor: Taking taylor expansion of k in k 1536754433.001 * [misc]backup-simplify: Simplify 0 into 0 1536754433.001 * [misc]backup-simplify: Simplify 1 into 1 1536754433.001 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754433.001 * [misc]taylor: Taking taylor expansion of n in k 1536754433.002 * [misc]backup-simplify: Simplify n into n 1536754433.002 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754433.002 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754433.002 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.002 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.002 * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 1536754433.002 * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 1536754433.002 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536754433.002 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536754433.002 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536754433.002 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754433.002 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.002 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.003 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754433.003 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.003 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.003 * [misc]taylor: Taking taylor expansion of k in k 1536754433.003 * [misc]backup-simplify: Simplify 0 into 0 1536754433.003 * [misc]backup-simplify: Simplify 1 into 1 1536754433.003 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.003 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.003 * [misc]backup-simplify: Simplify PI into PI 1536754433.003 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.003 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754433.003 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.004 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.004 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754433.005 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536754433.005 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754433.005 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.005 * [misc]taylor: Taking taylor expansion of k in k 1536754433.005 * [misc]backup-simplify: Simplify 0 into 0 1536754433.005 * [misc]backup-simplify: Simplify 1 into 1 1536754433.005 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.005 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.006 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754433.006 * [misc]backup-simplify: Simplify (* (pow n 1/2) (pow PI 1/2)) into (sqrt (* n PI)) 1536754433.006 * [misc]backup-simplify: Simplify (* (sqrt (* n PI)) 0) into 0 1536754433.006 * [misc]backup-simplify: Simplify 0 into 0 1536754433.009 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754433.009 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536754433.009 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.010 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.010 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log PI))) into 0 1536754433.012 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754433.014 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1536754433.015 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536754433.015 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.015 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.015 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754433.015 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 1536754433.016 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754433.016 * [misc]backup-simplify: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))) into 0 1536754433.016 * [misc]backup-simplify: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1536754433.016 * [misc]taylor: Taking taylor expansion of 0 in k 1536754433.016 * [misc]backup-simplify: Simplify 0 into 0 1536754433.018 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754433.018 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754433.018 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.019 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.019 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1536754433.021 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1536754433.022 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536754433.022 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754433.022 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.022 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.022 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 1536754433.023 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 1536754433.024 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt n) (log n))) (pow PI 1/2))) into (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) 1536754433.024 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n PI)) +nan.0) (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) 0)) into (- (* +nan.0 (sqrt (* n PI)))) 1536754433.025 * [misc]backup-simplify: Simplify (- (* +nan.0 (sqrt (* n PI)))) into (- (* +nan.0 (sqrt (* n PI)))) 1536754433.025 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.025 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536754433.028 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754433.028 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536754433.028 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.029 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.029 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 1536754433.030 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754433.033 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1536754433.033 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536754433.034 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.034 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.034 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754433.034 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 1536754433.035 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754433.035 * [misc]backup-simplify: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 k)))))) into 0 1536754433.036 * [misc]backup-simplify: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1536754433.036 * [misc]taylor: Taking taylor expansion of 0 in k 1536754433.036 * [misc]backup-simplify: Simplify 0 into 0 1536754433.036 * [misc]backup-simplify: Simplify 0 into 0 1536754433.036 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754433.037 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754433.040 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754433.040 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754433.040 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.040 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.041 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1536754433.044 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536754433.045 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536754433.046 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754433.046 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.046 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.046 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 1536754433.047 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 1536754433.051 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2))))) 1536754433.054 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) +nan.0) (* (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2))))) 0))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) 1536754433.055 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) 1536754433.055 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.055 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536754433.064 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754433.064 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536754433.064 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.064 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.066 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536754433.072 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536754433.079 * [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 1536754433.079 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536754433.080 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.080 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.080 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536754433.080 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 1536754433.084 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536754433.084 * [misc]backup-simplify: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))))) into 0 1536754433.085 * [misc]backup-simplify: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1536754433.085 * [misc]taylor: Taking taylor expansion of 0 in k 1536754433.085 * [misc]backup-simplify: Simplify 0 into 0 1536754433.085 * [misc]backup-simplify: Simplify 0 into 0 1536754433.085 * [misc]backup-simplify: Simplify 0 into 0 1536754433.086 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754433.087 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754433.095 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754433.095 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754433.096 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.096 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.098 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536754433.107 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1536754433.110 * [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 1536754433.111 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754433.111 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.111 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.112 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 1536754433.114 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) 1536754433.127 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (sqrt (* n PI)) (pow (log PI) 3))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log PI) 2) (log n)))) (+ (* 1/48 (* (sqrt (* n PI)) (pow (log n) 3))) (* 1/16 (* (sqrt (* n PI)) (* (log PI) (pow (log n) 2)))))))) 1536754433.147 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2))))) +nan.0) (* (- (+ (* 1/48 (* (sqrt (* n PI)) (pow (log PI) 3))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log PI) 2) (log n)))) (+ (* 1/48 (* (sqrt (* n PI)) (pow (log n) 3))) (* 1/16 (* (sqrt (* n PI)) (* (log PI) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) 1536754433.160 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) 1536754433.177 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) (* k 1)) (- (* +nan.0 (sqrt (* n PI)))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (pow k 2)))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (pow k 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (pow k 2)))))))))))))))))))))) 1536754433.178 * [misc]backup-simplify: Simplify (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1536754433.178 * [misc]approximate: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (n k) around 0 1536754433.178 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.178 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.178 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.178 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.178 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of k in k 1536754433.178 * [misc]backup-simplify: Simplify 0 into 0 1536754433.178 * [misc]backup-simplify: Simplify 1 into 1 1536754433.178 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.178 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.178 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.178 * [misc]backup-simplify: Simplify PI into PI 1536754433.179 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.179 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.179 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.179 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.180 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536754433.180 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754433.180 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754433.180 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 1536754433.180 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 1536754433.180 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754433.181 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.181 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.181 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.181 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.181 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.181 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.181 * [misc]taylor: Taking taylor expansion of k in k 1536754433.181 * [misc]backup-simplify: Simplify 0 into 0 1536754433.181 * [misc]backup-simplify: Simplify 1 into 1 1536754433.181 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.181 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in k 1536754433.181 * [misc]taylor: Taking taylor expansion of (/ 1 n) in k 1536754433.181 * [misc]taylor: Taking taylor expansion of n in k 1536754433.181 * [misc]backup-simplify: Simplify n into n 1536754433.181 * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) 1536754433.181 * [misc]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) 1536754433.181 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.181 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.182 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.182 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 1536754433.182 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 1536754433.182 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754433.182 * [misc]taylor: Taking taylor expansion of k in k 1536754433.182 * [misc]backup-simplify: Simplify 0 into 0 1536754433.182 * [misc]backup-simplify: Simplify 1 into 1 1536754433.182 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.183 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754433.183 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.183 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.183 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.183 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.183 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of k in n 1536754433.183 * [misc]backup-simplify: Simplify k into k 1536754433.183 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.183 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754433.183 * [misc]taylor: Taking taylor expansion of PI in n 1536754433.183 * [misc]backup-simplify: Simplify PI into PI 1536754433.184 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.184 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754433.184 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754433.184 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754433.184 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536754433.185 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754433.185 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754433.185 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536754433.185 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536754433.185 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754433.185 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.185 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.185 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754433.185 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.185 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.185 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.185 * [misc]taylor: Taking taylor expansion of k in n 1536754433.185 * [misc]backup-simplify: Simplify k into k 1536754433.185 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.185 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536754433.185 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536754433.185 * [misc]taylor: Taking taylor expansion of n in n 1536754433.185 * [misc]backup-simplify: Simplify 0 into 0 1536754433.185 * [misc]backup-simplify: Simplify 1 into 1 1536754433.185 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.186 * [misc]backup-simplify: Simplify (log 1) into 0 1536754433.186 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754433.186 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754433.186 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754433.186 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754433.186 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536754433.186 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536754433.187 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of k in n 1536754433.187 * [misc]backup-simplify: Simplify k into k 1536754433.187 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754433.187 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754433.187 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.187 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.187 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.187 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.187 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of k in n 1536754433.187 * [misc]backup-simplify: Simplify k into k 1536754433.187 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.187 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754433.187 * [misc]taylor: Taking taylor expansion of PI in n 1536754433.187 * [misc]backup-simplify: Simplify PI into PI 1536754433.187 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.188 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754433.188 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754433.188 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754433.188 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536754433.188 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754433.188 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536754433.188 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536754433.188 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536754433.188 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536754433.188 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.188 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.188 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754433.188 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.188 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.188 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.188 * [misc]taylor: Taking taylor expansion of k in n 1536754433.188 * [misc]backup-simplify: Simplify k into k 1536754433.188 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.188 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536754433.188 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536754433.188 * [misc]taylor: Taking taylor expansion of n in n 1536754433.188 * [misc]backup-simplify: Simplify 0 into 0 1536754433.188 * [misc]backup-simplify: Simplify 1 into 1 1536754433.189 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.189 * [misc]backup-simplify: Simplify (log 1) into 0 1536754433.189 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754433.189 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536754433.189 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536754433.189 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754433.189 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536754433.189 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536754433.189 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536754433.189 * [misc]taylor: Taking taylor expansion of k in n 1536754433.189 * [misc]backup-simplify: Simplify k into k 1536754433.189 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536754433.189 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536754433.190 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536754433.190 * [misc]backup-simplify: Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) into (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1536754433.190 * [misc]taylor: Taking taylor expansion of (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of -1 in k 1536754433.190 * [misc]backup-simplify: Simplify -1 into -1 1536754433.190 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.190 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.190 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.190 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.190 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of k in k 1536754433.190 * [misc]backup-simplify: Simplify 0 into 0 1536754433.190 * [misc]backup-simplify: Simplify 1 into 1 1536754433.190 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.190 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754433.190 * [misc]taylor: Taking taylor expansion of n in k 1536754433.190 * [misc]backup-simplify: Simplify n into n 1536754433.190 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754433.190 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.191 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.191 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.191 * [misc]backup-simplify: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 1536754433.191 * [misc]backup-simplify: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 1536754433.191 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536754433.191 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754433.191 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536754433.191 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536754433.191 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754433.191 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.191 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.191 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.191 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.191 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.191 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.191 * [misc]taylor: Taking taylor expansion of k in k 1536754433.191 * [misc]backup-simplify: Simplify 0 into 0 1536754433.191 * [misc]backup-simplify: Simplify 1 into 1 1536754433.191 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.191 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.191 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.191 * [misc]backup-simplify: Simplify PI into PI 1536754433.191 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.192 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.192 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.192 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.192 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536754433.192 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754433.192 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754433.192 * [misc]taylor: Taking taylor expansion of k in k 1536754433.192 * [misc]backup-simplify: Simplify 0 into 0 1536754433.192 * [misc]backup-simplify: Simplify 1 into 1 1536754433.193 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.193 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754433.193 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536754433.193 * [misc]backup-simplify: Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1536754433.193 * [misc]backup-simplify: Simplify 0 into 0 1536754433.193 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754433.195 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1536754433.195 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754433.195 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754433.195 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.195 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.195 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754433.196 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 1536754433.196 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754433.198 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754433.198 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754433.198 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754433.198 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.198 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.199 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 1536754433.200 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754433.200 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 1536754433.200 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (sqrt k))) into 0 1536754433.200 * [misc]taylor: Taking taylor expansion of 0 in k 1536754433.200 * [misc]backup-simplify: Simplify 0 into 0 1536754433.200 * [misc]backup-simplify: Simplify 0 into 0 1536754433.201 * [misc]backup-simplify: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1536754433.201 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754433.201 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754433.202 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536754433.202 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754433.207 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1536754433.207 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.207 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754433.207 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.207 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.208 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754433.208 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 1536754433.209 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754433.212 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754433.212 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.212 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754433.212 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.212 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.213 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 1536754433.214 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754433.215 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))))) into 0 1536754433.215 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1536754433.215 * [misc]taylor: Taking taylor expansion of 0 in k 1536754433.215 * [misc]backup-simplify: Simplify 0 into 0 1536754433.215 * [misc]backup-simplify: Simplify 0 into 0 1536754433.215 * [misc]backup-simplify: Simplify 0 into 0 1536754433.216 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754433.216 * [misc]backup-simplify: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536754433.217 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754433.217 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754433.217 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536754433.218 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754433.222 * [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 1536754433.222 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.222 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754433.223 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.223 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.223 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536754433.223 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 1536754433.225 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536754433.231 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754433.231 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.231 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536754433.231 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.231 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.232 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536754433.234 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536754433.235 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))))) into 0 1536754433.235 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1536754433.235 * [misc]taylor: Taking taylor expansion of 0 in k 1536754433.235 * [misc]backup-simplify: Simplify 0 into 0 1536754433.236 * [misc]backup-simplify: Simplify 0 into 0 1536754433.236 * [misc]backup-simplify: Simplify 0 into 0 1536754433.236 * [misc]backup-simplify: Simplify 0 into 0 1536754433.237 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754433.238 * [misc]backup-simplify: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536754433.238 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754433.239 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536754433.241 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1536754433.242 * [misc]backup-simplify: Simplify (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1536754433.242 * [misc]approximate: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (n k) around 0 1536754433.242 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.242 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.242 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of k in k 1536754433.242 * [misc]backup-simplify: Simplify 0 into 0 1536754433.242 * [misc]backup-simplify: Simplify 1 into 1 1536754433.242 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.242 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.242 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.242 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of (/ -1 n) in k 1536754433.242 * [misc]taylor: Taking taylor expansion of -1 in k 1536754433.242 * [misc]backup-simplify: Simplify -1 into -1 1536754433.242 * [misc]taylor: Taking taylor expansion of n in k 1536754433.242 * [misc]backup-simplify: Simplify n into n 1536754433.243 * [misc]backup-simplify: Simplify (/ -1 n) into (/ -1 n) 1536754433.243 * [misc]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) 1536754433.243 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.243 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.243 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 1536754433.243 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1536754433.243 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754433.243 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536754433.243 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536754433.243 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754433.243 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.243 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.243 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.243 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.243 * [misc]taylor: Taking taylor expansion of k in k 1536754433.243 * [misc]backup-simplify: Simplify 0 into 0 1536754433.244 * [misc]backup-simplify: Simplify 1 into 1 1536754433.244 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.244 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.244 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.244 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.244 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.244 * [misc]backup-simplify: Simplify PI into PI 1536754433.244 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.244 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.245 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.245 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754433.246 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754433.246 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754433.246 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754433.246 * [misc]taylor: Taking taylor expansion of -1 in k 1536754433.246 * [misc]backup-simplify: Simplify -1 into -1 1536754433.246 * [misc]taylor: Taking taylor expansion of k in k 1536754433.246 * [misc]backup-simplify: Simplify 0 into 0 1536754433.246 * [misc]backup-simplify: Simplify 1 into 1 1536754433.246 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754433.246 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.247 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754433.247 * [misc]backup-simplify: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754433.247 * [misc]backup-simplify: Simplify (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754433.247 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1536754433.247 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754433.247 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754433.247 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536754433.248 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536754433.248 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754433.248 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754433.248 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.248 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.248 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.248 * [misc]taylor: Taking taylor expansion of k in n 1536754433.248 * [misc]backup-simplify: Simplify k into k 1536754433.248 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.248 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.248 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.248 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536754433.248 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536754433.248 * [misc]taylor: Taking taylor expansion of -1 in n 1536754433.248 * [misc]backup-simplify: Simplify -1 into -1 1536754433.248 * [misc]taylor: Taking taylor expansion of n in n 1536754433.248 * [misc]backup-simplify: Simplify 0 into 0 1536754433.248 * [misc]backup-simplify: Simplify 1 into 1 1536754433.248 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754433.248 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536754433.248 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754433.249 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754433.249 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754433.249 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536754433.250 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536754433.250 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754433.250 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536754433.250 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536754433.250 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754433.250 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754433.250 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.250 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.250 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.250 * [misc]taylor: Taking taylor expansion of k in n 1536754433.250 * [misc]backup-simplify: Simplify k into k 1536754433.250 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.250 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.250 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.250 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754433.250 * [misc]taylor: Taking taylor expansion of PI in n 1536754433.250 * [misc]backup-simplify: Simplify PI into PI 1536754433.250 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.251 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754433.251 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754433.251 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536754433.251 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754433.252 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754433.252 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754433.252 * [misc]taylor: Taking taylor expansion of -1 in n 1536754433.252 * [misc]backup-simplify: Simplify -1 into -1 1536754433.252 * [misc]taylor: Taking taylor expansion of k in n 1536754433.252 * [misc]backup-simplify: Simplify k into k 1536754433.252 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754433.252 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754433.252 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754433.252 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754433.253 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754433.253 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1536754433.253 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1536754433.253 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536754433.253 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754433.253 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536754433.253 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536754433.253 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754433.253 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754433.253 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.253 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.253 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.254 * [misc]taylor: Taking taylor expansion of k in n 1536754433.254 * [misc]backup-simplify: Simplify k into k 1536754433.254 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.254 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.254 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.254 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536754433.254 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536754433.254 * [misc]taylor: Taking taylor expansion of -1 in n 1536754433.254 * [misc]backup-simplify: Simplify -1 into -1 1536754433.254 * [misc]taylor: Taking taylor expansion of n in n 1536754433.254 * [misc]backup-simplify: Simplify 0 into 0 1536754433.254 * [misc]backup-simplify: Simplify 1 into 1 1536754433.254 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754433.254 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536754433.254 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754433.254 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754433.255 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754433.255 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536754433.255 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536754433.255 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536754433.255 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536754433.256 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536754433.256 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536754433.256 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536754433.256 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.256 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.256 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536754433.256 * [misc]taylor: Taking taylor expansion of k in n 1536754433.256 * [misc]backup-simplify: Simplify k into k 1536754433.256 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536754433.256 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536754433.256 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.256 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536754433.256 * [misc]taylor: Taking taylor expansion of PI in n 1536754433.256 * [misc]backup-simplify: Simplify PI into PI 1536754433.257 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.257 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536754433.257 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536754433.257 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536754433.258 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754433.258 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536754433.258 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536754433.258 * [misc]taylor: Taking taylor expansion of -1 in n 1536754433.258 * [misc]backup-simplify: Simplify -1 into -1 1536754433.258 * [misc]taylor: Taking taylor expansion of k in n 1536754433.258 * [misc]backup-simplify: Simplify k into k 1536754433.258 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536754433.258 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536754433.258 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536754433.258 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536754433.259 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754433.259 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1536754433.259 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.260 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.260 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of k in k 1536754433.260 * [misc]backup-simplify: Simplify 0 into 0 1536754433.260 * [misc]backup-simplify: Simplify 1 into 1 1536754433.260 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.260 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.260 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.260 * [misc]taylor: Taking taylor expansion of (- (log -1) (log n)) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of (log -1) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of -1 in k 1536754433.260 * [misc]backup-simplify: Simplify -1 into -1 1536754433.260 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536754433.260 * [misc]taylor: Taking taylor expansion of (log n) in k 1536754433.260 * [misc]taylor: Taking taylor expansion of n in k 1536754433.260 * [misc]backup-simplify: Simplify n into n 1536754433.260 * [misc]backup-simplify: Simplify (log n) into (log n) 1536754433.261 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.261 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.261 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536754433.261 * [misc]backup-simplify: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 1536754433.261 * [misc]backup-simplify: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 1536754433.262 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536754433.262 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754433.262 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536754433.262 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536754433.262 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754433.262 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.262 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.262 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.262 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.262 * [misc]taylor: Taking taylor expansion of k in k 1536754433.262 * [misc]backup-simplify: Simplify 0 into 0 1536754433.262 * [misc]backup-simplify: Simplify 1 into 1 1536754433.262 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.262 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.262 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.262 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.262 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.262 * [misc]backup-simplify: Simplify PI into PI 1536754433.263 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.263 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.263 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.263 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754433.264 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754433.264 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754433.264 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754433.264 * [misc]taylor: Taking taylor expansion of -1 in k 1536754433.264 * [misc]backup-simplify: Simplify -1 into -1 1536754433.264 * [misc]taylor: Taking taylor expansion of k in k 1536754433.264 * [misc]backup-simplify: Simplify 0 into 0 1536754433.264 * [misc]backup-simplify: Simplify 1 into 1 1536754433.264 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754433.264 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.264 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754433.264 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754433.265 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754433.265 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754433.267 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754433.267 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754433.267 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754433.267 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.268 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 1536754433.268 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754433.269 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754433.270 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 1536754433.270 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536754433.270 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536754433.270 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.271 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754433.271 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 1536754433.272 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536754433.272 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1536754433.272 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536754433.272 * [misc]taylor: Taking taylor expansion of 0 in k 1536754433.273 * [misc]backup-simplify: Simplify 0 into 0 1536754433.273 * [misc]backup-simplify: Simplify 0 into 0 1536754433.273 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1536754433.273 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754433.274 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754433.274 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754433.275 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754433.278 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754433.278 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.278 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754433.278 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.279 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 1536754433.280 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754433.281 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754433.283 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 1536754433.283 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.284 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536754433.284 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.284 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536754433.284 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 1536754433.285 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536754433.286 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536754433.286 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536754433.286 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536754433.287 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536754433.287 * [misc]taylor: Taking taylor expansion of 0 in k 1536754433.287 * [misc]backup-simplify: Simplify 0 into 0 1536754433.287 * [misc]backup-simplify: Simplify 0 into 0 1536754433.287 * [misc]backup-simplify: Simplify 0 into 0 1536754433.287 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536754433.288 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754433.288 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754433.289 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754433.290 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536754433.291 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))))))))) 1536754433.292 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 2) 1536754433.292 * [misc]backup-simplify: Simplify (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) 1536754433.292 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) in (k) around 0 1536754433.292 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) in k 1536754433.292 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754433.292 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.292 * [misc]taylor: Taking taylor expansion of k in k 1536754433.292 * [misc]backup-simplify: Simplify 0 into 0 1536754433.292 * [misc]backup-simplify: Simplify 1 into 1 1536754433.292 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.292 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.293 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754433.293 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536754433.293 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536754433.293 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536754433.293 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754433.293 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.293 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.293 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754433.293 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.293 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.293 * [misc]taylor: Taking taylor expansion of k in k 1536754433.293 * [misc]backup-simplify: Simplify 0 into 0 1536754433.293 * [misc]backup-simplify: Simplify 1 into 1 1536754433.293 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.293 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.293 * [misc]backup-simplify: Simplify PI into PI 1536754433.293 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.293 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754433.293 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.293 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.294 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754433.294 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536754433.294 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) in k 1536754433.294 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536754433.294 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.294 * [misc]taylor: Taking taylor expansion of k in k 1536754433.294 * [misc]backup-simplify: Simplify 0 into 0 1536754433.294 * [misc]backup-simplify: Simplify 1 into 1 1536754433.294 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.294 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.295 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754433.295 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536754433.295 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536754433.295 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536754433.295 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536754433.295 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.295 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.295 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536754433.295 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.295 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.295 * [misc]taylor: Taking taylor expansion of k in k 1536754433.295 * [misc]backup-simplify: Simplify 0 into 0 1536754433.295 * [misc]backup-simplify: Simplify 1 into 1 1536754433.295 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.295 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.295 * [misc]backup-simplify: Simplify PI into PI 1536754433.295 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.295 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536754433.295 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.296 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.296 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754433.296 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536754433.297 * [misc]backup-simplify: Simplify (* 0 (pow PI 1/2)) into 0 1536754433.297 * [misc]backup-simplify: Simplify 0 into 0 1536754433.298 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536754433.299 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536754433.299 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.299 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.299 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1536754433.302 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1536754433.303 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/2 (* (log PI) (sqrt PI)))) (* +nan.0 (pow PI 1/2))) into (- (* +nan.0 (sqrt PI))) 1536754433.304 * [misc]backup-simplify: Simplify (- (* +nan.0 (sqrt PI))) into (- (* +nan.0 (sqrt PI))) 1536754433.307 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536754433.307 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536754433.307 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.307 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.308 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1536754433.314 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536754433.314 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536754433.315 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754433.321 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* +nan.0 (* -1/2 (* (log PI) (sqrt PI)))) (* +nan.0 (pow PI 1/2)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) 1536754433.324 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) 1536754433.332 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536754433.332 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536754433.332 * [misc]backup-simplify: Simplify (- 0) into 0 1536754433.333 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536754433.334 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536754433.343 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1536754433.343 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754433.344 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754433.355 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* +nan.0 (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* +nan.0 (* -1/2 (* (log PI) (sqrt PI)))) (* +nan.0 (pow PI 1/2))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) 1536754433.362 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) 1536754433.371 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) k) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (pow k 2))) (- (+ (* +nan.0 (* (* (log PI) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))))))))))))) 1536754433.371 * [misc]backup-simplify: Simplify (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 1536754433.371 * [misc]approximate: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (k) around 0 1536754433.371 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1536754433.371 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754433.371 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536754433.371 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536754433.371 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754433.371 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.371 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.371 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.371 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.371 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.371 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.371 * [misc]taylor: Taking taylor expansion of k in k 1536754433.371 * [misc]backup-simplify: Simplify 0 into 0 1536754433.371 * [misc]backup-simplify: Simplify 1 into 1 1536754433.371 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.371 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.371 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.371 * [misc]backup-simplify: Simplify PI into PI 1536754433.372 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.372 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.372 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.372 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.372 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536754433.372 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754433.373 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of k in k 1536754433.373 * [misc]backup-simplify: Simplify 0 into 0 1536754433.373 * [misc]backup-simplify: Simplify 1 into 1 1536754433.373 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.373 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754433.373 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.373 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.373 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.373 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.373 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of k in k 1536754433.373 * [misc]backup-simplify: Simplify 0 into 0 1536754433.373 * [misc]backup-simplify: Simplify 1 into 1 1536754433.373 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.373 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.373 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.373 * [misc]backup-simplify: Simplify PI into PI 1536754433.374 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.374 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.374 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536754433.374 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536754433.374 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536754433.374 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536754433.374 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536754433.374 * [misc]taylor: Taking taylor expansion of k in k 1536754433.374 * [misc]backup-simplify: Simplify 0 into 0 1536754433.374 * [misc]backup-simplify: Simplify 1 into 1 1536754433.375 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.375 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536754433.375 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 1536754433.375 * [misc]backup-simplify: Simplify 0 into 0 1536754433.375 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754433.375 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754433.376 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754433.376 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754433.377 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754433.377 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754433.378 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754433.378 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536754433.379 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 3))) (- (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2)))))))) 1536754433.379 * [misc]backup-simplify: Simplify (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1536754433.379 * [misc]approximate: Taking taylor expansion of (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k) around 0 1536754433.379 * [misc]taylor: Taking taylor expansion of (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536754433.379 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754433.379 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536754433.379 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536754433.379 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754433.379 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.379 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.379 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.379 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.379 * [misc]taylor: Taking taylor expansion of k in k 1536754433.379 * [misc]backup-simplify: Simplify 0 into 0 1536754433.379 * [misc]backup-simplify: Simplify 1 into 1 1536754433.379 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.379 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.379 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.379 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.379 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.379 * [misc]backup-simplify: Simplify PI into PI 1536754433.379 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.380 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.380 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.380 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754433.380 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754433.380 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754433.380 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754433.380 * [misc]taylor: Taking taylor expansion of -1 in k 1536754433.380 * [misc]backup-simplify: Simplify -1 into -1 1536754433.380 * [misc]taylor: Taking taylor expansion of k in k 1536754433.380 * [misc]backup-simplify: Simplify 0 into 0 1536754433.380 * [misc]backup-simplify: Simplify 1 into 1 1536754433.381 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754433.381 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.381 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754433.381 * [misc]backup-simplify: Simplify (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754433.381 * [misc]taylor: Taking taylor expansion of (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536754433.381 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536754433.381 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536754433.381 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536754433.381 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536754433.381 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536754433.381 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.381 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.381 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536754433.381 * [misc]taylor: Taking taylor expansion of k in k 1536754433.381 * [misc]backup-simplify: Simplify 0 into 0 1536754433.381 * [misc]backup-simplify: Simplify 1 into 1 1536754433.381 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536754433.381 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536754433.381 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536754433.381 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536754433.381 * [misc]taylor: Taking taylor expansion of PI in k 1536754433.381 * [misc]backup-simplify: Simplify PI into PI 1536754433.382 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536754433.382 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536754433.382 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536754433.382 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536754433.382 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536754433.382 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536754433.382 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536754433.382 * [misc]taylor: Taking taylor expansion of -1 in k 1536754433.382 * [misc]backup-simplify: Simplify -1 into -1 1536754433.383 * [misc]taylor: Taking taylor expansion of k in k 1536754433.383 * [misc]backup-simplify: Simplify 0 into 0 1536754433.383 * [misc]backup-simplify: Simplify 1 into 1 1536754433.383 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536754433.383 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536754433.383 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536754433.383 * [misc]backup-simplify: Simplify (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754433.383 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536754433.383 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536754433.384 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536754433.385 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754433.385 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754433.385 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536754433.386 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536754433.386 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754433.386 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536754433.387 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))) (/ 1 (- k))) (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) into (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k))))))))) 1536754433.387 * * * [misc]progress: simplifying candidates 1536754433.387 * * * * [misc]progress: [ 1 / 152 ] simplifiying candidate # 1536754433.387 * * * * [misc]progress: [ 2 / 152 ] simplifiying candidate # 1536754433.387 * * * * [misc]progress: [ 3 / 152 ] simplifiying candidate # 1536754433.387 * * * * [misc]progress: [ 4 / 152 ] simplifiying candidate # 1536754433.387 * [enter]simplify: Simplifying (pow PI (/ k 2)) 1536754433.388 * * [misc]simplify: iters left: 3 (5 enodes) 1536754433.389 * [exit]simplify: Simplified to (pow PI (/ k 2)) 1536754433.389 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI 1/2) (pow PI (/ k 2))) (sqrt k))))) 1536754433.389 * * * * [misc]progress: [ 5 / 152 ] simplifiying candidate # 1536754433.389 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536754433.389 * * [misc]simplify: iters left: 5 (6 enodes) 1536754433.390 * * [misc]simplify: iters left: 4 (8 enodes) 1536754433.392 * * [misc]simplify: iters left: 3 (11 enodes) 1536754433.396 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536754433.396 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))))) 1536754433.396 * * * * [misc]progress: [ 6 / 152 ] simplifiying candidate # 1536754433.396 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536754433.396 * * [misc]simplify: iters left: 5 (6 enodes) 1536754433.399 * * [misc]simplify: iters left: 4 (8 enodes) 1536754433.401 * * [misc]simplify: iters left: 3 (11 enodes) 1536754433.405 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536754433.405 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))))) 1536754433.405 * * * * [misc]progress: [ 7 / 152 ] simplifiying candidate # 1536754433.405 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536754433.406 * * [misc]simplify: iters left: 4 (5 enodes) 1536754433.408 * * [misc]simplify: iters left: 3 (7 enodes) 1536754433.411 * * [misc]simplify: iters left: 2 (10 enodes) 1536754433.412 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536754433.413 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI 1) (- 1/2 (/ k 2))) (sqrt k))))) 1536754433.413 * * * * [misc]progress: [ 8 / 152 ] simplifiying candidate # 1536754433.413 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1536754433.413 * * [misc]simplify: iters left: 5 (6 enodes) 1536754433.414 * * [misc]simplify: iters left: 4 (8 enodes) 1536754433.416 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1536754433.416 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (pow PI 1/2) (pow PI (/ (- k) 2))) (sqrt k))))) 1536754433.416 * * * * [misc]progress: [ 9 / 152 ] simplifiying candidate # 1536754433.416 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1536754433.416 * * [misc]simplify: iters left: 5 (6 enodes) 1536754433.418 * * [misc]simplify: iters left: 4 (8 enodes) 1536754433.419 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1536754433.419 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (pow PI 1/2) (pow PI (/ (- k) 2))) (sqrt k))))) 1536754433.419 * * * * [misc]progress: [ 10 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 11 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 12 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 13 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 14 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 15 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 16 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 17 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 18 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 19 / 152 ] simplifiying candidate # 1536754433.419 * * * * [misc]progress: [ 20 / 152 ] simplifiying candidate # 1536754433.420 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536754433.421 * * [misc]simplify: iters left: 6 (18 enodes) 1536754433.427 * * [misc]simplify: iters left: 5 (34 enodes) 1536754433.438 * * [misc]simplify: iters left: 4 (86 enodes) 1536754433.486 * * [misc]simplify: iters left: 3 (287 enodes) 1536754433.744 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (+ (log 2) (log PI)) (log n)) (- (log (sqrt k)))) 1536754433.744 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (+ (log 2) (log PI)) (log n)) (- (log (sqrt k)))))) 1536754433.744 * * * * [misc]progress: [ 21 / 152 ] simplifiying candidate # 1536754433.744 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))))) 1536754433.746 * * [misc]simplify: iters left: 6 (18 enodes) 1536754433.754 * * [misc]simplify: iters left: 5 (34 enodes) 1536754433.764 * * [misc]simplify: iters left: 4 (81 enodes) 1536754433.802 * * [misc]simplify: iters left: 3 (250 enodes) 1536754434.090 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (+ (log PI) (log n)) (log 2)) (- (log (sqrt k)))) 1536754434.090 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (+ (log PI) (log n)) (log 2)) (- (log (sqrt k)))))) 1536754434.090 * * * * [misc]progress: [ 22 / 152 ] simplifiying candidate # 1536754434.091 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754434.093 * * [misc]simplify: iters left: 6 (17 enodes) 1536754434.102 * * [misc]simplify: iters left: 5 (30 enodes) 1536754434.118 * * [misc]simplify: iters left: 4 (67 enodes) 1536754434.164 * * [misc]simplify: iters left: 3 (192 enodes) 1536754434.313 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log PI) (+ (log 2) (log n))) (- (log (sqrt k)))) 1536754434.313 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log PI) (+ (log 2) (log n))) (- (log (sqrt k)))))) 1536754434.313 * * * * [misc]progress: [ 23 / 152 ] simplifiying candidate # 1536754434.313 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536754434.315 * * [misc]simplify: iters left: 6 (18 enodes) 1536754434.320 * * [misc]simplify: iters left: 5 (34 enodes) 1536754434.330 * * [misc]simplify: iters left: 4 (80 enodes) 1536754434.369 * * [misc]simplify: iters left: 3 (239 enodes) 1536754434.595 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (+ (log n) (log PI))) (- (log (sqrt k)))) 1536754434.595 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (+ (log n) (log PI))) (- (log (sqrt k)))))) 1536754434.595 * * * * [misc]progress: [ 24 / 152 ] simplifiying candidate # 1536754434.596 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))))) 1536754434.597 * * [misc]simplify: iters left: 6 (18 enodes) 1536754434.602 * * [misc]simplify: iters left: 5 (34 enodes) 1536754434.611 * * [misc]simplify: iters left: 4 (75 enodes) 1536754434.640 * * [misc]simplify: iters left: 3 (202 enodes) 1536754434.843 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (+ (log 2) (log PI)) (log n)) (- (log (sqrt k)))) 1536754434.843 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (+ (log 2) (log PI)) (log n)) (- (log (sqrt k)))))) 1536754434.843 * * * * [misc]progress: [ 25 / 152 ] simplifiying candidate # 1536754434.844 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754434.845 * * [misc]simplify: iters left: 6 (17 enodes) 1536754434.849 * * [misc]simplify: iters left: 5 (30 enodes) 1536754434.857 * * [misc]simplify: iters left: 4 (62 enodes) 1536754434.879 * * [misc]simplify: iters left: 3 (152 enodes) 1536754435.024 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log n) (+ (log 2) (log PI))) (- (log (sqrt k)))) 1536754435.024 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log n) (+ (log 2) (log PI))) (- (log (sqrt k)))))) 1536754435.024 * * * * [misc]progress: [ 26 / 152 ] simplifiying candidate # 1536754435.024 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754435.026 * * [misc]simplify: iters left: 6 (16 enodes) 1536754435.034 * * [misc]simplify: iters left: 5 (27 enodes) 1536754435.047 * * [misc]simplify: iters left: 4 (53 enodes) 1536754435.068 * * [misc]simplify: iters left: 3 (108 enodes) 1536754435.113 * * [misc]simplify: iters left: 2 (276 enodes) 1536754435.536 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (+ (log PI) (log n))) (- (log (sqrt k)))) 1536754435.536 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (+ (log PI) (log n))) (- (log (sqrt k)))))) 1536754435.536 * * * * [misc]progress: [ 27 / 152 ] simplifiying candidate # 1536754435.536 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536754435.538 * * [misc]simplify: iters left: 6 (18 enodes) 1536754435.548 * * [misc]simplify: iters left: 5 (34 enodes) 1536754435.560 * * [misc]simplify: iters left: 4 (80 enodes) 1536754435.606 * * [misc]simplify: iters left: 3 (247 enodes) 1536754435.875 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (+ (log n) (log PI)) (log 2)) (- (log (sqrt k)))) 1536754435.875 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (+ (log n) (log PI)) (log 2)) (- (log (sqrt k)))))) 1536754435.875 * * * * [misc]progress: [ 28 / 152 ] simplifiying candidate # 1536754435.875 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))))) 1536754435.877 * * [misc]simplify: iters left: 6 (18 enodes) 1536754435.887 * * [misc]simplify: iters left: 5 (34 enodes) 1536754435.903 * * [misc]simplify: iters left: 4 (75 enodes) 1536754435.936 * * [misc]simplify: iters left: 3 (210 enodes) 1536754436.243 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log n) (+ (log 2) (log PI))) (- (log (sqrt k)))) 1536754436.243 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log n) (+ (log 2) (log PI))) (- (log (sqrt k)))))) 1536754436.243 * * * * [misc]progress: [ 29 / 152 ] simplifiying candidate # 1536754436.244 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754436.245 * * [misc]simplify: iters left: 6 (17 enodes) 1536754436.253 * * [misc]simplify: iters left: 5 (30 enodes) 1536754436.266 * * [misc]simplify: iters left: 4 (61 enodes) 1536754436.305 * * [misc]simplify: iters left: 3 (160 enodes) 1536754436.492 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (+ (log n) (log PI))) (- (log (sqrt k)))) 1536754436.492 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (+ (log n) (log PI))) (- (log (sqrt k)))))) 1536754436.492 * * * * [misc]progress: [ 30 / 152 ] simplifiying candidate # 1536754436.492 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536754436.494 * * [misc]simplify: iters left: 6 (18 enodes) 1536754436.504 * * [misc]simplify: iters left: 5 (34 enodes) 1536754436.524 * * [misc]simplify: iters left: 4 (74 enodes) 1536754436.569 * * [misc]simplify: iters left: 3 (198 enodes) 1536754436.798 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log n) (+ (log 2) (log PI))) (- (log (sqrt k)))) 1536754436.798 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log n) (+ (log 2) (log PI))) (- (log (sqrt k)))))) 1536754436.798 * * * * [misc]progress: [ 31 / 152 ] simplifiying candidate # 1536754436.798 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))))) 1536754436.800 * * [misc]simplify: iters left: 6 (18 enodes) 1536754436.805 * * [misc]simplify: iters left: 5 (34 enodes) 1536754436.815 * * [misc]simplify: iters left: 4 (69 enodes) 1536754436.839 * * [misc]simplify: iters left: 3 (162 enodes) 1536754437.074 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log n) (+ (log 2) (log PI))) (- (log (sqrt k)))) 1536754437.075 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log n) (+ (log 2) (log PI))) (- (log (sqrt k)))))) 1536754437.075 * * * * [misc]progress: [ 32 / 152 ] simplifiying candidate # 1536754437.075 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754437.077 * * [misc]simplify: iters left: 6 (17 enodes) 1536754437.085 * * [misc]simplify: iters left: 5 (30 enodes) 1536754437.099 * * [misc]simplify: iters left: 4 (56 enodes) 1536754437.130 * * [misc]simplify: iters left: 3 (120 enodes) 1536754437.221 * * [misc]simplify: iters left: 2 (428 enodes) 1536754437.749 * [exit]simplify: Simplified to (fma (+ (log PI) (+ (log 2) (log n))) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1536754437.749 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (+ (log PI) (+ (log 2) (log n))) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1536754437.749 * * * * [misc]progress: [ 33 / 152 ] simplifiying candidate # 1536754437.750 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754437.752 * * [misc]simplify: iters left: 6 (16 enodes) 1536754437.760 * * [misc]simplify: iters left: 5 (27 enodes) 1536754437.773 * * [misc]simplify: iters left: 4 (48 enodes) 1536754437.794 * * [misc]simplify: iters left: 3 (89 enodes) 1536754437.828 * * [misc]simplify: iters left: 2 (248 enodes) 1536754438.110 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (+ (log 2) (+ (log PI) (log n))) (- (log (sqrt k)))) 1536754438.110 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (+ (log 2) (+ (log PI) (log n))) (- (log (sqrt k)))))) 1536754438.110 * * * * [misc]progress: [ 34 / 152 ] simplifiying candidate # 1536754438.110 * * * * [misc]progress: [ 35 / 152 ] simplifiying candidate # 1536754438.110 * * * * [misc]progress: [ 36 / 152 ] simplifiying candidate # 1536754438.111 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))) 1536754438.112 * * [misc]simplify: iters left: 6 (22 enodes) 1536754438.118 * * [misc]simplify: iters left: 5 (45 enodes) 1536754438.145 * * [misc]simplify: iters left: 4 (167 enodes) 1536754438.420 * [exit]simplify: Simplified to (/ (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))) 1536754438.420 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (/ (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))))) 1536754438.420 * * * * [misc]progress: [ 37 / 152 ] simplifiying candidate # 1536754438.420 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754438.423 * * [misc]simplify: iters left: 6 (20 enodes) 1536754438.433 * * [misc]simplify: iters left: 5 (41 enodes) 1536754438.463 * * [misc]simplify: iters left: 4 (140 enodes) 1536754438.596 * [exit]simplify: Simplified to (* (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3)) 1536754438.597 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3)))) 1536754438.597 * * * * [misc]progress: [ 38 / 152 ] simplifiying candidate # 1536754438.597 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754438.599 * * [misc]simplify: iters left: 6 (18 enodes) 1536754438.609 * * [misc]simplify: iters left: 5 (36 enodes) 1536754438.636 * * [misc]simplify: iters left: 4 (116 enodes) 1536754438.713 * * [misc]simplify: iters left: 3 (465 enodes) 1536754439.473 * [exit]simplify: Simplified to (* (* (pow (pow 2 (- 1/2 (/ k 2))) 3) (pow (pow n (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3)) 1536754439.473 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (pow 2 (- 1/2 (/ k 2))) 3) (pow (pow n (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3)))) 1536754439.473 * * * * [misc]progress: [ 39 / 152 ] simplifiying candidate # 1536754439.474 * * * * [misc]progress: [ 40 / 152 ] simplifiying candidate # 1536754439.474 * * * * [misc]progress: [ 41 / 152 ] simplifiying candidate # 1536754439.474 * * * * [misc]progress: [ 42 / 152 ] simplifiying candidate # 1536754439.474 * [enter]simplify: Simplifying (* (pow 2 1/2) (* (pow n 1/2) (pow PI (- 1/2 (/ k 2))))) 1536754439.475 * * [misc]simplify: iters left: 6 (12 enodes) 1536754439.479 * * [misc]simplify: iters left: 5 (20 enodes) 1536754439.485 * * [misc]simplify: iters left: 4 (29 enodes) 1536754439.495 * * [misc]simplify: iters left: 3 (30 enodes) 1536754439.507 * [exit]simplify: Simplified to (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2)))) 1536754439.507 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k))))) 1536754439.507 * [enter]simplify: Simplifying (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k))) 1536754439.508 * * [misc]simplify: iters left: 6 (9 enodes) 1536754439.512 * * [misc]simplify: iters left: 5 (13 enodes) 1536754439.516 * * [misc]simplify: iters left: 4 (19 enodes) 1536754439.523 * * [misc]simplify: iters left: 3 (21 enodes) 1536754439.531 * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k))) 1536754439.531 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k))))) 1536754439.531 * * * * [misc]progress: [ 43 / 152 ] simplifiying candidate # 1536754439.531 * [enter]simplify: Simplifying (* (pow 2 1/2) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))) 1536754439.533 * * [misc]simplify: iters left: 6 (12 enodes) 1536754439.541 * * [misc]simplify: iters left: 5 (19 enodes) 1536754439.547 * * [misc]simplify: iters left: 4 (28 enodes) 1536754439.552 * * [misc]simplify: iters left: 3 (30 enodes) 1536754439.558 * [exit]simplify: Simplified to (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) 1536754439.558 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k)))) 1536754439.558 * [enter]simplify: Simplifying (* (pow 2 (/ k 2)) (sqrt k)) 1536754439.558 * * [misc]simplify: iters left: 5 (6 enodes) 1536754439.559 * * [misc]simplify: iters left: 4 (7 enodes) 1536754439.561 * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (sqrt k)) 1536754439.561 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k)))) 1536754439.561 * * * * [misc]progress: [ 44 / 152 ] simplifiying candidate # 1536754439.561 * [enter]simplify: Simplifying (* (pow 2 1/2) (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536754439.562 * * [misc]simplify: iters left: 6 (14 enodes) 1536754439.565 * * [misc]simplify: iters left: 5 (24 enodes) 1536754439.571 * * [misc]simplify: iters left: 4 (43 enodes) 1536754439.580 * * [misc]simplify: iters left: 3 (60 enodes) 1536754439.591 * * [misc]simplify: iters left: 2 (74 enodes) 1536754439.604 * * [misc]simplify: iters left: 1 (97 enodes) 1536754439.630 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2)))) 1536754439.630 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2)))) (* (pow 2 (/ k 2)) (pow n (/ k 2))))) 1536754439.630 * [enter]simplify: Simplifying (* (pow 2 (/ k 2)) (pow n (/ k 2))) 1536754439.631 * * [misc]simplify: iters left: 5 (7 enodes) 1536754439.633 * * [misc]simplify: iters left: 4 (8 enodes) 1536754439.636 * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (pow n (/ k 2))) 1536754439.636 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2)))) (* (pow 2 (/ k 2)) (pow n (/ k 2))))) 1536754439.636 * * * * [misc]progress: [ 45 / 152 ] simplifiying candidate # 1536754439.636 * * * * [misc]progress: [ 46 / 152 ] simplifiying candidate # 1536754439.637 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754439.637 * * [misc]simplify: iters left: 6 (9 enodes) 1536754439.641 * * [misc]simplify: iters left: 5 (11 enodes) 1536754439.645 * * [misc]simplify: iters left: 4 (14 enodes) 1536754439.650 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754439.650 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536754439.650 * * * * [misc]progress: [ 47 / 152 ] simplifiying candidate # 1536754439.650 * [enter]simplify: Simplifying (pow 2 1/2) 1536754439.650 * * [misc]simplify: iters left: 1 (3 enodes) 1536754439.653 * [exit]simplify: Simplified to (sqrt 2) 1536754439.653 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754439.653 * * * * [misc]progress: [ 48 / 152 ] simplifiying candidate # 1536754439.653 * [enter]simplify: Simplifying (pow 2 1/2) 1536754439.653 * * [misc]simplify: iters left: 1 (3 enodes) 1536754439.655 * [exit]simplify: Simplified to (sqrt 2) 1536754439.656 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754439.656 * * * * [misc]progress: [ 49 / 152 ] simplifiying candidate # 1536754439.656 * [enter]simplify: Simplifying (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1536754439.657 * * [misc]simplify: iters left: 6 (8 enodes) 1536754439.660 * * [misc]simplify: iters left: 5 (10 enodes) 1536754439.663 * * [misc]simplify: iters left: 4 (13 enodes) 1536754439.668 * [exit]simplify: Simplified to (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1536754439.668 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754439.668 * * * * [misc]progress: [ 50 / 152 ] simplifiying candidate # 1536754439.668 * [enter]simplify: Simplifying (sqrt (pow 2 (- 1/2 (/ k 2)))) 1536754439.669 * * [misc]simplify: iters left: 6 (7 enodes) 1536754439.671 * * [misc]simplify: iters left: 5 (9 enodes) 1536754439.675 * * [misc]simplify: iters left: 4 (12 enodes) 1536754439.679 * [exit]simplify: Simplified to (sqrt (pow 2 (- 1/2 (/ k 2)))) 1536754439.679 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754439.679 * * * * [misc]progress: [ 51 / 152 ] simplifiying candidate # 1536754439.679 * * * * [misc]progress: [ 52 / 152 ] simplifiying candidate # 1536754439.679 * [enter]simplify: Simplifying (* (pow n (/ k 2)) (sqrt k)) 1536754439.680 * * [misc]simplify: iters left: 5 (7 enodes) 1536754439.682 * * [misc]simplify: iters left: 4 (8 enodes) 1536754439.685 * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt k)) 1536754439.685 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (pow PI (- 1/2 (/ k 2))))) (* (pow n (/ k 2)) (sqrt k)))) 1536754439.685 * * * * [misc]progress: [ 53 / 152 ] simplifiying candidate # 1536754439.685 * [enter]simplify: Simplifying (sqrt k) 1536754439.686 * * [misc]simplify: iters left: 1 (2 enodes) 1536754439.686 * [exit]simplify: Simplified to (sqrt k) 1536754439.686 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))) (sqrt k))) 1536754439.686 * * * * [misc]progress: [ 54 / 152 ] simplifiying candidate # 1536754439.687 * [enter]simplify: Simplifying (pow n (/ k 2)) 1536754439.687 * * [misc]simplify: iters left: 3 (5 enodes) 1536754439.689 * [exit]simplify: Simplified to (pow n (/ k 2)) 1536754439.689 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (pow n (/ k 2)))) 1536754439.689 * * * * [misc]progress: [ 55 / 152 ] simplifiying candidate # 1536754439.689 * [enter]simplify: Simplifying (* (pow 2 1/2) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536754439.691 * * [misc]simplify: iters left: 6 (14 enodes) 1536754439.699 * * [misc]simplify: iters left: 5 (23 enodes) 1536754439.711 * * [misc]simplify: iters left: 4 (42 enodes) 1536754439.728 * * [misc]simplify: iters left: 3 (59 enodes) 1536754439.751 * * [misc]simplify: iters left: 2 (73 enodes) 1536754439.767 * * [misc]simplify: iters left: 1 (96 enodes) 1536754439.789 * [exit]simplify: Simplified to (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (* (pow n (- 1/2 (/ k 2))) (sqrt 2))) 1536754439.789 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (* (pow n (- 1/2 (/ k 2))) (sqrt 2))) (pow 2 (/ k 2)))) 1536754439.790 * * * * [misc]progress: [ 56 / 152 ] simplifiying candidate # 1536754439.790 * * * * [misc]progress: [ 57 / 152 ] simplifiying candidate # 1536754439.790 * * * * [misc]progress: [ 58 / 152 ] simplifiying candidate # 1536754439.790 * * * * [misc]progress: [ 59 / 152 ] simplifiying candidate # 1536754439.790 * * * * [misc]progress: [ 60 / 152 ] simplifiying candidate # 1536754439.790 * [enter]simplify: Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536754439.791 * * [misc]simplify: iters left: 6 (15 enodes) 1536754439.794 * * [misc]simplify: iters left: 5 (26 enodes) 1536754439.801 * * [misc]simplify: iters left: 4 (54 enodes) 1536754439.833 * * [misc]simplify: iters left: 3 (143 enodes) 1536754439.919 * * [misc]simplify: iters left: 2 (360 enodes) 1536754440.243 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log PI) (log n))) (log (sqrt k))) 1536754440.243 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log PI) (log n))) (log (sqrt k)))))) 1536754440.243 * * * * [misc]progress: [ 61 / 152 ] simplifiying candidate # 1536754440.244 * [enter]simplify: Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))) 1536754440.244 * * [misc]simplify: iters left: 6 (15 enodes) 1536754440.248 * * [misc]simplify: iters left: 5 (26 enodes) 1536754440.257 * * [misc]simplify: iters left: 4 (49 enodes) 1536754440.273 * * [misc]simplify: iters left: 3 (112 enodes) 1536754440.341 * * [misc]simplify: iters left: 2 (326 enodes) 1536754440.987 * [exit]simplify: Simplified to (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754440.987 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1536754440.987 * * * * [misc]progress: [ 62 / 152 ] simplifiying candidate # 1536754440.988 * [enter]simplify: Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536754440.989 * * [misc]simplify: iters left: 6 (14 enodes) 1536754440.996 * * [misc]simplify: iters left: 5 (22 enodes) 1536754441.006 * * [misc]simplify: iters left: 4 (40 enodes) 1536754441.021 * * [misc]simplify: iters left: 3 (84 enodes) 1536754441.046 * * [misc]simplify: iters left: 2 (193 enodes) 1536754441.157 * * [misc]simplify: iters left: 1 (474 enodes) 1536754441.782 * [exit]simplify: Simplified to (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754441.782 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1536754441.782 * * * * [misc]progress: [ 63 / 152 ] simplifiying candidate # 1536754441.783 * [enter]simplify: Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536754441.784 * * [misc]simplify: iters left: 6 (15 enodes) 1536754441.791 * * [misc]simplify: iters left: 5 (26 enodes) 1536754441.803 * * [misc]simplify: iters left: 4 (48 enodes) 1536754441.831 * * [misc]simplify: iters left: 3 (111 enodes) 1536754441.896 * * [misc]simplify: iters left: 2 (305 enodes) 1536754442.176 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k))) 1536754442.176 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k)))))) 1536754442.176 * * * * [misc]progress: [ 64 / 152 ] simplifiying candidate # 1536754442.177 * [enter]simplify: Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))) 1536754442.178 * * [misc]simplify: iters left: 6 (15 enodes) 1536754442.182 * * [misc]simplify: iters left: 5 (26 enodes) 1536754442.190 * * [misc]simplify: iters left: 4 (43 enodes) 1536754442.200 * * [misc]simplify: iters left: 3 (80 enodes) 1536754442.250 * * [misc]simplify: iters left: 2 (256 enodes) 1536754442.450 * [exit]simplify: Simplified to (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754442.451 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log n) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1536754442.451 * * * * [misc]progress: [ 65 / 152 ] simplifiying candidate # 1536754442.451 * [enter]simplify: Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536754442.453 * * [misc]simplify: iters left: 6 (14 enodes) 1536754442.462 * * [misc]simplify: iters left: 5 (22 enodes) 1536754442.469 * * [misc]simplify: iters left: 4 (35 enodes) 1536754442.477 * * [misc]simplify: iters left: 3 (60 enodes) 1536754442.499 * * [misc]simplify: iters left: 2 (162 enodes) 1536754442.584 * * [misc]simplify: iters left: 1 (471 enodes) 1536754443.270 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k))) 1536754443.270 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k)))))) 1536754443.270 * * * * [misc]progress: [ 66 / 152 ] simplifiying candidate # 1536754443.270 * * * * [misc]progress: [ 67 / 152 ] simplifiying candidate # 1536754443.270 * * * * [misc]progress: [ 68 / 152 ] simplifiying candidate # 1536754443.271 * [enter]simplify: Simplifying (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1536754443.273 * * [misc]simplify: iters left: 6 (18 enodes) 1536754443.282 * * [misc]simplify: iters left: 5 (35 enodes) 1536754443.306 * * [misc]simplify: iters left: 4 (111 enodes) 1536754443.424 * * [misc]simplify: iters left: 3 (435 enodes) 1536754444.150 * [exit]simplify: Simplified to (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2))))) 1536754444.150 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))))))) 1536754444.151 * * * * [misc]progress: [ 69 / 152 ] simplifiying candidate # 1536754444.151 * [enter]simplify: Simplifying (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536754444.153 * * [misc]simplify: iters left: 6 (16 enodes) 1536754444.161 * * [misc]simplify: iters left: 5 (31 enodes) 1536754444.182 * * [misc]simplify: iters left: 4 (89 enodes) 1536754444.245 * * [misc]simplify: iters left: 3 (229 enodes) 1536754444.431 * [exit]simplify: Simplified to (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (* (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (/ k (pow PI (- 1/2 (/ k 2)))))) 1536754444.431 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (* (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (/ k (pow PI (- 1/2 (/ k 2))))))))) 1536754444.431 * * * * [misc]progress: [ 70 / 152 ] simplifiying candidate # 1536754444.431 * * * * [misc]progress: [ 71 / 152 ] simplifiying candidate # 1536754444.431 * * * * [misc]progress: [ 72 / 152 ] simplifiying candidate # 1536754444.431 * * * * [misc]progress: [ 73 / 152 ] simplifiying candidate # 1536754444.431 * [enter]simplify: Simplifying (* (pow n 1/2) (pow PI (- 1/2 (/ k 2)))) 1536754444.432 * * [misc]simplify: iters left: 6 (10 enodes) 1536754444.434 * * [misc]simplify: iters left: 5 (14 enodes) 1536754444.436 * * [misc]simplify: iters left: 4 (17 enodes) 1536754444.439 * [exit]simplify: Simplified to (* (sqrt n) (pow PI (- 1/2 (/ k 2)))) 1536754444.439 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (sqrt n) (pow PI (- 1/2 (/ k 2)))) (* (pow n (/ k 2)) (sqrt k))))) 1536754444.439 * [enter]simplify: Simplifying (* (pow n (/ k 2)) (sqrt k)) 1536754444.440 * * [misc]simplify: iters left: 5 (7 enodes) 1536754444.441 * * [misc]simplify: iters left: 4 (8 enodes) 1536754444.442 * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt k)) 1536754444.442 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (sqrt n) (pow PI (- 1/2 (/ k 2)))) (* (pow n (/ k 2)) (sqrt k))))) 1536754444.442 * * * * [misc]progress: [ 74 / 152 ] simplifiying candidate # 1536754444.442 * * * * [misc]progress: [ 75 / 152 ] simplifiying candidate # 1536754444.442 * [enter]simplify: Simplifying (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536754444.443 * * [misc]simplify: iters left: 6 (10 enodes) 1536754444.445 * * [misc]simplify: iters left: 5 (12 enodes) 1536754444.447 * * [misc]simplify: iters left: 4 (15 enodes) 1536754444.449 * [exit]simplify: Simplified to (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536754444.449 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (* (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754444.449 * * * * [misc]progress: [ 76 / 152 ] simplifiying candidate # 1536754444.449 * [enter]simplify: Simplifying (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536754444.450 * * [misc]simplify: iters left: 6 (10 enodes) 1536754444.452 * * [misc]simplify: iters left: 5 (12 enodes) 1536754444.454 * * [misc]simplify: iters left: 4 (15 enodes) 1536754444.456 * [exit]simplify: Simplified to (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536754444.456 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754444.456 * * * * [misc]progress: [ 77 / 152 ] simplifiying candidate # 1536754444.456 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))) 1536754444.457 * * [misc]simplify: iters left: 6 (9 enodes) 1536754444.460 * * [misc]simplify: iters left: 5 (11 enodes) 1536754444.462 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))) 1536754444.462 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))))) 1536754444.462 * * * * [misc]progress: [ 78 / 152 ] simplifiying candidate # 1536754444.462 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536754444.463 * * [misc]simplify: iters left: 6 (9 enodes) 1536754444.464 * * [misc]simplify: iters left: 5 (11 enodes) 1536754444.466 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536754444.466 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (sqrt (sqrt k)))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))))) 1536754444.466 * * * * [misc]progress: [ 79 / 152 ] simplifiying candidate # 1536754444.467 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt k)) 1536754444.467 * * [misc]simplify: iters left: 6 (8 enodes) 1536754444.469 * * [misc]simplify: iters left: 5 (10 enodes) 1536754444.470 * [exit]simplify: Simplified to (/ (pow PI (- (/ k 2))) (sqrt k)) 1536754444.470 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) 1)) (/ (pow PI (- (/ k 2))) (sqrt k))))) 1536754444.471 * * * * [misc]progress: [ 80 / 152 ] simplifiying candidate # 1536754444.471 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))) 1536754444.471 * * [misc]simplify: iters left: 6 (9 enodes) 1536754444.474 * * [misc]simplify: iters left: 5 (11 enodes) 1536754444.479 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))) 1536754444.479 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))))) 1536754444.479 * * * * [misc]progress: [ 81 / 152 ] simplifiying candidate # 1536754444.479 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536754444.480 * * [misc]simplify: iters left: 6 (9 enodes) 1536754444.484 * * [misc]simplify: iters left: 5 (11 enodes) 1536754444.488 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536754444.488 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (sqrt (sqrt k)))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))))) 1536754444.488 * * * * [misc]progress: [ 82 / 152 ] simplifiying candidate # 1536754444.488 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt k)) 1536754444.489 * * [misc]simplify: iters left: 6 (8 enodes) 1536754444.492 * * [misc]simplify: iters left: 5 (10 enodes) 1536754444.496 * [exit]simplify: Simplified to (/ (pow PI (- (/ k 2))) (sqrt k)) 1536754444.496 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) 1)) (/ (pow PI (- (/ k 2))) (sqrt k))))) 1536754444.496 * * * * [misc]progress: [ 83 / 152 ] simplifiying candidate # 1536754444.496 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754444.497 * * [misc]simplify: iters left: 6 (11 enodes) 1536754444.501 * * [misc]simplify: iters left: 5 (13 enodes) 1536754444.506 * * [misc]simplify: iters left: 4 (16 enodes) 1536754444.512 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754444.512 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536754444.512 * * * * [misc]progress: [ 84 / 152 ] simplifiying candidate # 1536754444.513 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754444.514 * * [misc]simplify: iters left: 6 (11 enodes) 1536754444.517 * * [misc]simplify: iters left: 5 (13 enodes) 1536754444.522 * * [misc]simplify: iters left: 4 (16 enodes) 1536754444.528 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754444.528 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536754444.528 * * * * [misc]progress: [ 85 / 152 ] simplifiying candidate # 1536754444.528 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536754444.529 * * [misc]simplify: iters left: 6 (10 enodes) 1536754444.533 * * [misc]simplify: iters left: 5 (12 enodes) 1536754444.537 * * [misc]simplify: iters left: 4 (15 enodes) 1536754444.542 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536754444.542 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))) 1536754444.542 * * * * [misc]progress: [ 86 / 152 ] simplifiying candidate # 1536754444.543 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754444.544 * * [misc]simplify: iters left: 6 (11 enodes) 1536754444.547 * * [misc]simplify: iters left: 5 (13 enodes) 1536754444.551 * * [misc]simplify: iters left: 4 (16 enodes) 1536754444.557 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754444.557 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536754444.557 * * * * [misc]progress: [ 87 / 152 ] simplifiying candidate # 1536754444.558 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754444.559 * * [misc]simplify: iters left: 6 (11 enodes) 1536754444.562 * * [misc]simplify: iters left: 5 (13 enodes) 1536754444.567 * * [misc]simplify: iters left: 4 (16 enodes) 1536754444.573 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754444.573 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536754444.573 * * * * [misc]progress: [ 88 / 152 ] simplifiying candidate # 1536754444.573 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536754444.574 * * [misc]simplify: iters left: 6 (10 enodes) 1536754444.577 * * [misc]simplify: iters left: 5 (12 enodes) 1536754444.582 * * [misc]simplify: iters left: 4 (15 enodes) 1536754444.587 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536754444.588 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))) 1536754444.588 * * * * [misc]progress: [ 89 / 152 ] simplifiying candidate # 1536754444.588 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754444.590 * * [misc]simplify: iters left: 6 (10 enodes) 1536754444.594 * * [misc]simplify: iters left: 5 (12 enodes) 1536754444.598 * * [misc]simplify: iters left: 4 (15 enodes) 1536754444.603 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754444.603 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536754444.603 * * * * [misc]progress: [ 90 / 152 ] simplifiying candidate # 1536754444.604 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754444.604 * * [misc]simplify: iters left: 6 (10 enodes) 1536754444.608 * * [misc]simplify: iters left: 5 (12 enodes) 1536754444.612 * * [misc]simplify: iters left: 4 (15 enodes) 1536754444.617 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754444.617 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536754444.617 * * * * [misc]progress: [ 91 / 152 ] simplifiying candidate # 1536754444.617 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754444.618 * * [misc]simplify: iters left: 6 (9 enodes) 1536754444.621 * * [misc]simplify: iters left: 5 (11 enodes) 1536754444.624 * * [misc]simplify: iters left: 4 (14 enodes) 1536754444.626 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754444.626 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754444.627 * * * * [misc]progress: [ 92 / 152 ] simplifiying candidate # 1536754444.627 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754444.627 * * [misc]simplify: iters left: 6 (9 enodes) 1536754444.629 * * [misc]simplify: iters left: 5 (11 enodes) 1536754444.631 * * [misc]simplify: iters left: 4 (14 enodes) 1536754444.633 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754444.633 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536754444.633 * * * * [misc]progress: [ 93 / 152 ] simplifiying candidate # 1536754444.633 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1536754444.633 * * [misc]simplify: iters left: 3 (4 enodes) 1536754444.634 * * [misc]simplify: iters left: 2 (6 enodes) 1536754444.635 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1536754444.635 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ 1 (sqrt k))))) 1536754444.635 * * * * [misc]progress: [ 94 / 152 ] simplifiying candidate # 1536754444.635 * [enter]simplify: Simplifying (pow n 1/2) 1536754444.635 * * [misc]simplify: iters left: 1 (3 enodes) 1536754444.636 * [exit]simplify: Simplified to (sqrt n) 1536754444.636 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt n) (* (pow n (- (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754444.636 * * * * [misc]progress: [ 95 / 152 ] simplifiying candidate # 1536754444.636 * [enter]simplify: Simplifying (pow n 1/2) 1536754444.636 * * [misc]simplify: iters left: 1 (3 enodes) 1536754444.637 * [exit]simplify: Simplified to (sqrt n) 1536754444.637 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt n) (* (pow n (- (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754444.637 * * * * [misc]progress: [ 96 / 152 ] simplifiying candidate # 1536754444.637 * [enter]simplify: Simplifying (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) 1536754444.638 * * [misc]simplify: iters left: 6 (9 enodes) 1536754444.639 * * [misc]simplify: iters left: 5 (11 enodes) 1536754444.641 * * [misc]simplify: iters left: 4 (14 enodes) 1536754444.643 * [exit]simplify: Simplified to (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) 1536754444.643 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) (* (cbrt (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754444.644 * * * * [misc]progress: [ 97 / 152 ] simplifiying candidate # 1536754444.644 * [enter]simplify: Simplifying (sqrt (pow n (- 1/2 (/ k 2)))) 1536754444.644 * * [misc]simplify: iters left: 6 (8 enodes) 1536754444.646 * * [misc]simplify: iters left: 5 (10 enodes) 1536754444.647 * * [misc]simplify: iters left: 4 (13 enodes) 1536754444.649 * [exit]simplify: Simplified to (sqrt (pow n (- 1/2 (/ k 2)))) 1536754444.649 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow n (- 1/2 (/ k 2)))) (* (sqrt (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754444.649 * * * * [misc]progress: [ 98 / 152 ] simplifiying candidate # 1536754444.649 * * * * [misc]progress: [ 99 / 152 ] simplifiying candidate # 1536754444.650 * [enter]simplify: Simplifying (sqrt k) 1536754444.650 * * [misc]simplify: iters left: 1 (2 enodes) 1536754444.650 * [exit]simplify: Simplified to (sqrt k) 1536754444.650 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))) 1536754444.650 * * * * [misc]progress: [ 100 / 152 ] simplifiying candidate # 1536754444.650 * [enter]simplify: Simplifying (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536754444.651 * * [misc]simplify: iters left: 6 (12 enodes) 1536754444.653 * * [misc]simplify: iters left: 5 (18 enodes) 1536754444.657 * * [misc]simplify: iters left: 4 (25 enodes) 1536754444.660 * * [misc]simplify: iters left: 3 (27 enodes) 1536754444.665 * * [misc]simplify: iters left: 2 (29 enodes) 1536754444.674 * * [misc]simplify: iters left: 1 (30 enodes) 1536754444.684 * [exit]simplify: Simplified to (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt n) (sqrt k))) 1536754444.684 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt n) (sqrt k))) (pow n (/ k 2))))) 1536754444.685 * * * * [misc]progress: [ 101 / 152 ] simplifiying candidate # 1536754444.685 * * * * [misc]progress: [ 102 / 152 ] simplifiying candidate # 1536754444.685 * * * * [misc]progress: [ 103 / 152 ] simplifiying candidate # 1536754444.685 * * * * [misc]progress: [ 104 / 152 ] simplifiying candidate # 1536754444.685 * * * * [misc]progress: [ 105 / 152 ] simplifiying candidate # 1536754444.685 * [enter]simplify: Simplifying (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))) 1536754444.687 * * [misc]simplify: iters left: 6 (11 enodes) 1536754444.693 * * [misc]simplify: iters left: 5 (17 enodes) 1536754444.700 * * [misc]simplify: iters left: 4 (28 enodes) 1536754444.714 * * [misc]simplify: iters left: 3 (52 enodes) 1536754444.735 * * [misc]simplify: iters left: 2 (89 enodes) 1536754444.763 * * [misc]simplify: iters left: 1 (127 enodes) 1536754444.795 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k))) 1536754444.795 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k))))))) 1536754444.795 * * * * [misc]progress: [ 106 / 152 ] simplifiying candidate # 1536754444.796 * [enter]simplify: Simplifying (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))) 1536754444.797 * * [misc]simplify: iters left: 6 (11 enodes) 1536754444.801 * * [misc]simplify: iters left: 5 (17 enodes) 1536754444.807 * * [misc]simplify: iters left: 4 (23 enodes) 1536754444.815 * * [misc]simplify: iters left: 3 (32 enodes) 1536754444.824 * * [misc]simplify: iters left: 2 (68 enodes) 1536754444.839 * * [misc]simplify: iters left: 1 (115 enodes) 1536754444.880 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k))) 1536754444.880 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k))))))) 1536754444.880 * * * * [misc]progress: [ 107 / 152 ] simplifiying candidate # 1536754444.880 * * * * [misc]progress: [ 108 / 152 ] simplifiying candidate # 1536754444.880 * * * * [misc]progress: [ 109 / 152 ] simplifiying candidate # 1536754444.881 * [enter]simplify: Simplifying (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1536754444.882 * * [misc]simplify: iters left: 6 (13 enodes) 1536754444.888 * * [misc]simplify: iters left: 5 (24 enodes) 1536754444.903 * * [misc]simplify: iters left: 4 (55 enodes) 1536754444.930 * * [misc]simplify: iters left: 3 (110 enodes) 1536754444.989 * * [misc]simplify: iters left: 2 (193 enodes) 1536754445.071 * * [misc]simplify: iters left: 1 (324 enodes) 1536754445.277 * [exit]simplify: Simplified to (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (* (sqrt k) k))) 1536754445.277 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (cbrt (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (* (sqrt k) k))))))) 1536754445.277 * * * * [misc]progress: [ 110 / 152 ] simplifiying candidate # 1536754445.277 * * * * [misc]progress: [ 111 / 152 ] simplifiying candidate # 1536754445.277 * * * * [misc]progress: [ 112 / 152 ] simplifiying candidate # 1536754445.277 * * * * [misc]progress: [ 113 / 152 ] simplifiying candidate # 1536754445.277 * * * * [misc]progress: [ 114 / 152 ] simplifiying candidate # 1536754445.277 * [enter]simplify: Simplifying (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754445.278 * * [misc]simplify: iters left: 6 (8 enodes) 1536754445.282 * * [misc]simplify: iters left: 5 (11 enodes) 1536754445.286 * [exit]simplify: Simplified to (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) 1536754445.286 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))))))) 1536754445.286 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))) 1536754445.287 * * [misc]simplify: iters left: 6 (9 enodes) 1536754445.290 * * [misc]simplify: iters left: 5 (11 enodes) 1536754445.293 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))) 1536754445.293 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))))))) 1536754445.293 * * * * [misc]progress: [ 115 / 152 ] simplifiying candidate # 1536754445.293 * [enter]simplify: Simplifying (/ (pow PI 1/2) (sqrt (sqrt k))) 1536754445.293 * * [misc]simplify: iters left: 4 (7 enodes) 1536754445.295 * * [misc]simplify: iters left: 3 (8 enodes) 1536754445.296 * [exit]simplify: Simplified to (/ (sqrt PI) (sqrt (sqrt k))) 1536754445.296 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))))))) 1536754445.296 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536754445.297 * * [misc]simplify: iters left: 6 (9 enodes) 1536754445.298 * * [misc]simplify: iters left: 5 (11 enodes) 1536754445.300 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536754445.300 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))))))) 1536754445.300 * * * * [misc]progress: [ 116 / 152 ] simplifiying candidate # 1536754445.300 * [enter]simplify: Simplifying (/ (pow PI 1/2) 1) 1536754445.301 * * [misc]simplify: iters left: 3 (5 enodes) 1536754445.302 * * [misc]simplify: iters left: 2 (8 enodes) 1536754445.303 * * [misc]simplify: iters left: 1 (10 enodes) 1536754445.304 * [exit]simplify: Simplified to (sqrt PI) 1536754445.304 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k)))))) 1536754445.305 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt k)) 1536754445.305 * * [misc]simplify: iters left: 6 (8 enodes) 1536754445.306 * * [misc]simplify: iters left: 5 (10 enodes) 1536754445.308 * [exit]simplify: Simplified to (/ (pow PI (- (/ k 2))) (sqrt k)) 1536754445.308 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k)))))) 1536754445.308 * * * * [misc]progress: [ 117 / 152 ] simplifiying candidate # 1536754445.308 * [enter]simplify: Simplifying (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754445.309 * * [misc]simplify: iters left: 6 (8 enodes) 1536754445.310 * * [misc]simplify: iters left: 5 (11 enodes) 1536754445.312 * [exit]simplify: Simplified to (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) 1536754445.312 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))))))) 1536754445.312 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))) 1536754445.313 * * [misc]simplify: iters left: 6 (9 enodes) 1536754445.314 * * [misc]simplify: iters left: 5 (11 enodes) 1536754445.316 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))) 1536754445.316 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))))))) 1536754445.316 * * * * [misc]progress: [ 118 / 152 ] simplifiying candidate # 1536754445.317 * [enter]simplify: Simplifying (/ (pow PI 1/2) (sqrt (sqrt k))) 1536754445.317 * * [misc]simplify: iters left: 4 (7 enodes) 1536754445.318 * * [misc]simplify: iters left: 3 (8 enodes) 1536754445.320 * [exit]simplify: Simplified to (/ (sqrt PI) (sqrt (sqrt k))) 1536754445.320 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))))))) 1536754445.320 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536754445.321 * * [misc]simplify: iters left: 6 (9 enodes) 1536754445.324 * * [misc]simplify: iters left: 5 (11 enodes) 1536754445.328 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536754445.328 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))))))) 1536754445.328 * * * * [misc]progress: [ 119 / 152 ] simplifiying candidate # 1536754445.328 * [enter]simplify: Simplifying (/ (pow PI 1/2) 1) 1536754445.329 * * [misc]simplify: iters left: 3 (5 enodes) 1536754445.331 * * [misc]simplify: iters left: 2 (8 enodes) 1536754445.334 * * [misc]simplify: iters left: 1 (10 enodes) 1536754445.336 * [exit]simplify: Simplified to (sqrt PI) 1536754445.336 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k)))))) 1536754445.337 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt k)) 1536754445.338 * * [misc]simplify: iters left: 6 (8 enodes) 1536754445.341 * * [misc]simplify: iters left: 5 (10 enodes) 1536754445.345 * [exit]simplify: Simplified to (/ (pow PI (- (/ k 2))) (sqrt k)) 1536754445.345 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k)))))) 1536754445.345 * * * * [misc]progress: [ 120 / 152 ] simplifiying candidate # 1536754445.345 * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754445.348 * * [misc]simplify: iters left: 6 (13 enodes) 1536754445.354 * * [misc]simplify: iters left: 5 (21 enodes) 1536754445.361 * * [misc]simplify: iters left: 4 (33 enodes) 1536754445.366 * * [misc]simplify: iters left: 3 (36 enodes) 1536754445.372 * * [misc]simplify: iters left: 2 (39 enodes) 1536754445.380 * [exit]simplify: Simplified to (* (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1536754445.380 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))) 1536754445.380 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754445.381 * * [misc]simplify: iters left: 6 (11 enodes) 1536754445.383 * * [misc]simplify: iters left: 5 (13 enodes) 1536754445.385 * * [misc]simplify: iters left: 4 (16 enodes) 1536754445.389 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754445.389 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))) 1536754445.389 * * * * [misc]progress: [ 121 / 152 ] simplifiying candidate # 1536754445.389 * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536754445.390 * * [misc]simplify: iters left: 6 (12 enodes) 1536754445.395 * * [misc]simplify: iters left: 5 (16 enodes) 1536754445.401 * * [misc]simplify: iters left: 4 (21 enodes) 1536754445.408 * * [misc]simplify: iters left: 3 (22 enodes) 1536754445.417 * [exit]simplify: Simplified to (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536754445.417 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))) 1536754445.417 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754445.418 * * [misc]simplify: iters left: 6 (11 enodes) 1536754445.422 * * [misc]simplify: iters left: 5 (13 enodes) 1536754445.426 * * [misc]simplify: iters left: 4 (16 enodes) 1536754445.432 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754445.432 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))) 1536754445.432 * * * * [misc]progress: [ 122 / 152 ] simplifiying candidate # 1536754445.432 * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1) 1536754445.433 * * [misc]simplify: iters left: 6 (11 enodes) 1536754445.438 * * [misc]simplify: iters left: 5 (17 enodes) 1536754445.444 * * [misc]simplify: iters left: 4 (26 enodes) 1536754445.448 * * [misc]simplify: iters left: 3 (28 enodes) 1536754445.453 * * [misc]simplify: iters left: 2 (33 enodes) 1536754445.458 * [exit]simplify: Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1536754445.458 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))) 1536754445.458 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536754445.459 * * [misc]simplify: iters left: 6 (10 enodes) 1536754445.460 * * [misc]simplify: iters left: 5 (12 enodes) 1536754445.463 * * [misc]simplify: iters left: 4 (15 enodes) 1536754445.465 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536754445.465 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))) 1536754445.465 * * * * [misc]progress: [ 123 / 152 ] simplifiying candidate # 1536754445.466 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754445.466 * * [misc]simplify: iters left: 6 (12 enodes) 1536754445.469 * * [misc]simplify: iters left: 5 (16 enodes) 1536754445.471 * * [misc]simplify: iters left: 4 (19 enodes) 1536754445.475 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754445.475 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))) 1536754445.475 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754445.476 * * [misc]simplify: iters left: 6 (11 enodes) 1536754445.478 * * [misc]simplify: iters left: 5 (13 enodes) 1536754445.480 * * [misc]simplify: iters left: 4 (16 enodes) 1536754445.483 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536754445.483 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))) 1536754445.483 * * * * [misc]progress: [ 124 / 152 ] simplifiying candidate # 1536754445.483 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754445.484 * * [misc]simplify: iters left: 6 (11 enodes) 1536754445.485 * * [misc]simplify: iters left: 5 (13 enodes) 1536754445.488 * * [misc]simplify: iters left: 4 (16 enodes) 1536754445.494 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754445.494 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))) 1536754445.495 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754445.496 * * [misc]simplify: iters left: 6 (11 enodes) 1536754445.501 * * [misc]simplify: iters left: 5 (13 enodes) 1536754445.506 * * [misc]simplify: iters left: 4 (16 enodes) 1536754445.512 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536754445.512 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))) 1536754445.512 * * * * [misc]progress: [ 125 / 152 ] simplifiying candidate # 1536754445.513 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) 1) 1536754445.514 * * [misc]simplify: iters left: 6 (10 enodes) 1536754445.517 * * [misc]simplify: iters left: 5 (14 enodes) 1536754445.523 * * [misc]simplify: iters left: 4 (19 enodes) 1536754445.528 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1536754445.528 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))) 1536754445.528 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536754445.529 * * [misc]simplify: iters left: 6 (10 enodes) 1536754445.533 * * [misc]simplify: iters left: 5 (12 enodes) 1536754445.537 * * [misc]simplify: iters left: 4 (15 enodes) 1536754445.542 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536754445.543 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))) 1536754445.543 * * * * [misc]progress: [ 126 / 152 ] simplifiying candidate # 1536754445.543 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536754445.544 * * [misc]simplify: iters left: 6 (6 enodes) 1536754445.546 * * [misc]simplify: iters left: 5 (10 enodes) 1536754445.550 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536754445.550 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))) 1536754445.550 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754445.551 * * [misc]simplify: iters left: 6 (10 enodes) 1536754445.555 * * [misc]simplify: iters left: 5 (12 enodes) 1536754445.559 * * [misc]simplify: iters left: 4 (15 enodes) 1536754445.566 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536754445.566 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))) 1536754445.566 * * * * [misc]progress: [ 127 / 152 ] simplifiying candidate # 1536754445.567 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536754445.567 * * [misc]simplify: iters left: 4 (5 enodes) 1536754445.569 * * [misc]simplify: iters left: 3 (7 enodes) 1536754445.571 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536754445.571 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))) 1536754445.571 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754445.572 * * [misc]simplify: iters left: 6 (10 enodes) 1536754445.576 * * [misc]simplify: iters left: 5 (12 enodes) 1536754445.580 * * [misc]simplify: iters left: 4 (15 enodes) 1536754445.586 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536754445.586 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))) 1536754445.586 * * * * [misc]progress: [ 128 / 152 ] simplifiying candidate # 1536754445.586 * [enter]simplify: Simplifying (/ 1 1) 1536754445.586 * * [misc]simplify: iters left: 2 (2 enodes) 1536754445.587 * * [misc]simplify: iters left: 1 (4 enodes) 1536754445.588 * [exit]simplify: Simplified to 1 1536754445.588 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* 1 (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754445.588 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754445.589 * * [misc]simplify: iters left: 6 (9 enodes) 1536754445.592 * * [misc]simplify: iters left: 5 (11 enodes) 1536754445.594 * * [misc]simplify: iters left: 4 (14 enodes) 1536754445.596 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536754445.596 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* 1 (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536754445.596 * * * * [misc]progress: [ 129 / 152 ] simplifiying candidate # 1536754445.596 * * * * [misc]progress: [ 130 / 152 ] simplifiying candidate # 1536754445.596 * * * * [misc]progress: [ 131 / 152 ] simplifiying candidate # 1536754445.596 * * * * [misc]progress: [ 132 / 152 ] simplifiying candidate # 1536754445.596 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536754445.596 * * [misc]simplify: iters left: 2 (3 enodes) 1536754445.597 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536754445.597 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))) 1536754445.597 * * * * [misc]progress: [ 133 / 152 ] simplifiying candidate # 1536754445.597 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536754445.597 * * [misc]simplify: iters left: 2 (3 enodes) 1536754445.598 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536754445.598 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))))) 1536754445.598 * * * * [misc]progress: [ 134 / 152 ] simplifiying candidate # 1536754445.598 * [enter]simplify: Simplifying (sqrt k) 1536754445.598 * * [misc]simplify: iters left: 1 (2 enodes) 1536754445.599 * [exit]simplify: Simplified to (sqrt k) 1536754445.599 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) 1) (sqrt k))))) 1536754445.599 * * * * [misc]progress: [ 135 / 152 ] simplifiying candidate # 1536754445.599 * [enter]simplify: Simplifying (pow PI 1/2) 1536754445.599 * * [misc]simplify: iters left: 1 (3 enodes) 1536754445.600 * [exit]simplify: Simplified to (sqrt PI) 1536754445.600 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (/ (sqrt k) (pow PI (- (/ k 2)))))))) 1536754445.600 * * * * [misc]progress: [ 136 / 152 ] simplifiying candidate # 1536754445.600 * [enter]simplify: Simplifying (pow PI 1/2) 1536754445.600 * * [misc]simplify: iters left: 1 (3 enodes) 1536754445.600 * [exit]simplify: Simplified to (sqrt PI) 1536754445.600 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (/ (sqrt k) (pow PI (- (/ k 2)))))))) 1536754445.601 * * * * [misc]progress: [ 137 / 152 ] simplifiying candidate # 1536754445.601 * [enter]simplify: Simplifying (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1536754445.601 * * [misc]simplify: iters left: 6 (9 enodes) 1536754445.603 * * [misc]simplify: iters left: 5 (11 enodes) 1536754445.605 * * [misc]simplify: iters left: 4 (14 enodes) 1536754445.607 * [exit]simplify: Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1536754445.607 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow PI (- 1/2 (/ k 2))))))))) 1536754445.607 * * * * [misc]progress: [ 138 / 152 ] simplifiying candidate # 1536754445.608 * [enter]simplify: Simplifying (sqrt (pow PI (- 1/2 (/ k 2)))) 1536754445.608 * * [misc]simplify: iters left: 6 (8 enodes) 1536754445.609 * * [misc]simplify: iters left: 5 (10 enodes) 1536754445.611 * * [misc]simplify: iters left: 4 (13 enodes) 1536754445.613 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1536754445.613 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1/2 (/ k 2))))))))) 1536754445.613 * * * * [misc]progress: [ 139 / 152 ] simplifiying candidate # 1536754445.613 * * * * [misc]progress: [ 140 / 152 ] simplifiying candidate # 1536754445.614 * [enter]simplify: Simplifying (pow PI 1/2) 1536754445.614 * * [misc]simplify: iters left: 1 (3 enodes) 1536754445.614 * [exit]simplify: Simplified to (sqrt PI) 1536754445.614 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (* (sqrt k) (pow PI (/ k 2))))))) 1536754445.614 * * * * [misc]progress: [ 141 / 152 ] simplifiying candidate # 1536754445.615 * [enter]simplify: Simplifying (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1536754445.616 * * [misc]simplify: iters left: 6 (18 enodes) 1536754445.621 * * [misc]simplify: iters left: 5 (39 enodes) 1536754445.646 * * [misc]simplify: iters left: 4 (110 enodes) 1536754445.730 * * [misc]simplify: iters left: 3 (321 enodes) 1536754446.041 * [exit]simplify: Simplified to (fma (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8) (fma (* k (log PI)) (* -1/2 (sqrt PI)) (sqrt PI))) 1536754446.041 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (fma (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8) (fma (* k (log PI)) (* -1/2 (sqrt PI)) (sqrt PI))) (sqrt k))))) 1536754446.041 * * * * [misc]progress: [ 142 / 152 ] simplifiying candidate # 1536754446.041 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1536754446.041 * * [misc]simplify: iters left: 5 (6 enodes) 1536754446.043 * * [misc]simplify: iters left: 4 (9 enodes) 1536754446.045 * * [misc]simplify: iters left: 3 (17 enodes) 1536754446.050 * * [misc]simplify: iters left: 2 (24 enodes) 1536754446.053 * * [misc]simplify: iters left: 1 (28 enodes) 1536754446.061 * [exit]simplify: Simplified to (pow PI (fma k -1/2 1/2)) 1536754446.061 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (fma k -1/2 1/2)) (sqrt k))))) 1536754446.061 * * * * [misc]progress: [ 143 / 152 ] simplifiying candidate # 1536754446.062 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1536754446.062 * * [misc]simplify: iters left: 5 (6 enodes) 1536754446.063 * * [misc]simplify: iters left: 4 (9 enodes) 1536754446.066 * * [misc]simplify: iters left: 3 (17 enodes) 1536754446.069 * * [misc]simplify: iters left: 2 (24 enodes) 1536754446.072 * * [misc]simplify: iters left: 1 (28 enodes) 1536754446.079 * [exit]simplify: Simplified to (pow PI (fma k -1/2 1/2)) 1536754446.079 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (fma k -1/2 1/2)) (sqrt k))))) 1536754446.079 * * * * [misc]progress: [ 144 / 152 ] simplifiying candidate # 1536754446.079 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1536754446.079 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754446.079 * * * * [misc]progress: [ 145 / 152 ] simplifiying candidate # 1536754446.080 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2)))))))) 1536754446.080 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754446.080 * * * * [misc]progress: [ 146 / 152 ] simplifiying candidate # 1536754446.080 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k))))))) 1536754446.080 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536754446.080 * * * * [misc]progress: [ 147 / 152 ] simplifiying candidate # 1536754446.081 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (pow k 2)))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (pow k 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (pow k 2)))))))))))))))))))))) 1536754446.081 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536754446.081 * * * * [misc]progress: [ 148 / 152 ] simplifiying candidate # 1536754446.081 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1536754446.081 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536754446.081 * * * * [misc]progress: [ 149 / 152 ] simplifiying candidate # 1536754446.081 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))))))))) 1536754446.081 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536754446.081 * * * * [misc]progress: [ 150 / 152 ] simplifiying candidate # 1536754446.082 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (pow k 2))) (- (+ (* +nan.0 (* (* (log PI) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))))))))))))) 1536754446.082 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0))) 1536754446.082 * * * * [misc]progress: [ 151 / 152 ] simplifiying candidate # 1536754446.082 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 3))) (- (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2)))))))) 1536754446.082 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0))) 1536754446.082 * * * * [misc]progress: [ 152 / 152 ] simplifiying candidate # 1536754446.082 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k))))))))) 1536754446.082 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0))) 1536754446.083 * * * [misc]progress: adding candidates to table 1536754449.261 * [misc]progress: [Phase 3 of 3] Extracting. 1536754449.262 * * [misc]regime: Finding splitpoints for: (# # # # # # # #) 1536754449.269 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1536754449.269 * * * * [misc]regimes: Trying to branch on n from (# # # # # # # #) 1536754449.367 * * * * [misc]regimes: Trying to branch on k from (# # # # # # # #) 1536754449.504 * * * [misc]regime: Found split indices: #