1539426646.934 * [misc]progress: [Phase 1 of 3] Setting up. 1539426646.934 * * * [misc]progress: [1/2] Preparing points 1539426646.934 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1539426646.935 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision 1539426646.939 * * * * [misc]points: Setting MPFR precision to 64 1539426646.940 * * * * [misc]points: Setting MPFR precision to 320 1539426646.941 * * * * [misc]points: Setting MPFR precision to 576 1539426646.941 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision 1539426646.947 * * * * [misc]points: Setting MPFR precision to 320 1539426646.948 * * * * [misc]points: Setting MPFR precision to 576 1539426646.949 * * * * [misc]points: Setting MPFR precision to 832 1539426646.950 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision 1539426646.955 * * * * [misc]points: Setting MPFR precision to 576 1539426646.957 * * * * [misc]points: Setting MPFR precision to 832 1539426646.960 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision 1539426646.965 * * * * [misc]points: Setting MPFR precision to 576 1539426646.968 * * * * [misc]points: Setting MPFR precision to 832 1539426646.972 * * * * [misc]points: Setting MPFR precision to 1088 1539426646.976 * * * * [misc]points: Setting MPFR precision to 1344 1539426646.980 * * * * [misc]points: Computing exacts for 256 points 1539426646.989 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.016 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.036 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.037 * * * * [misc]points: Sampling 201 additional inputs, on iter 1 have 55 / 256 1539426647.038 * * * * [misc]points: Computing exacts on every 12 of 201 points to ramp up precision 1539426647.058 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.059 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.061 * * * * [misc]points: Computing exacts on every 6 of 201 points to ramp up precision 1539426647.080 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.083 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.085 * * * * [misc]points: Computing exacts on every 3 of 201 points to ramp up precision 1539426647.117 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.122 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.126 * * * * [misc]points: Computing exacts for 201 points 1539426647.146 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.161 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.179 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.179 * * * * [misc]points: Sampling 158 additional inputs, on iter 2 have 98 / 256 1539426647.180 * * * * [misc]points: Computing exacts on every 9 of 158 points to ramp up precision 1539426647.211 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.212 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.213 * * * * [misc]points: Computing exacts on every 4 of 158 points to ramp up precision 1539426647.222 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.223 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.225 * * * * [misc]points: Computing exacts on every 2 of 158 points to ramp up precision 1539426647.237 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.240 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.246 * * * * [misc]points: Computing exacts for 158 points 1539426647.265 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.278 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.285 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.285 * * * * [misc]points: Sampling 130 additional inputs, on iter 3 have 126 / 256 1539426647.286 * * * * [misc]points: Computing exacts on every 8 of 130 points to ramp up precision 1539426647.295 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.296 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.297 * * * * [misc]points: Computing exacts on every 4 of 130 points to ramp up precision 1539426647.319 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.321 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.323 * * * * [misc]points: Computing exacts on every 2 of 130 points to ramp up precision 1539426647.343 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.347 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.349 * * * * [misc]points: Computing exacts for 130 points 1539426647.362 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.367 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.373 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.373 * * * * [misc]points: Sampling 100 additional inputs, on iter 4 have 156 / 256 1539426647.373 * * * * [misc]points: Computing exacts on every 6 of 100 points to ramp up precision 1539426647.382 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.383 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.384 * * * * [misc]points: Computing exacts on every 3 of 100 points to ramp up precision 1539426647.394 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.395 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.397 * * * * [misc]points: Computing exacts for 100 points 1539426647.423 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.432 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.437 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.437 * * * * [misc]points: Sampling 82 additional inputs, on iter 5 have 174 / 256 1539426647.437 * * * * [misc]points: Computing exacts on every 5 of 82 points to ramp up precision 1539426647.447 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.448 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.448 * * * * [misc]points: Computing exacts on every 2 of 82 points to ramp up precision 1539426647.463 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.464 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.466 * * * * [misc]points: Computing exacts for 82 points 1539426647.475 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.481 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.487 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.487 * * * * [misc]points: Sampling 72 additional inputs, on iter 6 have 184 / 256 1539426647.488 * * * * [misc]points: Computing exacts on every 4 of 72 points to ramp up precision 1539426647.508 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.509 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.510 * * * * [misc]points: Computing exacts on every 2 of 72 points to ramp up precision 1539426647.538 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.540 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.542 * * * * [misc]points: Computing exacts for 72 points 1539426647.562 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.567 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.573 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.573 * * * * [misc]points: Sampling 54 additional inputs, on iter 7 have 202 / 256 1539426647.573 * * * * [misc]points: Computing exacts on every 3 of 54 points to ramp up precision 1539426647.598 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.599 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.601 * * * * [misc]points: Computing exacts for 54 points 1539426647.621 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.625 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.629 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.629 * * * * [misc]points: Sampling 48 additional inputs, on iter 8 have 208 / 256 1539426647.629 * * * * [misc]points: Computing exacts on every 3 of 48 points to ramp up precision 1539426647.649 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.650 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.651 * * * * [misc]points: Computing exacts for 48 points 1539426647.676 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.681 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.685 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.685 * * * * [misc]points: Sampling 36 additional inputs, on iter 9 have 220 / 256 1539426647.686 * * * * [misc]points: Computing exacts on every 2 of 36 points to ramp up precision 1539426647.705 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.706 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.708 * * * * [misc]points: Computing exacts for 36 points 1539426647.731 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.733 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.736 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.736 * * * * [misc]points: Sampling 32 additional inputs, on iter 10 have 224 / 256 1539426647.737 * * * * [misc]points: Computing exacts on every 2 of 32 points to ramp up precision 1539426647.756 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.757 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.759 * * * * [misc]points: Computing exacts for 32 points 1539426647.778 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.781 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.784 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.784 * * * * [misc]points: Sampling 20 additional inputs, on iter 11 have 236 / 256 1539426647.784 * * * * [misc]points: Computing exacts for 20 points 1539426647.809 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.810 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.812 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.812 * * * * [misc]points: Sampling 18 additional inputs, on iter 12 have 238 / 256 1539426647.812 * * * * [misc]points: Computing exacts for 18 points 1539426647.832 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.834 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.835 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.835 * * * * [misc]points: Sampling 16 additional inputs, on iter 13 have 240 / 256 1539426647.836 * * * * [misc]points: Computing exacts for 16 points 1539426647.855 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.860 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.860 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.860 * * * * [misc]points: Sampling 12 additional inputs, on iter 14 have 244 / 256 1539426647.860 * * * * [misc]points: Computing exacts for 12 points 1539426647.870 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.871 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.872 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.872 * * * * [misc]points: Sampling 8 additional inputs, on iter 15 have 248 / 256 1539426647.872 * * * * [misc]points: Computing exacts for 8 points 1539426647.881 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.881 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.882 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.882 * * * * [misc]points: Sampling 6 additional inputs, on iter 16 have 250 / 256 1539426647.882 * * * * [misc]points: Computing exacts for 6 points 1539426647.894 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.896 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.897 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.897 * * * * [misc]points: Sampling 4 additional inputs, on iter 17 have 252 / 256 1539426647.897 * * * * [misc]points: Computing exacts for 4 points 1539426647.910 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.910 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.910 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.910 * * * * [misc]points: Sampling 4 additional inputs, on iter 18 have 253 / 256 1539426647.910 * * * * [misc]points: Computing exacts for 4 points 1539426647.919 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.920 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.920 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.920 * * * * [misc]points: Sampling 4 additional inputs, on iter 19 have 254 / 256 1539426647.920 * * * * [misc]points: Computing exacts for 4 points 1539426647.936 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.937 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.937 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.937 * * * * [misc]points: Sampling 4 additional inputs, on iter 20 have 254 / 256 1539426647.937 * * * * [misc]points: Computing exacts for 4 points 1539426647.956 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.957 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.958 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.958 * * * * [misc]points: Sampling 4 additional inputs, on iter 21 have 254 / 256 1539426647.958 * * * * [misc]points: Computing exacts for 4 points 1539426647.977 * * * * [misc]points: Setting MPFR precision to 1088 1539426647.978 * * * * [misc]points: Setting MPFR precision to 1344 1539426647.980 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426647.980 * * * * [misc]points: Sampling 4 additional inputs, on iter 22 have 255 / 256 1539426647.980 * * * * [misc]points: Computing exacts for 4 points 1539426648.000 * * * * [misc]points: Setting MPFR precision to 1088 1539426648.001 * * * * [misc]points: Setting MPFR precision to 1344 1539426648.001 * * * * [misc]points: Filtering points with unrepresentable outputs 1539426648.001 * * * * [exit]points: Sampled 256 points with exact outputs 1539426648.001 * * * [misc]progress: [2/2] Setting up program. 1539426648.007 * [misc]progress: [Phase 2 of 3] Improving. 1539426648.007 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1539426648.008 * * [misc]simplify: iters left: 6 (13 enodes) 1539426648.013 * * [misc]simplify: iters left: 5 (28 enodes) 1539426648.020 * * [misc]simplify: iters left: 4 (44 enodes) 1539426648.033 * * [misc]simplify: iters left: 3 (54 enodes) 1539426648.044 * * [misc]simplify: iters left: 2 (57 enodes) 1539426648.055 * * [misc]simplify: iters left: 1 (65 enodes) 1539426648.071 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1539426648.083 * * [misc]progress: iteration 1 / 4 1539426648.083 * * * [misc]progress: picking best candidate 1539426648.096 * * * * [misc]pick: Picked # 1539426648.096 * * * [misc]progress: localizing error 1539426648.129 * * * [misc]progress: generating rewritten candidates 1539426648.129 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1 1) 1539426648.132 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1) 1539426648.137 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1539426648.151 * * * [misc]progress: generating series expansions 1539426648.151 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1 1) 1539426648.151 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539426648.151 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539426648.151 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426648.151 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.151 * [misc]backup-simplify: Simplify 2 into 2 1539426648.151 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426648.151 * [misc]taylor: Taking taylor expansion of n in n 1539426648.151 * [misc]backup-simplify: Simplify 0 into 0 1539426648.151 * [misc]backup-simplify: Simplify 1 into 1 1539426648.151 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.151 * [misc]backup-simplify: Simplify PI into PI 1539426648.151 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426648.151 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.151 * [misc]backup-simplify: Simplify 2 into 2 1539426648.151 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426648.151 * [misc]taylor: Taking taylor expansion of n in n 1539426648.152 * [misc]backup-simplify: Simplify 0 into 0 1539426648.152 * [misc]backup-simplify: Simplify 1 into 1 1539426648.152 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.152 * [misc]backup-simplify: Simplify PI into PI 1539426648.152 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426648.152 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426648.152 * [misc]backup-simplify: Simplify 0 into 0 1539426648.153 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426648.154 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426648.154 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.155 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426648.156 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426648.156 * [misc]backup-simplify: Simplify 0 into 0 1539426648.157 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.159 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426648.159 * [misc]backup-simplify: Simplify 0 into 0 1539426648.161 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426648.163 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426648.163 * [misc]backup-simplify: Simplify 0 into 0 1539426648.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426648.169 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539426648.169 * [misc]backup-simplify: Simplify 0 into 0 1539426648.172 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426648.175 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539426648.175 * [misc]backup-simplify: Simplify 0 into 0 1539426648.179 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539426648.183 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539426648.183 * [misc]backup-simplify: Simplify 0 into 0 1539426648.184 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539426648.184 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539426648.184 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539426648.184 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426648.184 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.184 * [misc]backup-simplify: Simplify 2 into 2 1539426648.184 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.184 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.184 * [misc]backup-simplify: Simplify PI into PI 1539426648.184 * [misc]taylor: Taking taylor expansion of n in n 1539426648.184 * [misc]backup-simplify: Simplify 0 into 0 1539426648.184 * [misc]backup-simplify: Simplify 1 into 1 1539426648.184 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.184 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426648.184 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.184 * [misc]backup-simplify: Simplify 2 into 2 1539426648.185 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.185 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.185 * [misc]backup-simplify: Simplify PI into PI 1539426648.185 * [misc]taylor: Taking taylor expansion of n in n 1539426648.185 * [misc]backup-simplify: Simplify 0 into 0 1539426648.185 * [misc]backup-simplify: Simplify 1 into 1 1539426648.185 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.185 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.185 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.186 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426648.187 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426648.187 * [misc]backup-simplify: Simplify 0 into 0 1539426648.188 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.189 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426648.189 * [misc]backup-simplify: Simplify 0 into 0 1539426648.191 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.192 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.192 * [misc]backup-simplify: Simplify 0 into 0 1539426648.194 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.196 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426648.196 * [misc]backup-simplify: Simplify 0 into 0 1539426648.198 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.201 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426648.201 * [misc]backup-simplify: Simplify 0 into 0 1539426648.203 * [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 1539426648.206 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426648.206 * [misc]backup-simplify: Simplify 0 into 0 1539426648.207 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539426648.207 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539426648.207 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539426648.207 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426648.207 * [misc]taylor: Taking taylor expansion of -2 in n 1539426648.207 * [misc]backup-simplify: Simplify -2 into -2 1539426648.207 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.207 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.207 * [misc]backup-simplify: Simplify PI into PI 1539426648.207 * [misc]taylor: Taking taylor expansion of n in n 1539426648.207 * [misc]backup-simplify: Simplify 0 into 0 1539426648.207 * [misc]backup-simplify: Simplify 1 into 1 1539426648.207 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.207 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426648.207 * [misc]taylor: Taking taylor expansion of -2 in n 1539426648.207 * [misc]backup-simplify: Simplify -2 into -2 1539426648.207 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.207 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.207 * [misc]backup-simplify: Simplify PI into PI 1539426648.207 * [misc]taylor: Taking taylor expansion of n in n 1539426648.208 * [misc]backup-simplify: Simplify 0 into 0 1539426648.208 * [misc]backup-simplify: Simplify 1 into 1 1539426648.208 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.208 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426648.208 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426648.209 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426648.210 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426648.210 * [misc]backup-simplify: Simplify 0 into 0 1539426648.211 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.212 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426648.213 * [misc]backup-simplify: Simplify 0 into 0 1539426648.214 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.221 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.221 * [misc]backup-simplify: Simplify 0 into 0 1539426648.223 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.225 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426648.225 * [misc]backup-simplify: Simplify 0 into 0 1539426648.228 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.230 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426648.231 * [misc]backup-simplify: Simplify 0 into 0 1539426648.233 * [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 1539426648.236 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426648.236 * [misc]backup-simplify: Simplify 0 into 0 1539426648.237 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539426648.237 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1) 1539426648.237 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1539426648.237 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1539426648.237 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1539426648.237 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539426648.237 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539426648.237 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1539426648.237 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.237 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.237 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426648.237 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.237 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.237 * [misc]taylor: Taking taylor expansion of k in k 1539426648.237 * [misc]backup-simplify: Simplify 0 into 0 1539426648.237 * [misc]backup-simplify: Simplify 1 into 1 1539426648.237 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539426648.237 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539426648.237 * [misc]taylor: Taking taylor expansion of 2 in k 1539426648.237 * [misc]backup-simplify: Simplify 2 into 2 1539426648.237 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426648.238 * [misc]taylor: Taking taylor expansion of n in k 1539426648.238 * [misc]backup-simplify: Simplify n into n 1539426648.238 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.238 * [misc]backup-simplify: Simplify PI into PI 1539426648.238 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426648.238 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539426648.238 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539426648.238 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426648.238 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.238 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539426648.238 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1539426648.239 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1539426648.239 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1539426648.239 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426648.239 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426648.239 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1539426648.239 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.239 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.239 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426648.239 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.239 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.239 * [misc]taylor: Taking taylor expansion of k in n 1539426648.239 * [misc]backup-simplify: Simplify k into k 1539426648.239 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426648.239 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426648.239 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.239 * [misc]backup-simplify: Simplify 2 into 2 1539426648.239 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426648.239 * [misc]taylor: Taking taylor expansion of n in n 1539426648.239 * [misc]backup-simplify: Simplify 0 into 0 1539426648.239 * [misc]backup-simplify: Simplify 1 into 1 1539426648.239 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.239 * [misc]backup-simplify: Simplify PI into PI 1539426648.240 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426648.240 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426648.240 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426648.241 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426648.241 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.242 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426648.242 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426648.242 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1539426648.242 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.243 * [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)))) 1539426648.244 * [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))))) 1539426648.244 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1539426648.244 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426648.244 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426648.244 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1539426648.244 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.244 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.244 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426648.244 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.244 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.244 * [misc]taylor: Taking taylor expansion of k in n 1539426648.244 * [misc]backup-simplify: Simplify k into k 1539426648.244 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426648.244 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426648.244 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.244 * [misc]backup-simplify: Simplify 2 into 2 1539426648.244 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426648.244 * [misc]taylor: Taking taylor expansion of n in n 1539426648.244 * [misc]backup-simplify: Simplify 0 into 0 1539426648.244 * [misc]backup-simplify: Simplify 1 into 1 1539426648.244 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.244 * [misc]backup-simplify: Simplify PI into PI 1539426648.244 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426648.245 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426648.245 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426648.246 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426648.246 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.246 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426648.246 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426648.247 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1539426648.247 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.248 * [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)))) 1539426648.248 * [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))))) 1539426648.249 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1539426648.249 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1539426648.249 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1539426648.249 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.249 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426648.249 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.249 * [misc]taylor: Taking taylor expansion of k in k 1539426648.249 * [misc]backup-simplify: Simplify 0 into 0 1539426648.249 * [misc]backup-simplify: Simplify 1 into 1 1539426648.249 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539426648.249 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426648.249 * [misc]taylor: Taking taylor expansion of n in k 1539426648.249 * [misc]backup-simplify: Simplify n into n 1539426648.249 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426648.249 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426648.249 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426648.249 * [misc]taylor: Taking taylor expansion of 2 in k 1539426648.249 * [misc]backup-simplify: Simplify 2 into 2 1539426648.249 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.249 * [misc]backup-simplify: Simplify PI into PI 1539426648.249 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.250 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.250 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426648.250 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.251 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539426648.251 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.252 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1539426648.252 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539426648.253 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539426648.254 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426648.255 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426648.258 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426648.258 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1539426648.258 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.258 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.259 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.260 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539426648.261 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426648.261 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.261 * [misc]backup-simplify: Simplify 0 into 0 1539426648.261 * [misc]backup-simplify: Simplify 0 into 0 1539426648.262 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539426648.263 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426648.265 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426648.266 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.266 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539426648.266 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426648.266 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539426648.267 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1539426648.268 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1539426648.270 * [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))))))) 1539426648.271 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.273 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426648.278 * [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 1539426648.279 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1539426648.279 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.279 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.280 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.280 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539426648.283 * [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 1539426648.283 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.283 * [misc]backup-simplify: Simplify 0 into 0 1539426648.283 * [misc]backup-simplify: Simplify 0 into 0 1539426648.283 * [misc]backup-simplify: Simplify 0 into 0 1539426648.285 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1539426648.286 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426648.291 * [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 1539426648.291 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.291 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1539426648.291 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.291 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.292 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539426648.295 * [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))))) 1539426648.297 * [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))))) 1539426648.302 * [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))))) 1539426648.303 * [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)))) 1539426648.303 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1539426648.303 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1539426648.303 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539426648.303 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539426648.303 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1539426648.303 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.303 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426648.303 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.303 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.303 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.303 * [misc]taylor: Taking taylor expansion of k in k 1539426648.303 * [misc]backup-simplify: Simplify 0 into 0 1539426648.303 * [misc]backup-simplify: Simplify 1 into 1 1539426648.304 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.304 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539426648.304 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539426648.304 * [misc]taylor: Taking taylor expansion of 2 in k 1539426648.304 * [misc]backup-simplify: Simplify 2 into 2 1539426648.304 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426648.304 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.304 * [misc]backup-simplify: Simplify PI into PI 1539426648.304 * [misc]taylor: Taking taylor expansion of n in k 1539426648.304 * [misc]backup-simplify: Simplify n into n 1539426648.304 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426648.304 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539426648.304 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539426648.304 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426648.304 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426648.305 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539426648.305 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539426648.305 * [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)))) 1539426648.305 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1539426648.305 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426648.305 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426648.305 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1539426648.305 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.305 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426648.305 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.305 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.305 * [misc]taylor: Taking taylor expansion of k in n 1539426648.305 * [misc]backup-simplify: Simplify k into k 1539426648.305 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.305 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426648.305 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426648.306 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.306 * [misc]backup-simplify: Simplify 2 into 2 1539426648.306 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.306 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.306 * [misc]backup-simplify: Simplify PI into PI 1539426648.306 * [misc]taylor: Taking taylor expansion of n in n 1539426648.306 * [misc]backup-simplify: Simplify 0 into 0 1539426648.306 * [misc]backup-simplify: Simplify 1 into 1 1539426648.306 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.306 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.307 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.307 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426648.307 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426648.307 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1539426648.308 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.309 * [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))) 1539426648.309 * [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)))) 1539426648.309 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1539426648.309 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426648.309 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426648.309 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1539426648.309 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.309 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.309 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426648.309 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.309 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.309 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.310 * [misc]taylor: Taking taylor expansion of k in n 1539426648.310 * [misc]backup-simplify: Simplify k into k 1539426648.310 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.310 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426648.310 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426648.310 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.310 * [misc]backup-simplify: Simplify 2 into 2 1539426648.310 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.310 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.310 * [misc]backup-simplify: Simplify PI into PI 1539426648.310 * [misc]taylor: Taking taylor expansion of n in n 1539426648.310 * [misc]backup-simplify: Simplify 0 into 0 1539426648.310 * [misc]backup-simplify: Simplify 1 into 1 1539426648.310 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.310 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.311 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.311 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426648.311 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426648.311 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1539426648.312 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.313 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1539426648.313 * [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)))) 1539426648.313 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1539426648.313 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1539426648.313 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1539426648.313 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.313 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.313 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426648.313 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.313 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.314 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.314 * [misc]taylor: Taking taylor expansion of k in k 1539426648.314 * [misc]backup-simplify: Simplify 0 into 0 1539426648.314 * [misc]backup-simplify: Simplify 1 into 1 1539426648.314 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.314 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426648.314 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426648.314 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426648.314 * [misc]taylor: Taking taylor expansion of 2 in k 1539426648.314 * [misc]backup-simplify: Simplify 2 into 2 1539426648.314 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.314 * [misc]backup-simplify: Simplify PI into PI 1539426648.314 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.315 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.315 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426648.315 * [misc]taylor: Taking taylor expansion of n in k 1539426648.315 * [misc]backup-simplify: Simplify n into n 1539426648.315 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426648.315 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426648.315 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426648.315 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539426648.315 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426648.316 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426648.316 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426648.317 * [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)))) 1539426648.318 * [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)))) 1539426648.319 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426648.320 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426648.322 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426648.322 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426648.323 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426648.323 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.323 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.324 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.324 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539426648.326 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426648.326 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.326 * [misc]backup-simplify: Simplify 0 into 0 1539426648.326 * [misc]backup-simplify: Simplify 0 into 0 1539426648.326 * [misc]backup-simplify: Simplify 0 into 0 1539426648.328 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.329 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426648.334 * [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 1539426648.334 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.335 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539426648.335 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.335 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.336 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.337 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539426648.339 * [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 1539426648.339 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.339 * [misc]backup-simplify: Simplify 0 into 0 1539426648.339 * [misc]backup-simplify: Simplify 0 into 0 1539426648.339 * [misc]backup-simplify: Simplify 0 into 0 1539426648.339 * [misc]backup-simplify: Simplify 0 into 0 1539426648.341 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.342 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.350 * [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 1539426648.350 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.351 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1539426648.351 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.351 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.352 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.353 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539426648.357 * [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 1539426648.357 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.357 * [misc]backup-simplify: Simplify 0 into 0 1539426648.357 * [misc]backup-simplify: Simplify 0 into 0 1539426648.357 * [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))))) 1539426648.358 * [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)) 1539426648.358 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1539426648.358 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1539426648.358 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1539426648.358 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1539426648.358 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1539426648.358 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426648.358 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.358 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.358 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.358 * [misc]taylor: Taking taylor expansion of k in k 1539426648.358 * [misc]backup-simplify: Simplify 0 into 0 1539426648.358 * [misc]backup-simplify: Simplify 1 into 1 1539426648.358 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.358 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.358 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.358 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539426648.358 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426648.358 * [misc]taylor: Taking taylor expansion of -2 in k 1539426648.358 * [misc]backup-simplify: Simplify -2 into -2 1539426648.359 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426648.359 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.359 * [misc]backup-simplify: Simplify PI into PI 1539426648.359 * [misc]taylor: Taking taylor expansion of n in k 1539426648.359 * [misc]backup-simplify: Simplify n into n 1539426648.359 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426648.359 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426648.359 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539426648.359 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426648.359 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539426648.359 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539426648.360 * [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))) 1539426648.360 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.360 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.360 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of k in n 1539426648.360 * [misc]backup-simplify: Simplify k into k 1539426648.360 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.360 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.360 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.360 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of -2 in n 1539426648.360 * [misc]backup-simplify: Simplify -2 into -2 1539426648.360 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.360 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.360 * [misc]backup-simplify: Simplify PI into PI 1539426648.360 * [misc]taylor: Taking taylor expansion of n in n 1539426648.360 * [misc]backup-simplify: Simplify 0 into 0 1539426648.360 * [misc]backup-simplify: Simplify 1 into 1 1539426648.361 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.361 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426648.361 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426648.361 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426648.362 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1539426648.362 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.363 * [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))) 1539426648.363 * [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)))) 1539426648.364 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.364 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.364 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of k in n 1539426648.364 * [misc]backup-simplify: Simplify k into k 1539426648.364 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.364 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.364 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.364 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of -2 in n 1539426648.364 * [misc]backup-simplify: Simplify -2 into -2 1539426648.364 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.364 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.364 * [misc]backup-simplify: Simplify PI into PI 1539426648.364 * [misc]taylor: Taking taylor expansion of n in n 1539426648.364 * [misc]backup-simplify: Simplify 0 into 0 1539426648.364 * [misc]backup-simplify: Simplify 1 into 1 1539426648.364 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.365 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426648.365 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426648.365 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426648.365 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1539426648.366 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.367 * [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))) 1539426648.367 * [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)))) 1539426648.367 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1539426648.367 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1539426648.368 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1539426648.368 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426648.368 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.368 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.368 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.368 * [misc]taylor: Taking taylor expansion of k in k 1539426648.368 * [misc]backup-simplify: Simplify 0 into 0 1539426648.368 * [misc]backup-simplify: Simplify 1 into 1 1539426648.368 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.368 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.368 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.368 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539426648.368 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539426648.368 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539426648.368 * [misc]taylor: Taking taylor expansion of -2 in k 1539426648.368 * [misc]backup-simplify: Simplify -2 into -2 1539426648.368 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.368 * [misc]backup-simplify: Simplify PI into PI 1539426648.368 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426648.369 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426648.369 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426648.369 * [misc]taylor: Taking taylor expansion of n in k 1539426648.369 * [misc]backup-simplify: Simplify n into n 1539426648.369 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426648.369 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426648.369 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539426648.369 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426648.370 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539426648.370 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539426648.371 * [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)))) 1539426648.372 * [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)))) 1539426648.373 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426648.373 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426648.376 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426648.376 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426648.377 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426648.377 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.377 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.378 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426648.380 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426648.380 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.380 * [misc]backup-simplify: Simplify 0 into 0 1539426648.380 * [misc]backup-simplify: Simplify 0 into 0 1539426648.380 * [misc]backup-simplify: Simplify 0 into 0 1539426648.381 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.382 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426648.389 * [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 1539426648.389 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.390 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539426648.390 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.390 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.391 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1539426648.393 * [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 1539426648.394 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.394 * [misc]backup-simplify: Simplify 0 into 0 1539426648.394 * [misc]backup-simplify: Simplify 0 into 0 1539426648.394 * [misc]backup-simplify: Simplify 0 into 0 1539426648.394 * [misc]backup-simplify: Simplify 0 into 0 1539426648.396 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.397 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.405 * [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 1539426648.406 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.406 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1539426648.406 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.407 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.408 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1539426648.412 * [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 1539426648.412 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.412 * [misc]backup-simplify: Simplify 0 into 0 1539426648.412 * [misc]backup-simplify: Simplify 0 into 0 1539426648.413 * [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))))) 1539426648.413 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1539426648.413 * [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)))) 1539426648.413 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1539426648.413 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1539426648.413 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1539426648.413 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.413 * [misc]taylor: Taking taylor expansion of k in k 1539426648.413 * [misc]backup-simplify: Simplify 0 into 0 1539426648.413 * [misc]backup-simplify: Simplify 1 into 1 1539426648.413 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.413 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426648.414 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1539426648.414 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1539426648.414 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539426648.414 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539426648.414 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1539426648.414 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.414 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.414 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426648.414 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.414 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.414 * [misc]taylor: Taking taylor expansion of k in k 1539426648.414 * [misc]backup-simplify: Simplify 0 into 0 1539426648.414 * [misc]backup-simplify: Simplify 1 into 1 1539426648.414 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539426648.414 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539426648.415 * [misc]taylor: Taking taylor expansion of 2 in k 1539426648.415 * [misc]backup-simplify: Simplify 2 into 2 1539426648.415 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426648.415 * [misc]taylor: Taking taylor expansion of n in k 1539426648.415 * [misc]backup-simplify: Simplify n into n 1539426648.415 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.415 * [misc]backup-simplify: Simplify PI into PI 1539426648.415 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426648.415 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539426648.415 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539426648.415 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426648.415 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.415 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539426648.416 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1539426648.416 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1539426648.416 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of k in n 1539426648.416 * [misc]backup-simplify: Simplify k into k 1539426648.416 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.416 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1539426648.416 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426648.416 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1539426648.416 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.416 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.416 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.416 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.416 * [misc]taylor: Taking taylor expansion of k in n 1539426648.416 * [misc]backup-simplify: Simplify k into k 1539426648.416 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426648.416 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426648.417 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.417 * [misc]backup-simplify: Simplify 2 into 2 1539426648.417 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426648.417 * [misc]taylor: Taking taylor expansion of n in n 1539426648.417 * [misc]backup-simplify: Simplify 0 into 0 1539426648.417 * [misc]backup-simplify: Simplify 1 into 1 1539426648.417 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.417 * [misc]backup-simplify: Simplify PI into PI 1539426648.417 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426648.417 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426648.418 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426648.418 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426648.419 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.419 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426648.419 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426648.419 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1539426648.420 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.420 * [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)))) 1539426648.421 * [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))))) 1539426648.421 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1539426648.421 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1539426648.421 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.421 * [misc]taylor: Taking taylor expansion of k in n 1539426648.421 * [misc]backup-simplify: Simplify k into k 1539426648.421 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.421 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1539426648.421 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426648.421 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1539426648.421 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1539426648.422 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426648.422 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426648.422 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1539426648.422 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.422 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.422 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426648.422 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.422 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.422 * [misc]taylor: Taking taylor expansion of k in n 1539426648.422 * [misc]backup-simplify: Simplify k into k 1539426648.422 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426648.422 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426648.422 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.422 * [misc]backup-simplify: Simplify 2 into 2 1539426648.422 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426648.422 * [misc]taylor: Taking taylor expansion of n in n 1539426648.422 * [misc]backup-simplify: Simplify 0 into 0 1539426648.422 * [misc]backup-simplify: Simplify 1 into 1 1539426648.422 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.422 * [misc]backup-simplify: Simplify PI into PI 1539426648.422 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426648.422 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426648.423 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426648.424 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426648.424 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.424 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426648.424 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426648.424 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1539426648.425 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.426 * [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)))) 1539426648.426 * [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))))) 1539426648.427 * [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))) 1539426648.427 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1539426648.427 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1539426648.427 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1539426648.427 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1539426648.427 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.427 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.427 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426648.427 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.427 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.427 * [misc]taylor: Taking taylor expansion of k in k 1539426648.427 * [misc]backup-simplify: Simplify 0 into 0 1539426648.427 * [misc]backup-simplify: Simplify 1 into 1 1539426648.427 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539426648.427 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426648.428 * [misc]taylor: Taking taylor expansion of n in k 1539426648.428 * [misc]backup-simplify: Simplify n into n 1539426648.428 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426648.428 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426648.428 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426648.428 * [misc]taylor: Taking taylor expansion of 2 in k 1539426648.428 * [misc]backup-simplify: Simplify 2 into 2 1539426648.428 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.428 * [misc]backup-simplify: Simplify PI into PI 1539426648.428 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.428 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.429 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426648.429 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.429 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539426648.429 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.430 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1539426648.431 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539426648.431 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1539426648.431 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.431 * [misc]taylor: Taking taylor expansion of k in k 1539426648.431 * [misc]backup-simplify: Simplify 0 into 0 1539426648.431 * [misc]backup-simplify: Simplify 1 into 1 1539426648.431 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.431 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426648.432 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1539426648.432 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1539426648.432 * [misc]backup-simplify: Simplify 0 into 0 1539426648.433 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426648.434 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426648.437 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426648.438 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1539426648.438 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.438 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.439 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.439 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539426648.441 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426648.442 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1539426648.442 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.442 * [misc]backup-simplify: Simplify 0 into 0 1539426648.443 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539426648.443 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426648.446 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426648.446 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.446 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539426648.446 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426648.447 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539426648.447 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1539426648.449 * [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))))))) 1539426648.451 * [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))))))) 1539426648.452 * [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))))))) 1539426648.453 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.455 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426648.460 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1539426648.460 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1539426648.460 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.460 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.461 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.462 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539426648.464 * [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 1539426648.464 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.465 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1539426648.466 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1539426648.466 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.466 * [misc]backup-simplify: Simplify 0 into 0 1539426648.466 * [misc]backup-simplify: Simplify 0 into 0 1539426648.466 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1539426648.467 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539426648.468 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1539426648.469 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426648.472 * [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 1539426648.472 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.472 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1539426648.472 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.472 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.473 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539426648.474 * [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))))) 1539426648.477 * [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)))))))) 1539426648.478 * [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)))))))) 1539426648.480 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426648.481 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426648.485 * [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 1539426648.486 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1539426648.486 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.486 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.486 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426648.487 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1539426648.489 * [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 1539426648.489 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.490 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1539426648.490 * [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 1539426648.490 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.490 * [misc]backup-simplify: Simplify 0 into 0 1539426648.490 * [misc]backup-simplify: Simplify 0 into 0 1539426648.490 * [misc]backup-simplify: Simplify 0 into 0 1539426648.491 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.491 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1539426648.493 * [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 1539426648.494 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.498 * [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 1539426648.498 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.499 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539426648.499 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.499 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.500 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1539426648.503 * [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))))))) 1539426648.512 * [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)))))))))))))) 1539426648.519 * [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)))))))))))))) 1539426648.530 * [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)))))))))))))))))))))) 1539426648.531 * [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))))) 1539426648.531 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1539426648.531 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1539426648.531 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1539426648.531 * [misc]taylor: Taking taylor expansion of k in k 1539426648.531 * [misc]backup-simplify: Simplify 0 into 0 1539426648.531 * [misc]backup-simplify: Simplify 1 into 1 1539426648.531 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426648.532 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1539426648.532 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.532 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.532 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.532 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.532 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of k in k 1539426648.532 * [misc]backup-simplify: Simplify 0 into 0 1539426648.532 * [misc]backup-simplify: Simplify 1 into 1 1539426648.532 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.532 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of 2 in k 1539426648.532 * [misc]backup-simplify: Simplify 2 into 2 1539426648.532 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426648.532 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.532 * [misc]backup-simplify: Simplify PI into PI 1539426648.533 * [misc]taylor: Taking taylor expansion of n in k 1539426648.533 * [misc]backup-simplify: Simplify n into n 1539426648.533 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426648.533 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539426648.533 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539426648.533 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426648.533 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426648.533 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539426648.533 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539426648.534 * [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)))) 1539426648.534 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of k in n 1539426648.534 * [misc]backup-simplify: Simplify k into k 1539426648.534 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1539426648.534 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1539426648.534 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.534 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.534 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.534 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.534 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of k in n 1539426648.534 * [misc]backup-simplify: Simplify k into k 1539426648.534 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.534 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.534 * [misc]backup-simplify: Simplify 2 into 2 1539426648.534 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.534 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.535 * [misc]backup-simplify: Simplify PI into PI 1539426648.535 * [misc]taylor: Taking taylor expansion of n in n 1539426648.535 * [misc]backup-simplify: Simplify 0 into 0 1539426648.535 * [misc]backup-simplify: Simplify 1 into 1 1539426648.535 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.535 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.536 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.536 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426648.536 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426648.536 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1539426648.537 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.538 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1539426648.538 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1539426648.538 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1539426648.538 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1539426648.538 * [misc]taylor: Taking taylor expansion of k in n 1539426648.538 * [misc]backup-simplify: Simplify k into k 1539426648.539 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1539426648.539 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1539426648.539 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.539 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.539 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.539 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.539 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of k in n 1539426648.539 * [misc]backup-simplify: Simplify k into k 1539426648.539 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.539 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of 2 in n 1539426648.539 * [misc]backup-simplify: Simplify 2 into 2 1539426648.539 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.539 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.539 * [misc]backup-simplify: Simplify PI into PI 1539426648.539 * [misc]taylor: Taking taylor expansion of n in n 1539426648.539 * [misc]backup-simplify: Simplify 0 into 0 1539426648.539 * [misc]backup-simplify: Simplify 1 into 1 1539426648.539 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.540 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.540 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.540 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426648.540 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426648.540 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1539426648.541 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.542 * [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))) 1539426648.542 * [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)))) 1539426648.543 * [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)) 1539426648.543 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1539426648.543 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1539426648.543 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1539426648.543 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1539426648.543 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.543 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.543 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426648.543 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.543 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.543 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.544 * [misc]taylor: Taking taylor expansion of k in k 1539426648.544 * [misc]backup-simplify: Simplify 0 into 0 1539426648.544 * [misc]backup-simplify: Simplify 1 into 1 1539426648.544 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.544 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426648.544 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426648.544 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426648.544 * [misc]taylor: Taking taylor expansion of 2 in k 1539426648.544 * [misc]backup-simplify: Simplify 2 into 2 1539426648.544 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.544 * [misc]backup-simplify: Simplify PI into PI 1539426648.544 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426648.545 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426648.545 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426648.545 * [misc]taylor: Taking taylor expansion of n in k 1539426648.545 * [misc]backup-simplify: Simplify n into n 1539426648.545 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426648.545 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426648.545 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426648.545 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539426648.545 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426648.546 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426648.546 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426648.547 * [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)))) 1539426648.547 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1539426648.547 * [misc]taylor: Taking taylor expansion of k in k 1539426648.547 * [misc]backup-simplify: Simplify 0 into 0 1539426648.547 * [misc]backup-simplify: Simplify 1 into 1 1539426648.547 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426648.548 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1539426648.548 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1539426648.548 * [misc]backup-simplify: Simplify 0 into 0 1539426648.550 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426648.550 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426648.553 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426648.553 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426648.553 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426648.553 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.554 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.554 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.555 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539426648.556 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426648.557 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1539426648.557 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.557 * [misc]backup-simplify: Simplify 0 into 0 1539426648.557 * [misc]backup-simplify: Simplify 0 into 0 1539426648.558 * [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)))))) 1539426648.559 * [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)))))) 1539426648.560 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.561 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426648.566 * [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 1539426648.566 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.567 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539426648.567 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.567 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.568 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.569 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539426648.571 * [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 1539426648.572 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1539426648.572 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1539426648.573 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.573 * [misc]backup-simplify: Simplify 0 into 0 1539426648.573 * [misc]backup-simplify: Simplify 0 into 0 1539426648.573 * [misc]backup-simplify: Simplify 0 into 0 1539426648.574 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539426648.574 * [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)))))) 1539426648.575 * [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)))))) 1539426648.577 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.578 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426648.586 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1539426648.586 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.587 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1539426648.587 * [misc]backup-simplify: Simplify (- 0) into 0 1539426648.587 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.588 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426648.588 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539426648.590 * [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 1539426648.591 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1539426648.591 * [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 1539426648.591 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.591 * [misc]backup-simplify: Simplify 0 into 0 1539426648.591 * [misc]backup-simplify: Simplify 0 into 0 1539426648.591 * [misc]backup-simplify: Simplify 0 into 0 1539426648.591 * [misc]backup-simplify: Simplify 0 into 0 1539426648.592 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1539426648.593 * [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)))))) 1539426648.593 * [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)))))) 1539426648.595 * [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)))))))) 1539426648.595 * [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))) 1539426648.595 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1539426648.595 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.595 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.595 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of k in k 1539426648.595 * [misc]backup-simplify: Simplify 0 into 0 1539426648.595 * [misc]backup-simplify: Simplify 1 into 1 1539426648.595 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.595 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.595 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.595 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of -2 in k 1539426648.595 * [misc]backup-simplify: Simplify -2 into -2 1539426648.595 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426648.595 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.595 * [misc]backup-simplify: Simplify PI into PI 1539426648.595 * [misc]taylor: Taking taylor expansion of n in k 1539426648.595 * [misc]backup-simplify: Simplify n into n 1539426648.596 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426648.596 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426648.596 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539426648.596 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426648.596 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539426648.596 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539426648.596 * [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))) 1539426648.596 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426648.596 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426648.596 * [misc]taylor: Taking taylor expansion of -1 in k 1539426648.596 * [misc]backup-simplify: Simplify -1 into -1 1539426648.596 * [misc]taylor: Taking taylor expansion of k in k 1539426648.596 * [misc]backup-simplify: Simplify 0 into 0 1539426648.596 * [misc]backup-simplify: Simplify 1 into 1 1539426648.596 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426648.596 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426648.597 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426648.597 * [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)))) 1539426648.597 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.597 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.597 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of k in n 1539426648.597 * [misc]backup-simplify: Simplify k into k 1539426648.597 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.597 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.597 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.597 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of -2 in n 1539426648.597 * [misc]backup-simplify: Simplify -2 into -2 1539426648.597 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.597 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.597 * [misc]backup-simplify: Simplify PI into PI 1539426648.597 * [misc]taylor: Taking taylor expansion of n in n 1539426648.597 * [misc]backup-simplify: Simplify 0 into 0 1539426648.597 * [misc]backup-simplify: Simplify 1 into 1 1539426648.597 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.598 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426648.598 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426648.598 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426648.598 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1539426648.598 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.599 * [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))) 1539426648.599 * [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)))) 1539426648.599 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539426648.599 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539426648.599 * [misc]taylor: Taking taylor expansion of -1 in n 1539426648.599 * [misc]backup-simplify: Simplify -1 into -1 1539426648.599 * [misc]taylor: Taking taylor expansion of k in n 1539426648.599 * [misc]backup-simplify: Simplify k into k 1539426648.599 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539426648.599 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539426648.599 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539426648.599 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539426648.600 * [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))) 1539426648.600 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.600 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.600 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of k in n 1539426648.600 * [misc]backup-simplify: Simplify k into k 1539426648.600 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426648.600 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426648.600 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.600 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of -2 in n 1539426648.600 * [misc]backup-simplify: Simplify -2 into -2 1539426648.600 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426648.600 * [misc]taylor: Taking taylor expansion of PI in n 1539426648.600 * [misc]backup-simplify: Simplify PI into PI 1539426648.600 * [misc]taylor: Taking taylor expansion of n in n 1539426648.600 * [misc]backup-simplify: Simplify 0 into 0 1539426648.600 * [misc]backup-simplify: Simplify 1 into 1 1539426648.600 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426648.601 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426648.601 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426648.601 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426648.601 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1539426648.601 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.602 * [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))) 1539426648.602 * [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)))) 1539426648.602 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539426648.602 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539426648.602 * [misc]taylor: Taking taylor expansion of -1 in n 1539426648.602 * [misc]backup-simplify: Simplify -1 into -1 1539426648.602 * [misc]taylor: Taking taylor expansion of k in n 1539426648.602 * [misc]backup-simplify: Simplify k into k 1539426648.602 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539426648.602 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539426648.602 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539426648.603 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539426648.603 * [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))) 1539426648.603 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.603 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.603 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of k in k 1539426648.603 * [misc]backup-simplify: Simplify 0 into 0 1539426648.603 * [misc]backup-simplify: Simplify 1 into 1 1539426648.603 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426648.603 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426648.603 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426648.603 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539426648.603 * [misc]taylor: Taking taylor expansion of -2 in k 1539426648.603 * [misc]backup-simplify: Simplify -2 into -2 1539426648.603 * [misc]taylor: Taking taylor expansion of PI in k 1539426648.603 * [misc]backup-simplify: Simplify PI into PI 1539426648.604 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426648.604 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426648.604 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426648.604 * [misc]taylor: Taking taylor expansion of n in k 1539426648.604 * [misc]backup-simplify: Simplify n into n 1539426648.604 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426648.604 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426648.604 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539426648.604 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426648.605 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539426648.605 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539426648.605 * [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)))) 1539426648.605 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426648.605 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426648.605 * [misc]taylor: Taking taylor expansion of -1 in k 1539426648.605 * [misc]backup-simplify: Simplify -1 into -1 1539426648.605 * [misc]taylor: Taking taylor expansion of k in k 1539426648.605 * [misc]backup-simplify: Simplify 0 into 0 1539426648.605 * [misc]backup-simplify: Simplify 1 into 1 1539426648.605 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426648.606 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426648.606 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426648.606 * [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))))) 1539426648.607 * [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))))) 1539426648.607 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426648.608 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426648.609 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426648.609 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426648.610 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426648.610 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.610 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.611 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426648.611 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426648.612 * [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 1539426648.612 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.612 * [misc]backup-simplify: Simplify 0 into 0 1539426648.612 * [misc]backup-simplify: Simplify 0 into 0 1539426648.612 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539426648.613 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539426648.614 * [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)))))) 1539426648.614 * [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)))))) 1539426648.615 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.615 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426648.618 * [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 1539426648.618 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.619 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539426648.619 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426648.619 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426648.620 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1539426648.621 * [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 1539426648.621 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426648.622 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1539426648.622 * [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 1539426648.622 * [misc]taylor: Taking taylor expansion of 0 in k 1539426648.622 * [misc]backup-simplify: Simplify 0 into 0 1539426648.622 * [misc]backup-simplify: Simplify 0 into 0 1539426648.622 * [misc]backup-simplify: Simplify 0 into 0 1539426648.622 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426648.623 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1539426648.624 * [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)))))) 1539426648.625 * [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)))))) 1539426648.626 * [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))))))))))) 1539426648.626 * * * [misc]progress: simplifying candidates 1539426648.626 * * * * [misc]progress: [ 1 / 83 ] simplifiying candidate # 1539426648.626 * * * * [misc]progress: [ 2 / 83 ] simplifiying candidate # 1539426648.626 * * * * [misc]progress: [ 3 / 83 ] simplifiying candidate # 1539426648.626 * * * * [misc]progress: [ 4 / 83 ] simplifiying candidate # 1539426648.626 * * * * [misc]progress: [ 5 / 83 ] simplifiying candidate # 1539426648.626 * * * * [misc]progress: [ 6 / 83 ] simplifiying candidate # 1539426648.626 * * * * [misc]progress: [ 7 / 83 ] simplifiying candidate # 1539426648.626 * * * * [misc]progress: [ 8 / 83 ] simplifiying candidate # 1539426648.626 * * * * [misc]progress: [ 9 / 83 ] simplifiying candidate # 1539426648.627 * * * * [misc]progress: [ 10 / 83 ] simplifiying candidate # 1539426648.627 * * * * [misc]progress: [ 11 / 83 ] simplifiying candidate # 1539426648.627 * * * * [misc]progress: [ 12 / 83 ] simplifiying candidate # 1539426648.627 * * * * [misc]progress: [ 13 / 83 ] simplifiying candidate # 1539426648.627 * * * * [misc]progress: [ 14 / 83 ] simplifiying candidate # 1539426648.627 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1539426648.627 * * [misc]simplify: iters left: 6 (11 enodes) 1539426648.629 * * [misc]simplify: iters left: 5 (21 enodes) 1539426648.632 * * [misc]simplify: iters left: 4 (47 enodes) 1539426648.641 * * [misc]simplify: iters left: 3 (113 enodes) 1539426648.678 * * [misc]simplify: iters left: 2 (328 enodes) 1539426648.913 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1539426648.913 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1539426648.913 * * * * [misc]progress: [ 15 / 83 ] simplifiying candidate # 1539426648.913 * * * * [misc]progress: [ 16 / 83 ] simplifiying candidate # 1539426648.914 * [enter]simplify: Simplifying (* PI (* n 2)) 1539426648.914 * * [misc]simplify: iters left: 4 (5 enodes) 1539426648.914 * * [misc]simplify: iters left: 3 (9 enodes) 1539426648.916 * * [misc]simplify: iters left: 2 (15 enodes) 1539426648.918 * * [misc]simplify: iters left: 1 (17 enodes) 1539426648.920 * [exit]simplify: Simplified to (* (* 2 n) PI) 1539426648.920 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1539426648.920 * * * * [misc]progress: [ 17 / 83 ] simplifiying candidate # 1539426648.920 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539426648.920 * * [misc]simplify: iters left: 5 (8 enodes) 1539426648.923 * * [misc]simplify: iters left: 4 (12 enodes) 1539426648.926 * * [misc]simplify: iters left: 3 (18 enodes) 1539426648.930 * * [misc]simplify: iters left: 2 (20 enodes) 1539426648.935 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539426648.935 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1539426648.935 * * * * [misc]progress: [ 18 / 83 ] simplifiying candidate # 1539426648.935 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1539426648.935 * * [misc]simplify: iters left: 5 (6 enodes) 1539426648.937 * * [misc]simplify: iters left: 4 (8 enodes) 1539426648.939 * * [misc]simplify: iters left: 3 (11 enodes) 1539426648.942 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1539426648.942 * [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))) 1539426648.942 * * * * [misc]progress: [ 19 / 83 ] simplifiying candidate # 1539426648.942 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1539426648.942 * * [misc]simplify: iters left: 5 (6 enodes) 1539426648.944 * * [misc]simplify: iters left: 4 (8 enodes) 1539426648.946 * * [misc]simplify: iters left: 3 (11 enodes) 1539426648.949 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1539426648.949 * [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))) 1539426648.949 * * * * [misc]progress: [ 20 / 83 ] simplifiying candidate # 1539426648.949 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1539426648.949 * * [misc]simplify: iters left: 4 (5 enodes) 1539426648.951 * * [misc]simplify: iters left: 3 (7 enodes) 1539426648.953 * * [misc]simplify: iters left: 2 (10 enodes) 1539426648.955 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1539426648.955 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1539426648.956 * * * * [misc]progress: [ 21 / 83 ] simplifiying candidate # 1539426648.956 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1539426648.956 * * [misc]simplify: iters left: 5 (9 enodes) 1539426648.959 * * [misc]simplify: iters left: 4 (15 enodes) 1539426648.963 * * [misc]simplify: iters left: 3 (21 enodes) 1539426648.968 * * [misc]simplify: iters left: 2 (22 enodes) 1539426648.974 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1539426648.974 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1539426648.974 * * * * [misc]progress: [ 22 / 83 ] simplifiying candidate # 1539426648.974 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1539426648.974 * * [misc]simplify: iters left: 5 (9 enodes) 1539426648.977 * * [misc]simplify: iters left: 4 (15 enodes) 1539426648.984 * * [misc]simplify: iters left: 3 (21 enodes) 1539426648.990 * * [misc]simplify: iters left: 2 (22 enodes) 1539426648.995 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1539426648.996 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1539426648.996 * * * * [misc]progress: [ 23 / 83 ] simplifiying candidate # 1539426648.996 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1539426648.996 * * [misc]simplify: iters left: 5 (7 enodes) 1539426648.998 * * [misc]simplify: iters left: 4 (9 enodes) 1539426649.001 * * [misc]simplify: iters left: 3 (12 enodes) 1539426649.004 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1539426649.004 * [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))) 1539426649.005 * * * * [misc]progress: [ 24 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 25 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 26 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 27 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 28 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 29 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 30 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 31 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 32 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 33 / 83 ] simplifiying candidate # 1539426649.005 * * * * [misc]progress: [ 34 / 83 ] simplifiying candidate # 1539426649.005 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1539426649.006 * * [misc]simplify: iters left: 6 (14 enodes) 1539426649.010 * * [misc]simplify: iters left: 5 (27 enodes) 1539426649.019 * * [misc]simplify: iters left: 4 (55 enodes) 1539426649.041 * * [misc]simplify: iters left: 3 (144 enodes) 1539426649.116 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1539426649.116 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1539426649.116 * * * * [misc]progress: [ 35 / 83 ] simplifiying candidate # 1539426649.117 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1539426649.117 * * [misc]simplify: iters left: 6 (14 enodes) 1539426649.121 * * [misc]simplify: iters left: 5 (27 enodes) 1539426649.130 * * [misc]simplify: iters left: 4 (55 enodes) 1539426649.145 * * [misc]simplify: iters left: 3 (144 enodes) 1539426649.211 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1539426649.211 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1539426649.211 * * * * [misc]progress: [ 36 / 83 ] simplifiying candidate # 1539426649.211 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1539426649.211 * * [misc]simplify: iters left: 6 (14 enodes) 1539426649.213 * * [misc]simplify: iters left: 5 (24 enodes) 1539426649.217 * * [misc]simplify: iters left: 4 (43 enodes) 1539426649.223 * * [misc]simplify: iters left: 3 (73 enodes) 1539426649.240 * * [misc]simplify: iters left: 2 (220 enodes) 1539426649.435 * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1539426649.435 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1539426649.435 * * * * [misc]progress: [ 37 / 83 ] simplifiying candidate # 1539426649.435 * * * * [misc]progress: [ 38 / 83 ] simplifiying candidate # 1539426649.436 * * * * [misc]progress: [ 39 / 83 ] simplifiying candidate # 1539426649.436 * [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))) 1539426649.436 * * [misc]simplify: iters left: 6 (16 enodes) 1539426649.441 * * [misc]simplify: iters left: 5 (31 enodes) 1539426649.451 * * [misc]simplify: iters left: 4 (67 enodes) 1539426649.474 * * [misc]simplify: iters left: 3 (124 enodes) 1539426649.510 * * [misc]simplify: iters left: 2 (195 enodes) 1539426649.569 * * [misc]simplify: iters left: 1 (309 enodes) 1539426649.733 * [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)))) 1539426649.733 * [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)))))) 1539426649.733 * * * * [misc]progress: [ 40 / 83 ] simplifiying candidate # 1539426649.733 * * * * [misc]progress: [ 41 / 83 ] simplifiying candidate # 1539426649.733 * * * * [misc]progress: [ 42 / 83 ] simplifiying candidate # 1539426649.733 * * * * [misc]progress: [ 43 / 83 ] simplifiying candidate # 1539426649.733 * * * * [misc]progress: [ 44 / 83 ] simplifiying candidate # 1539426649.734 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426649.734 * * [misc]simplify: iters left: 6 (12 enodes) 1539426649.738 * * [misc]simplify: iters left: 5 (19 enodes) 1539426649.743 * * [misc]simplify: iters left: 4 (25 enodes) 1539426649.751 * * [misc]simplify: iters left: 3 (26 enodes) 1539426649.757 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426649.757 * [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))))) 1539426649.757 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1539426649.758 * * [misc]simplify: iters left: 6 (12 enodes) 1539426649.761 * * [misc]simplify: iters left: 5 (18 enodes) 1539426649.766 * * [misc]simplify: iters left: 4 (24 enodes) 1539426649.769 * * [misc]simplify: iters left: 3 (25 enodes) 1539426649.772 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1539426649.772 * [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))))) 1539426649.772 * * * * [misc]progress: [ 45 / 83 ] simplifiying candidate # 1539426649.773 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1539426649.773 * * [misc]simplify: iters left: 6 (11 enodes) 1539426649.774 * * [misc]simplify: iters left: 5 (16 enodes) 1539426649.776 * * [misc]simplify: iters left: 4 (22 enodes) 1539426649.779 * * [misc]simplify: iters left: 3 (24 enodes) 1539426649.782 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1539426649.782 * [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))))) 1539426649.782 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1539426649.782 * * [misc]simplify: iters left: 6 (12 enodes) 1539426649.784 * * [misc]simplify: iters left: 5 (18 enodes) 1539426649.787 * * [misc]simplify: iters left: 4 (24 enodes) 1539426649.790 * * [misc]simplify: iters left: 3 (25 enodes) 1539426649.793 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1539426649.793 * [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))))) 1539426649.793 * * * * [misc]progress: [ 46 / 83 ] simplifiying candidate # 1539426649.793 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1539426649.793 * * [misc]simplify: iters left: 6 (9 enodes) 1539426649.794 * * [misc]simplify: iters left: 5 (16 enodes) 1539426649.797 * * [misc]simplify: iters left: 4 (24 enodes) 1539426649.800 * * [misc]simplify: iters left: 3 (26 enodes) 1539426649.802 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1539426649.802 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426649.802 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1539426649.802 * * [misc]simplify: iters left: 6 (11 enodes) 1539426649.804 * * [misc]simplify: iters left: 5 (17 enodes) 1539426649.806 * * [misc]simplify: iters left: 4 (23 enodes) 1539426649.809 * * [misc]simplify: iters left: 3 (24 enodes) 1539426649.813 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1539426649.813 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1539426649.813 * * * * [misc]progress: [ 47 / 83 ] simplifiying candidate # 1539426649.813 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426649.813 * * [misc]simplify: iters left: 6 (12 enodes) 1539426649.817 * * [misc]simplify: iters left: 5 (19 enodes) 1539426649.822 * * [misc]simplify: iters left: 4 (25 enodes) 1539426649.828 * * [misc]simplify: iters left: 3 (26 enodes) 1539426649.835 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426649.835 * [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))))) 1539426649.835 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1539426649.835 * * [misc]simplify: iters left: 6 (12 enodes) 1539426649.839 * * [misc]simplify: iters left: 5 (18 enodes) 1539426649.844 * * [misc]simplify: iters left: 4 (24 enodes) 1539426649.849 * * [misc]simplify: iters left: 3 (25 enodes) 1539426649.852 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1539426649.852 * [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))))) 1539426649.852 * * * * [misc]progress: [ 48 / 83 ] simplifiying candidate # 1539426649.852 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1539426649.852 * * [misc]simplify: iters left: 6 (11 enodes) 1539426649.854 * * [misc]simplify: iters left: 5 (16 enodes) 1539426649.856 * * [misc]simplify: iters left: 4 (22 enodes) 1539426649.859 * * [misc]simplify: iters left: 3 (24 enodes) 1539426649.861 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1539426649.862 * [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))))) 1539426649.862 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1539426649.862 * * [misc]simplify: iters left: 6 (12 enodes) 1539426649.863 * * [misc]simplify: iters left: 5 (18 enodes) 1539426649.866 * * [misc]simplify: iters left: 4 (24 enodes) 1539426649.869 * * [misc]simplify: iters left: 3 (25 enodes) 1539426649.872 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1539426649.872 * [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))))) 1539426649.872 * * * * [misc]progress: [ 49 / 83 ] simplifiying candidate # 1539426649.872 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1539426649.872 * * [misc]simplify: iters left: 6 (9 enodes) 1539426649.874 * * [misc]simplify: iters left: 5 (16 enodes) 1539426649.876 * * [misc]simplify: iters left: 4 (24 enodes) 1539426649.879 * * [misc]simplify: iters left: 3 (26 enodes) 1539426649.881 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1539426649.881 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426649.882 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1539426649.882 * * [misc]simplify: iters left: 6 (11 enodes) 1539426649.883 * * [misc]simplify: iters left: 5 (17 enodes) 1539426649.885 * * [misc]simplify: iters left: 4 (23 enodes) 1539426649.889 * * [misc]simplify: iters left: 3 (24 enodes) 1539426649.891 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1539426649.892 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1539426649.892 * * * * [misc]progress: [ 50 / 83 ] simplifiying candidate # 1539426649.892 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426649.892 * * [misc]simplify: iters left: 6 (11 enodes) 1539426649.893 * * [misc]simplify: iters left: 5 (15 enodes) 1539426649.895 * * [misc]simplify: iters left: 4 (18 enodes) 1539426649.898 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426649.898 * [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))))) 1539426649.898 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1539426649.898 * * [misc]simplify: iters left: 6 (11 enodes) 1539426649.899 * * [misc]simplify: iters left: 5 (14 enodes) 1539426649.901 * * [misc]simplify: iters left: 4 (17 enodes) 1539426649.903 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1539426649.903 * [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))))) 1539426649.903 * * * * [misc]progress: [ 51 / 83 ] simplifiying candidate # 1539426649.904 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539426649.904 * * [misc]simplify: iters left: 6 (10 enodes) 1539426649.905 * * [misc]simplify: iters left: 5 (12 enodes) 1539426649.906 * * [misc]simplify: iters left: 4 (15 enodes) 1539426649.908 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539426649.908 * [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))))) 1539426649.909 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539426649.909 * * [misc]simplify: iters left: 6 (11 enodes) 1539426649.910 * * [misc]simplify: iters left: 5 (14 enodes) 1539426649.912 * * [misc]simplify: iters left: 4 (17 enodes) 1539426649.914 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539426649.914 * [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))))) 1539426649.914 * * * * [misc]progress: [ 52 / 83 ] simplifiying candidate # 1539426649.914 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1539426649.914 * * [misc]simplify: iters left: 6 (9 enodes) 1539426649.916 * * [misc]simplify: iters left: 5 (13 enodes) 1539426649.918 * * [misc]simplify: iters left: 4 (18 enodes) 1539426649.921 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1539426649.921 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1539426649.922 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1539426649.922 * * [misc]simplify: iters left: 6 (10 enodes) 1539426649.925 * * [misc]simplify: iters left: 5 (13 enodes) 1539426649.929 * * [misc]simplify: iters left: 4 (16 enodes) 1539426649.933 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1539426649.933 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1539426649.933 * * * * [misc]progress: [ 53 / 83 ] simplifiying candidate # 1539426649.933 * [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)))) 1539426649.934 * * [misc]simplify: iters left: 6 (16 enodes) 1539426649.939 * * [misc]simplify: iters left: 5 (28 enodes) 1539426649.947 * * [misc]simplify: iters left: 4 (46 enodes) 1539426649.959 * * [misc]simplify: iters left: 3 (50 enodes) 1539426649.970 * * [misc]simplify: iters left: 2 (53 enodes) 1539426649.983 * [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)))) 1539426649.983 * [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))))) 1539426649.984 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1539426649.984 * * [misc]simplify: iters left: 6 (14 enodes) 1539426649.988 * * [misc]simplify: iters left: 5 (20 enodes) 1539426649.994 * * [misc]simplify: iters left: 4 (29 enodes) 1539426650.001 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.008 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1539426650.008 * [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))))) 1539426650.008 * * * * [misc]progress: [ 54 / 83 ] simplifiying candidate # 1539426650.009 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1539426650.009 * * [misc]simplify: iters left: 6 (15 enodes) 1539426650.013 * * [misc]simplify: iters left: 5 (23 enodes) 1539426650.020 * * [misc]simplify: iters left: 4 (34 enodes) 1539426650.029 * * [misc]simplify: iters left: 3 (37 enodes) 1539426650.038 * [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)))))) 1539426650.038 * [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))))) 1539426650.039 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539426650.039 * * [misc]simplify: iters left: 6 (14 enodes) 1539426650.043 * * [misc]simplify: iters left: 5 (20 enodes) 1539426650.048 * * [misc]simplify: iters left: 4 (29 enodes) 1539426650.057 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.064 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539426650.064 * [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))))) 1539426650.064 * * * * [misc]progress: [ 55 / 83 ] simplifiying candidate # 1539426650.064 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1539426650.065 * * [misc]simplify: iters left: 6 (14 enodes) 1539426650.069 * * [misc]simplify: iters left: 5 (24 enodes) 1539426650.077 * * [misc]simplify: iters left: 4 (39 enodes) 1539426650.088 * * [misc]simplify: iters left: 3 (54 enodes) 1539426650.101 * * [misc]simplify: iters left: 2 (80 enodes) 1539426650.121 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1539426650.121 * [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)))) 1539426650.121 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1539426650.121 * * [misc]simplify: iters left: 6 (13 enodes) 1539426650.125 * * [misc]simplify: iters left: 5 (19 enodes) 1539426650.131 * * [misc]simplify: iters left: 4 (28 enodes) 1539426650.138 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.145 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1539426650.145 * [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)))) 1539426650.145 * * * * [misc]progress: [ 56 / 83 ] simplifiying candidate # 1539426650.145 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426650.145 * * [misc]simplify: iters left: 6 (15 enodes) 1539426650.150 * * [misc]simplify: iters left: 5 (23 enodes) 1539426650.156 * * [misc]simplify: iters left: 4 (32 enodes) 1539426650.165 * * [misc]simplify: iters left: 3 (34 enodes) 1539426650.170 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426650.170 * [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))))) 1539426650.170 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1539426650.170 * * [misc]simplify: iters left: 6 (14 enodes) 1539426650.172 * * [misc]simplify: iters left: 5 (20 enodes) 1539426650.175 * * [misc]simplify: iters left: 4 (29 enodes) 1539426650.179 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.182 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1539426650.182 * [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))))) 1539426650.182 * * * * [misc]progress: [ 57 / 83 ] simplifiying candidate # 1539426650.182 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539426650.183 * * [misc]simplify: iters left: 6 (14 enodes) 1539426650.185 * * [misc]simplify: iters left: 5 (20 enodes) 1539426650.188 * * [misc]simplify: iters left: 4 (29 enodes) 1539426650.191 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.195 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539426650.195 * [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))))) 1539426650.195 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539426650.195 * * [misc]simplify: iters left: 6 (14 enodes) 1539426650.197 * * [misc]simplify: iters left: 5 (20 enodes) 1539426650.200 * * [misc]simplify: iters left: 4 (29 enodes) 1539426650.203 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.207 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539426650.207 * [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))))) 1539426650.207 * * * * [misc]progress: [ 58 / 83 ] simplifiying candidate # 1539426650.207 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1539426650.207 * * [misc]simplify: iters left: 6 (13 enodes) 1539426650.209 * * [misc]simplify: iters left: 5 (21 enodes) 1539426650.213 * * [misc]simplify: iters left: 4 (32 enodes) 1539426650.216 * * [misc]simplify: iters left: 3 (33 enodes) 1539426650.220 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1539426650.220 * [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)))) 1539426650.220 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1539426650.220 * * [misc]simplify: iters left: 6 (13 enodes) 1539426650.222 * * [misc]simplify: iters left: 5 (19 enodes) 1539426650.226 * * [misc]simplify: iters left: 4 (28 enodes) 1539426650.233 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.240 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1539426650.240 * [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)))) 1539426650.240 * * * * [misc]progress: [ 59 / 83 ] simplifiying candidate # 1539426650.241 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426650.241 * * [misc]simplify: iters left: 6 (6 enodes) 1539426650.243 * * [misc]simplify: iters left: 5 (10 enodes) 1539426650.245 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1539426650.245 * [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))))) 1539426650.246 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1539426650.246 * * [misc]simplify: iters left: 6 (13 enodes) 1539426650.250 * * [misc]simplify: iters left: 5 (19 enodes) 1539426650.255 * * [misc]simplify: iters left: 4 (28 enodes) 1539426650.262 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.269 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1539426650.269 * [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))))) 1539426650.269 * * * * [misc]progress: [ 60 / 83 ] simplifiying candidate # 1539426650.269 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1539426650.269 * * [misc]simplify: iters left: 4 (5 enodes) 1539426650.271 * * [misc]simplify: iters left: 3 (7 enodes) 1539426650.272 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1539426650.272 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1539426650.273 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539426650.273 * * [misc]simplify: iters left: 6 (13 enodes) 1539426650.276 * * [misc]simplify: iters left: 5 (19 enodes) 1539426650.282 * * [misc]simplify: iters left: 4 (28 enodes) 1539426650.290 * * [misc]simplify: iters left: 3 (30 enodes) 1539426650.297 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539426650.297 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1539426650.297 * * * * [misc]progress: [ 61 / 83 ] simplifiying candidate # 1539426650.297 * [enter]simplify: Simplifying (/ 1 1) 1539426650.297 * * [misc]simplify: iters left: 2 (2 enodes) 1539426650.298 * * [misc]simplify: iters left: 1 (4 enodes) 1539426650.299 * [exit]simplify: Simplified to 1 1539426650.299 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1539426650.299 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1539426650.299 * * [misc]simplify: iters left: 6 (12 enodes) 1539426650.303 * * [misc]simplify: iters left: 5 (18 enodes) 1539426650.308 * * [misc]simplify: iters left: 4 (27 enodes) 1539426650.311 * * [misc]simplify: iters left: 3 (29 enodes) 1539426650.315 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1539426650.315 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1539426650.315 * * * * [misc]progress: [ 62 / 83 ] simplifiying candidate # 1539426650.315 * * * * [misc]progress: [ 63 / 83 ] simplifiying candidate # 1539426650.315 * * * * [misc]progress: [ 64 / 83 ] simplifiying candidate # 1539426650.315 * * * * [misc]progress: [ 65 / 83 ] simplifiying candidate # 1539426650.315 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1539426650.315 * * [misc]simplify: iters left: 2 (3 enodes) 1539426650.315 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1539426650.316 * [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)))) 1539426650.316 * * * * [misc]progress: [ 66 / 83 ] simplifiying candidate # 1539426650.316 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1539426650.316 * * [misc]simplify: iters left: 2 (3 enodes) 1539426650.316 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1539426650.316 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1539426650.316 * * * * [misc]progress: [ 67 / 83 ] simplifiying candidate # 1539426650.316 * [enter]simplify: Simplifying (sqrt k) 1539426650.316 * * [misc]simplify: iters left: 1 (2 enodes) 1539426650.317 * [exit]simplify: Simplified to (sqrt k) 1539426650.317 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1539426650.317 * * * * [misc]progress: [ 68 / 83 ] simplifiying candidate # 1539426650.317 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1539426650.317 * * [misc]simplify: iters left: 5 (7 enodes) 1539426650.318 * * [misc]simplify: iters left: 4 (12 enodes) 1539426650.319 * * [misc]simplify: iters left: 3 (18 enodes) 1539426650.322 * * [misc]simplify: iters left: 2 (20 enodes) 1539426650.324 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539426650.324 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426650.324 * * * * [misc]progress: [ 69 / 83 ] simplifiying candidate # 1539426650.324 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1539426650.324 * * [misc]simplify: iters left: 5 (7 enodes) 1539426650.325 * * [misc]simplify: iters left: 4 (12 enodes) 1539426650.327 * * [misc]simplify: iters left: 3 (18 enodes) 1539426650.329 * * [misc]simplify: iters left: 2 (20 enodes) 1539426650.331 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539426650.331 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426650.331 * * * * [misc]progress: [ 70 / 83 ] simplifiying candidate # 1539426650.331 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1539426650.331 * * [misc]simplify: iters left: 5 (7 enodes) 1539426650.332 * * [misc]simplify: iters left: 4 (9 enodes) 1539426650.334 * * [misc]simplify: iters left: 3 (12 enodes) 1539426650.335 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1539426650.335 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1539426650.335 * * * * [misc]progress: [ 71 / 83 ] simplifiying candidate # 1539426650.336 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1539426650.336 * * [misc]simplify: iters left: 6 (12 enodes) 1539426650.337 * * [misc]simplify: iters left: 5 (18 enodes) 1539426650.340 * * [misc]simplify: iters left: 4 (27 enodes) 1539426650.348 * * [misc]simplify: iters left: 3 (29 enodes) 1539426650.355 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1539426650.355 * [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))))))) 1539426650.355 * * * * [misc]progress: [ 72 / 83 ] simplifiying candidate # 1539426650.355 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1539426650.355 * * [misc]simplify: iters left: 6 (11 enodes) 1539426650.358 * * [misc]simplify: iters left: 5 (17 enodes) 1539426650.363 * * [misc]simplify: iters left: 4 (26 enodes) 1539426650.369 * * [misc]simplify: iters left: 3 (27 enodes) 1539426650.375 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1539426650.375 * [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))))))) 1539426650.375 * * * * [misc]progress: [ 73 / 83 ] simplifiying candidate # 1539426650.376 * * * * [misc]progress: [ 74 / 83 ] simplifiying candidate # 1539426650.376 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1539426650.376 * * [misc]simplify: iters left: 5 (7 enodes) 1539426650.378 * * [misc]simplify: iters left: 4 (12 enodes) 1539426650.381 * * [misc]simplify: iters left: 3 (18 enodes) 1539426650.385 * * [misc]simplify: iters left: 2 (20 enodes) 1539426650.390 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539426650.390 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539426650.390 * * * * [misc]progress: [ 75 / 83 ] simplifiying candidate # 1539426650.390 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426650.390 * * [misc]simplify: iters left: 4 (5 enodes) 1539426650.393 * * [misc]simplify: iters left: 3 (9 enodes) 1539426650.395 * * [misc]simplify: iters left: 2 (15 enodes) 1539426650.399 * * [misc]simplify: iters left: 1 (17 enodes) 1539426650.403 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426650.403 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1539426650.403 * * * * [misc]progress: [ 76 / 83 ] simplifiying candidate # 1539426650.403 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426650.403 * * [misc]simplify: iters left: 4 (5 enodes) 1539426650.405 * * [misc]simplify: iters left: 3 (9 enodes) 1539426650.407 * * [misc]simplify: iters left: 2 (15 enodes) 1539426650.409 * * [misc]simplify: iters left: 1 (17 enodes) 1539426650.411 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426650.411 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1539426650.411 * * * * [misc]progress: [ 77 / 83 ] simplifiying candidate # 1539426650.411 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426650.411 * * [misc]simplify: iters left: 4 (5 enodes) 1539426650.412 * * [misc]simplify: iters left: 3 (9 enodes) 1539426650.413 * * [misc]simplify: iters left: 2 (15 enodes) 1539426650.415 * * [misc]simplify: iters left: 1 (17 enodes) 1539426650.417 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426650.417 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1539426650.417 * * * * [misc]progress: [ 78 / 83 ] simplifiying candidate # 1539426650.417 * [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))))) 1539426650.418 * * [misc]simplify: iters left: 6 (37 enodes) 1539426650.425 * * [misc]simplify: iters left: 5 (108 enodes) 1539426650.456 * * [misc]simplify: iters left: 4 (368 enodes) 1539426650.767 * [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)))))) 1539426650.767 * [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))) 1539426650.767 * * * * [misc]progress: [ 79 / 83 ] simplifiying candidate # 1539426650.768 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1539426650.768 * * [misc]simplify: iters left: 6 (15 enodes) 1539426650.774 * * [misc]simplify: iters left: 5 (33 enodes) 1539426650.785 * * [misc]simplify: iters left: 4 (64 enodes) 1539426650.810 * * [misc]simplify: iters left: 3 (179 enodes) 1539426650.926 * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) 1539426650.927 * [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))) 1539426650.927 * * * * [misc]progress: [ 80 / 83 ] simplifiying candidate # 1539426650.927 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1539426650.927 * * [misc]simplify: iters left: 6 (15 enodes) 1539426650.933 * * [misc]simplify: iters left: 5 (30 enodes) 1539426650.943 * * [misc]simplify: iters left: 4 (65 enodes) 1539426650.961 * * [misc]simplify: iters left: 3 (208 enodes) 1539426651.098 * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) 1539426651.098 * [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))) 1539426651.098 * * * * [misc]progress: [ 81 / 83 ] simplifiying candidate # 1539426651.098 * [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)))))))))))))))))))))) 1539426651.098 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426651.098 * * * * [misc]progress: [ 82 / 83 ] simplifiying candidate # 1539426651.099 * [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)))))))) 1539426651.099 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426651.099 * * * * [misc]progress: [ 83 / 83 ] simplifiying candidate # 1539426651.099 * [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))))))))))) 1539426651.099 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426651.099 * * * [misc]progress: adding candidates to table 1539426652.018 * * [misc]progress: iteration 2 / 4 1539426652.018 * * * [misc]progress: picking best candidate 1539426652.055 * * * * [misc]pick: Picked # 1539426652.055 * * * [misc]progress: localizing error 1539426652.110 * * * [misc]progress: generating rewritten candidates 1539426652.111 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 2 1) 1539426652.114 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) 1539426652.116 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) 1539426652.134 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1) 1539426652.136 * * * [misc]progress: generating series expansions 1539426652.137 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 2 1) 1539426652.137 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539426652.137 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539426652.137 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426652.137 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.137 * [misc]backup-simplify: Simplify 2 into 2 1539426652.137 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.137 * [misc]taylor: Taking taylor expansion of n in n 1539426652.137 * [misc]backup-simplify: Simplify 0 into 0 1539426652.137 * [misc]backup-simplify: Simplify 1 into 1 1539426652.137 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.137 * [misc]backup-simplify: Simplify PI into PI 1539426652.137 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426652.137 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.137 * [misc]backup-simplify: Simplify 2 into 2 1539426652.137 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.137 * [misc]taylor: Taking taylor expansion of n in n 1539426652.137 * [misc]backup-simplify: Simplify 0 into 0 1539426652.137 * [misc]backup-simplify: Simplify 1 into 1 1539426652.137 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.137 * [misc]backup-simplify: Simplify PI into PI 1539426652.138 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426652.138 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426652.138 * [misc]backup-simplify: Simplify 0 into 0 1539426652.138 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426652.139 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426652.139 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.140 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426652.140 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426652.140 * [misc]backup-simplify: Simplify 0 into 0 1539426652.141 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.142 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426652.142 * [misc]backup-simplify: Simplify 0 into 0 1539426652.144 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.146 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426652.146 * [misc]backup-simplify: Simplify 0 into 0 1539426652.149 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.151 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539426652.152 * [misc]backup-simplify: Simplify 0 into 0 1539426652.155 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.158 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539426652.158 * [misc]backup-simplify: Simplify 0 into 0 1539426652.162 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539426652.166 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539426652.166 * [misc]backup-simplify: Simplify 0 into 0 1539426652.167 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539426652.167 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539426652.167 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539426652.167 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426652.167 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.167 * [misc]backup-simplify: Simplify 2 into 2 1539426652.167 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.167 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.167 * [misc]backup-simplify: Simplify PI into PI 1539426652.167 * [misc]taylor: Taking taylor expansion of n in n 1539426652.167 * [misc]backup-simplify: Simplify 0 into 0 1539426652.167 * [misc]backup-simplify: Simplify 1 into 1 1539426652.167 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.167 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426652.167 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.167 * [misc]backup-simplify: Simplify 2 into 2 1539426652.167 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.167 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.167 * [misc]backup-simplify: Simplify PI into PI 1539426652.167 * [misc]taylor: Taking taylor expansion of n in n 1539426652.167 * [misc]backup-simplify: Simplify 0 into 0 1539426652.167 * [misc]backup-simplify: Simplify 1 into 1 1539426652.168 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.168 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.168 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.169 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.170 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426652.170 * [misc]backup-simplify: Simplify 0 into 0 1539426652.171 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.172 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426652.172 * [misc]backup-simplify: Simplify 0 into 0 1539426652.174 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.175 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.175 * [misc]backup-simplify: Simplify 0 into 0 1539426652.176 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.178 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.178 * [misc]backup-simplify: Simplify 0 into 0 1539426652.179 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.180 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.180 * [misc]backup-simplify: Simplify 0 into 0 1539426652.182 * [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 1539426652.184 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.184 * [misc]backup-simplify: Simplify 0 into 0 1539426652.184 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539426652.184 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539426652.184 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539426652.184 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426652.184 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.184 * [misc]backup-simplify: Simplify -2 into -2 1539426652.184 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.184 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.184 * [misc]backup-simplify: Simplify PI into PI 1539426652.184 * [misc]taylor: Taking taylor expansion of n in n 1539426652.184 * [misc]backup-simplify: Simplify 0 into 0 1539426652.184 * [misc]backup-simplify: Simplify 1 into 1 1539426652.184 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.184 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426652.184 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.185 * [misc]backup-simplify: Simplify -2 into -2 1539426652.185 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.185 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.185 * [misc]backup-simplify: Simplify PI into PI 1539426652.185 * [misc]taylor: Taking taylor expansion of n in n 1539426652.185 * [misc]backup-simplify: Simplify 0 into 0 1539426652.185 * [misc]backup-simplify: Simplify 1 into 1 1539426652.185 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.185 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.185 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.186 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.186 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426652.186 * [misc]backup-simplify: Simplify 0 into 0 1539426652.187 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.188 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426652.188 * [misc]backup-simplify: Simplify 0 into 0 1539426652.189 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.189 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.189 * [misc]backup-simplify: Simplify 0 into 0 1539426652.191 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.192 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.192 * [misc]backup-simplify: Simplify 0 into 0 1539426652.193 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.194 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.194 * [misc]backup-simplify: Simplify 0 into 0 1539426652.196 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.198 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.198 * [misc]backup-simplify: Simplify 0 into 0 1539426652.198 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539426652.198 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1) 1539426652.198 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539426652.198 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539426652.198 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426652.198 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.198 * [misc]backup-simplify: Simplify 2 into 2 1539426652.198 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.198 * [misc]taylor: Taking taylor expansion of n in n 1539426652.198 * [misc]backup-simplify: Simplify 0 into 0 1539426652.198 * [misc]backup-simplify: Simplify 1 into 1 1539426652.198 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.198 * [misc]backup-simplify: Simplify PI into PI 1539426652.198 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426652.198 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.198 * [misc]backup-simplify: Simplify 2 into 2 1539426652.198 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.198 * [misc]taylor: Taking taylor expansion of n in n 1539426652.198 * [misc]backup-simplify: Simplify 0 into 0 1539426652.198 * [misc]backup-simplify: Simplify 1 into 1 1539426652.198 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.198 * [misc]backup-simplify: Simplify PI into PI 1539426652.199 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426652.199 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426652.199 * [misc]backup-simplify: Simplify 0 into 0 1539426652.199 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426652.200 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426652.200 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.201 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426652.201 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426652.201 * [misc]backup-simplify: Simplify 0 into 0 1539426652.202 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.203 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426652.203 * [misc]backup-simplify: Simplify 0 into 0 1539426652.205 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.207 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426652.207 * [misc]backup-simplify: Simplify 0 into 0 1539426652.210 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.212 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539426652.212 * [misc]backup-simplify: Simplify 0 into 0 1539426652.216 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.219 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539426652.219 * [misc]backup-simplify: Simplify 0 into 0 1539426652.223 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539426652.228 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539426652.228 * [misc]backup-simplify: Simplify 0 into 0 1539426652.228 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539426652.228 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539426652.228 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539426652.228 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426652.228 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.228 * [misc]backup-simplify: Simplify 2 into 2 1539426652.228 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.228 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.228 * [misc]backup-simplify: Simplify PI into PI 1539426652.228 * [misc]taylor: Taking taylor expansion of n in n 1539426652.228 * [misc]backup-simplify: Simplify 0 into 0 1539426652.228 * [misc]backup-simplify: Simplify 1 into 1 1539426652.229 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.229 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426652.229 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.229 * [misc]backup-simplify: Simplify 2 into 2 1539426652.229 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.229 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.229 * [misc]backup-simplify: Simplify PI into PI 1539426652.229 * [misc]taylor: Taking taylor expansion of n in n 1539426652.229 * [misc]backup-simplify: Simplify 0 into 0 1539426652.229 * [misc]backup-simplify: Simplify 1 into 1 1539426652.229 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.230 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.230 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.231 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.232 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426652.232 * [misc]backup-simplify: Simplify 0 into 0 1539426652.233 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.234 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426652.234 * [misc]backup-simplify: Simplify 0 into 0 1539426652.235 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.238 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.238 * [misc]backup-simplify: Simplify 0 into 0 1539426652.239 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.240 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.240 * [misc]backup-simplify: Simplify 0 into 0 1539426652.241 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.243 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.243 * [misc]backup-simplify: Simplify 0 into 0 1539426652.244 * [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 1539426652.246 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.246 * [misc]backup-simplify: Simplify 0 into 0 1539426652.246 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539426652.246 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539426652.246 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539426652.246 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426652.246 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.246 * [misc]backup-simplify: Simplify -2 into -2 1539426652.246 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.246 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.246 * [misc]backup-simplify: Simplify PI into PI 1539426652.246 * [misc]taylor: Taking taylor expansion of n in n 1539426652.246 * [misc]backup-simplify: Simplify 0 into 0 1539426652.246 * [misc]backup-simplify: Simplify 1 into 1 1539426652.247 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.247 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426652.247 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.247 * [misc]backup-simplify: Simplify -2 into -2 1539426652.247 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.247 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.247 * [misc]backup-simplify: Simplify PI into PI 1539426652.247 * [misc]taylor: Taking taylor expansion of n in n 1539426652.247 * [misc]backup-simplify: Simplify 0 into 0 1539426652.247 * [misc]backup-simplify: Simplify 1 into 1 1539426652.247 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.247 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.247 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.248 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.248 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426652.248 * [misc]backup-simplify: Simplify 0 into 0 1539426652.249 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.250 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426652.250 * [misc]backup-simplify: Simplify 0 into 0 1539426652.251 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.252 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.252 * [misc]backup-simplify: Simplify 0 into 0 1539426652.253 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.254 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.254 * [misc]backup-simplify: Simplify 0 into 0 1539426652.255 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.257 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.257 * [misc]backup-simplify: Simplify 0 into 0 1539426652.258 * [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 1539426652.260 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.260 * [misc]backup-simplify: Simplify 0 into 0 1539426652.260 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539426652.260 * * * * [misc]progress: [ 3 / 4 ] generating series at (2) 1539426652.261 * [misc]backup-simplify: Simplify (/ (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)) into (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) 1539426652.261 * [misc]approximate: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in (n k) around 0 1539426652.261 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.261 * [misc]backup-simplify: Simplify 2 into 2 1539426652.261 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.261 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.261 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426652.261 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.261 * [misc]taylor: Taking taylor expansion of k in k 1539426652.261 * [misc]backup-simplify: Simplify 0 into 0 1539426652.261 * [misc]backup-simplify: Simplify 1 into 1 1539426652.261 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.261 * [misc]backup-simplify: Simplify 2 into 2 1539426652.261 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426652.261 * [misc]taylor: Taking taylor expansion of n in k 1539426652.261 * [misc]backup-simplify: Simplify n into n 1539426652.261 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.261 * [misc]backup-simplify: Simplify PI into PI 1539426652.261 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426652.261 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539426652.261 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539426652.261 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426652.262 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.262 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539426652.262 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.262 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539426652.262 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539426652.263 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539426652.263 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539426652.263 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426652.263 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1539426652.263 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426652.263 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1539426652.263 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in k 1539426652.263 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426652.263 * [misc]taylor: Taking taylor expansion of n in k 1539426652.263 * [misc]backup-simplify: Simplify n into n 1539426652.263 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.263 * [misc]backup-simplify: Simplify PI into PI 1539426652.263 * [misc]taylor: Taking taylor expansion of k in k 1539426652.263 * [misc]backup-simplify: Simplify 0 into 0 1539426652.263 * [misc]backup-simplify: Simplify 1 into 1 1539426652.264 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426652.264 * [misc]backup-simplify: Simplify (/ (* n PI) 1) into (* n PI) 1539426652.264 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.264 * [misc]backup-simplify: Simplify (/ (* n PI) (* 2 (sqrt 0))) into (* +nan.0 (* n PI)) 1539426652.264 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in n 1539426652.264 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in n 1539426652.264 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426652.264 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.264 * [misc]backup-simplify: Simplify 2 into 2 1539426652.264 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.264 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.264 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1539426652.265 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426652.265 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426652.265 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1539426652.265 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426652.265 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.265 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.265 * [misc]taylor: Taking taylor expansion of k in n 1539426652.265 * [misc]backup-simplify: Simplify k into k 1539426652.265 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426652.265 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426652.265 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.265 * [misc]backup-simplify: Simplify 2 into 2 1539426652.265 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.265 * [misc]taylor: Taking taylor expansion of n in n 1539426652.265 * [misc]backup-simplify: Simplify 0 into 0 1539426652.265 * [misc]backup-simplify: Simplify 1 into 1 1539426652.265 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.265 * [misc]backup-simplify: Simplify PI into PI 1539426652.265 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426652.266 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426652.266 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426652.267 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426652.267 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.267 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426652.267 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426652.268 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.269 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539426652.269 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539426652.269 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1539426652.269 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1539426652.269 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.269 * [misc]taylor: Taking taylor expansion of n in n 1539426652.269 * [misc]backup-simplify: Simplify 0 into 0 1539426652.269 * [misc]backup-simplify: Simplify 1 into 1 1539426652.269 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.269 * [misc]backup-simplify: Simplify PI into PI 1539426652.269 * [misc]taylor: Taking taylor expansion of k in n 1539426652.269 * [misc]backup-simplify: Simplify k into k 1539426652.270 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426652.270 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426652.270 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1539426652.270 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.271 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1539426652.271 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in n 1539426652.271 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in n 1539426652.271 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426652.271 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.271 * [misc]backup-simplify: Simplify 2 into 2 1539426652.271 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.271 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.271 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1539426652.271 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426652.271 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426652.271 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1539426652.271 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426652.271 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.271 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.271 * [misc]taylor: Taking taylor expansion of k in n 1539426652.272 * [misc]backup-simplify: Simplify k into k 1539426652.272 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426652.272 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426652.272 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.272 * [misc]backup-simplify: Simplify 2 into 2 1539426652.272 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.272 * [misc]taylor: Taking taylor expansion of n in n 1539426652.272 * [misc]backup-simplify: Simplify 0 into 0 1539426652.272 * [misc]backup-simplify: Simplify 1 into 1 1539426652.272 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.272 * [misc]backup-simplify: Simplify PI into PI 1539426652.272 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426652.272 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426652.273 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426652.274 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426652.275 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.275 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426652.275 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426652.275 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.276 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539426652.277 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539426652.277 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1539426652.277 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1539426652.277 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.277 * [misc]taylor: Taking taylor expansion of n in n 1539426652.277 * [misc]backup-simplify: Simplify 0 into 0 1539426652.277 * [misc]backup-simplify: Simplify 1 into 1 1539426652.277 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.277 * [misc]backup-simplify: Simplify PI into PI 1539426652.277 * [misc]taylor: Taking taylor expansion of k in n 1539426652.277 * [misc]backup-simplify: Simplify k into k 1539426652.277 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426652.278 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426652.278 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1539426652.278 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.279 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1539426652.280 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1539426652.280 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 0) into 0 1539426652.280 * [misc]taylor: Taking taylor expansion of 0 in k 1539426652.280 * [misc]backup-simplify: Simplify 0 into 0 1539426652.281 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426652.282 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426652.283 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426652.285 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426652.286 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1539426652.286 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.287 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.287 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539426652.289 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426652.289 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) into 0 1539426652.291 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) (* +nan.0 (/ PI k))) (* 0 0)) into (- (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k))) 1539426652.291 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k))) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k)) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.291 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.291 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.291 * [misc]backup-simplify: Simplify 2 into 2 1539426652.291 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.291 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.291 * [misc]taylor: Taking taylor expansion of (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.291 * [misc]backup-simplify: Simplify PI into PI 1539426652.291 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426652.291 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426652.291 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.291 * [misc]taylor: Taking taylor expansion of n in k 1539426652.291 * [misc]backup-simplify: Simplify n into n 1539426652.291 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.291 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426652.292 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426652.292 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.292 * [misc]backup-simplify: Simplify 2 into 2 1539426652.292 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.292 * [misc]backup-simplify: Simplify PI into PI 1539426652.292 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.292 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.292 * [misc]taylor: Taking taylor expansion of k in k 1539426652.292 * [misc]backup-simplify: Simplify 0 into 0 1539426652.292 * [misc]backup-simplify: Simplify 1 into 1 1539426652.292 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.293 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539426652.293 * [misc]backup-simplify: Simplify (* -1/2 0) into 0 1539426652.293 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539426652.294 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426652.295 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426652.295 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426652.296 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1539426652.296 * [misc]backup-simplify: Simplify (+ (* -1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1539426652.296 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426652.296 * [misc]taylor: Taking taylor expansion of k in k 1539426652.296 * [misc]backup-simplify: Simplify 0 into 0 1539426652.296 * [misc]backup-simplify: Simplify 1 into 1 1539426652.296 * [misc]backup-simplify: Simplify (* PI 1) into PI 1539426652.297 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1539426652.297 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) PI) 1) into (* (sqrt 2) PI) 1539426652.298 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) PI)) into (* +nan.0 (* (sqrt 2) PI)) 1539426652.298 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426652.299 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426652.299 * [misc]backup-simplify: Simplify 0 into 0 1539426652.299 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426652.300 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)))) into 0 1539426652.300 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow PI 2) (pow k 2))) 1539426652.300 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426652.301 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.302 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426652.305 * [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 1539426652.305 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.305 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1539426652.305 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.305 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.306 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539426652.307 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.308 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426652.309 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into 0 1539426652.310 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) (* +nan.0 (/ (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (/ PI k))) (* 0 0))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)))) 1539426652.310 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)))) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2))) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.310 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.310 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.310 * [misc]backup-simplify: Simplify 2 into 2 1539426652.310 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.310 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.310 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.310 * [misc]backup-simplify: Simplify PI into PI 1539426652.310 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426652.310 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426652.310 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of n in k 1539426652.310 * [misc]backup-simplify: Simplify n into n 1539426652.310 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.310 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426652.310 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.310 * [misc]backup-simplify: Simplify 2 into 2 1539426652.310 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.310 * [misc]backup-simplify: Simplify PI into PI 1539426652.310 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.311 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.311 * [misc]taylor: Taking taylor expansion of k in k 1539426652.311 * [misc]backup-simplify: Simplify 0 into 0 1539426652.311 * [misc]backup-simplify: Simplify 1 into 1 1539426652.311 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.312 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539426652.312 * [misc]backup-simplify: Simplify (* -1/2 0) into 0 1539426652.312 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539426652.312 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426652.314 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426652.314 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426652.315 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1539426652.315 * [misc]backup-simplify: Simplify (+ (* -1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1539426652.315 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426652.315 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1539426652.315 * [misc]taylor: Taking taylor expansion of k in k 1539426652.315 * [misc]backup-simplify: Simplify 0 into 0 1539426652.315 * [misc]backup-simplify: Simplify 1 into 1 1539426652.315 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426652.316 * [misc]backup-simplify: Simplify (* (pow PI 2) 1) into (pow PI 2) 1539426652.316 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539426652.316 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426652.317 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 2)) 1) into (* (sqrt 2) (pow PI 2)) 1539426652.317 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1539426652.318 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426652.319 * [misc]backup-simplify: Simplify (+ (* (pow PI 2) (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* 0 1)) into (- (+ (* 1/2 (* (pow PI 2) (log (* 2 PI)))) (* 1/2 (* (pow PI 2) (log n))))) 1539426652.320 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (- (+ (* 1/2 (* (pow PI 2) (log (* 2 PI)))) (* 1/2 (* (pow PI 2) (log n)))))) (* 0 (pow PI 2))) into (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1539426652.320 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426652.323 * [misc]backup-simplify: Simplify (- (/ (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1) (+ (* (* (sqrt 2) (pow PI 2)) (/ 0 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1539426652.327 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n))))))) (* 0 (* (sqrt 2) (pow PI 2)))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1539426652.330 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1539426652.332 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1539426652.333 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1539426652.334 * [misc]backup-simplify: Simplify (+ (* PI (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* 0 1)) into (- (+ (* 1/2 (* PI (log (* 2 PI)))) (* 1/2 (* PI (log n))))) 1539426652.336 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (- (+ (* 1/2 (* PI (log (* 2 PI)))) (* 1/2 (* PI (log n)))))) (* 0 PI)) into (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1539426652.339 * [misc]backup-simplify: Simplify (- (/ (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1) (+ (* (* (sqrt 2) PI) (/ 0 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1539426652.342 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* 0 (* (sqrt 2) PI))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426652.344 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426652.346 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426652.353 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* 1 n)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) (* (/ 1 k) (pow n 2))) (* (- (* +nan.0 (* (sqrt 2) PI))) (* (/ 1 k) n)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log n)))) k)) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log (* 2 PI))))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) 1539426652.353 * [misc]backup-simplify: Simplify (/ (* (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (- (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) into (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) 1539426652.353 * [misc]approximate: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in (n k) around 0 1539426652.353 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in k 1539426652.353 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in k 1539426652.353 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.353 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.353 * [misc]backup-simplify: Simplify 2 into 2 1539426652.353 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.354 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.354 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1539426652.354 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539426652.354 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539426652.354 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1539426652.354 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426652.354 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426652.354 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.354 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426652.354 * [misc]taylor: Taking taylor expansion of k in k 1539426652.354 * [misc]backup-simplify: Simplify 0 into 0 1539426652.354 * [misc]backup-simplify: Simplify 1 into 1 1539426652.354 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426652.354 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539426652.354 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539426652.354 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.354 * [misc]backup-simplify: Simplify 2 into 2 1539426652.354 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426652.355 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.355 * [misc]backup-simplify: Simplify PI into PI 1539426652.355 * [misc]taylor: Taking taylor expansion of n in k 1539426652.355 * [misc]backup-simplify: Simplify n into n 1539426652.355 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426652.355 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539426652.355 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539426652.355 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426652.355 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426652.355 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539426652.355 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1539426652.355 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in k 1539426652.355 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in k 1539426652.355 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539426652.355 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.355 * [misc]backup-simplify: Simplify PI into PI 1539426652.355 * [misc]taylor: Taking taylor expansion of k in k 1539426652.355 * [misc]backup-simplify: Simplify 0 into 0 1539426652.355 * [misc]backup-simplify: Simplify 1 into 1 1539426652.355 * [misc]taylor: Taking taylor expansion of n in k 1539426652.355 * [misc]backup-simplify: Simplify n into n 1539426652.356 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539426652.356 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539426652.356 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426652.356 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.356 * [misc]backup-simplify: Simplify (/ (/ PI n) (* 2 (sqrt 0))) into (* +nan.0 (/ PI n)) 1539426652.356 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in n 1539426652.356 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in n 1539426652.356 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426652.356 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.356 * [misc]backup-simplify: Simplify 2 into 2 1539426652.356 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.357 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.357 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.357 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.357 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of k in n 1539426652.357 * [misc]backup-simplify: Simplify k into k 1539426652.357 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426652.357 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.357 * [misc]backup-simplify: Simplify 2 into 2 1539426652.357 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.357 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.357 * [misc]backup-simplify: Simplify PI into PI 1539426652.357 * [misc]taylor: Taking taylor expansion of n in n 1539426652.357 * [misc]backup-simplify: Simplify 0 into 0 1539426652.357 * [misc]backup-simplify: Simplify 1 into 1 1539426652.357 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.357 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.358 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.358 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426652.358 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426652.358 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.359 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426652.359 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426652.359 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1539426652.359 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1539426652.359 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539426652.359 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.359 * [misc]backup-simplify: Simplify PI into PI 1539426652.359 * [misc]taylor: Taking taylor expansion of k in n 1539426652.359 * [misc]backup-simplify: Simplify k into k 1539426652.359 * [misc]taylor: Taking taylor expansion of n in n 1539426652.359 * [misc]backup-simplify: Simplify 0 into 0 1539426652.359 * [misc]backup-simplify: Simplify 1 into 1 1539426652.359 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539426652.359 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1539426652.359 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.359 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1539426652.359 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in n 1539426652.359 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in n 1539426652.359 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426652.359 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.359 * [misc]backup-simplify: Simplify 2 into 2 1539426652.360 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.360 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.360 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.360 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.360 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of k in n 1539426652.360 * [misc]backup-simplify: Simplify k into k 1539426652.360 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426652.360 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.360 * [misc]backup-simplify: Simplify 2 into 2 1539426652.360 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.360 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.360 * [misc]backup-simplify: Simplify PI into PI 1539426652.360 * [misc]taylor: Taking taylor expansion of n in n 1539426652.360 * [misc]backup-simplify: Simplify 0 into 0 1539426652.360 * [misc]backup-simplify: Simplify 1 into 1 1539426652.360 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.360 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.361 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.361 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426652.361 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426652.361 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.362 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426652.362 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426652.362 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1539426652.362 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1539426652.362 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539426652.362 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.362 * [misc]backup-simplify: Simplify PI into PI 1539426652.362 * [misc]taylor: Taking taylor expansion of k in n 1539426652.362 * [misc]backup-simplify: Simplify k into k 1539426652.362 * [misc]taylor: Taking taylor expansion of n in n 1539426652.362 * [misc]backup-simplify: Simplify 0 into 0 1539426652.362 * [misc]backup-simplify: Simplify 1 into 1 1539426652.362 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539426652.362 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1539426652.362 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.362 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1539426652.363 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 1539426652.363 * [misc]backup-simplify: Simplify (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 0) into 0 1539426652.364 * [misc]taylor: Taking taylor expansion of 0 in k 1539426652.364 * [misc]backup-simplify: Simplify 0 into 0 1539426652.364 * [misc]backup-simplify: Simplify 0 into 0 1539426652.364 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426652.364 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.365 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426652.366 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426652.367 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426652.367 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426652.367 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.367 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.368 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539426652.369 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426652.369 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 1539426652.370 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* PI k))) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))))) 1539426652.370 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))))) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k)))) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.370 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.370 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426652.370 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426652.370 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426652.370 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.370 * [misc]backup-simplify: Simplify 2 into 2 1539426652.370 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.370 * [misc]backup-simplify: Simplify PI into PI 1539426652.370 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.371 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.371 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.371 * [misc]taylor: Taking taylor expansion of n in k 1539426652.371 * [misc]backup-simplify: Simplify n into n 1539426652.371 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.371 * [misc]taylor: Taking taylor expansion of k in k 1539426652.371 * [misc]backup-simplify: Simplify 0 into 0 1539426652.371 * [misc]backup-simplify: Simplify 1 into 1 1539426652.371 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426652.371 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426652.371 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426652.372 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426652.372 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426652.372 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* PI k)) in k 1539426652.372 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.372 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.372 * [misc]backup-simplify: Simplify 2 into 2 1539426652.372 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.372 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.372 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539426652.372 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.372 * [misc]backup-simplify: Simplify PI into PI 1539426652.372 * [misc]taylor: Taking taylor expansion of k in k 1539426652.373 * [misc]backup-simplify: Simplify 0 into 0 1539426652.373 * [misc]backup-simplify: Simplify 1 into 1 1539426652.373 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539426652.373 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426652.373 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) into 0 1539426652.373 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1539426652.373 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.373 * [misc]backup-simplify: Simplify 0 into 0 1539426652.373 * [misc]backup-simplify: Simplify 0 into 0 1539426652.374 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 k)) into 0 1539426652.374 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)))) into 0 1539426652.374 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow PI 2) (pow k 2))) 1539426652.374 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426652.375 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.376 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426652.379 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1539426652.379 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.379 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426652.379 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539426652.380 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.380 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.380 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539426652.382 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.383 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426652.383 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1539426652.385 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))))) 1539426652.385 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))))) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2))))) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.385 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.385 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426652.385 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426652.385 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426652.385 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.385 * [misc]backup-simplify: Simplify 2 into 2 1539426652.385 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.385 * [misc]backup-simplify: Simplify PI into PI 1539426652.385 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.386 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.386 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.386 * [misc]taylor: Taking taylor expansion of n in k 1539426652.386 * [misc]backup-simplify: Simplify n into n 1539426652.386 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.386 * [misc]taylor: Taking taylor expansion of k in k 1539426652.386 * [misc]backup-simplify: Simplify 0 into 0 1539426652.386 * [misc]backup-simplify: Simplify 1 into 1 1539426652.386 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426652.387 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426652.387 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426652.388 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426652.388 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426652.388 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 2) (pow k 2))) in k 1539426652.388 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.388 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.388 * [misc]backup-simplify: Simplify 2 into 2 1539426652.389 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.389 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.389 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (pow k 2)) in k 1539426652.389 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539426652.389 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.389 * [misc]backup-simplify: Simplify PI into PI 1539426652.389 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1539426652.389 * [misc]taylor: Taking taylor expansion of k in k 1539426652.389 * [misc]backup-simplify: Simplify 0 into 0 1539426652.389 * [misc]backup-simplify: Simplify 1 into 1 1539426652.390 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539426652.391 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539426652.392 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (* 0 0)) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) 1539426652.393 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1539426652.394 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1539426652.395 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1539426652.395 * [misc]backup-simplify: Simplify 0 into 0 1539426652.396 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 k))) into 0 1539426652.396 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.397 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 2) (pow k 2))))))) (* 2 0)) into (* +nan.0 (* (pow PI 3) (pow k 3))) 1539426652.397 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426652.399 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.400 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.404 * [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 1539426652.404 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.404 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.405 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426652.405 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1539426652.405 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.405 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.406 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539426652.408 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426652.408 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426652.409 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539426652.410 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))))) 1539426652.410 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))))) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3))))) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.410 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.410 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426652.410 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426652.410 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426652.410 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.410 * [misc]backup-simplify: Simplify 2 into 2 1539426652.410 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.410 * [misc]backup-simplify: Simplify PI into PI 1539426652.411 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.411 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.411 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.411 * [misc]taylor: Taking taylor expansion of n in k 1539426652.411 * [misc]backup-simplify: Simplify n into n 1539426652.411 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.411 * [misc]taylor: Taking taylor expansion of k in k 1539426652.411 * [misc]backup-simplify: Simplify 0 into 0 1539426652.411 * [misc]backup-simplify: Simplify 1 into 1 1539426652.411 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426652.411 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426652.412 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426652.412 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426652.412 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426652.412 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 3) (pow k 3))) in k 1539426652.412 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.412 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.412 * [misc]backup-simplify: Simplify 2 into 2 1539426652.413 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.413 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.413 * [misc]taylor: Taking taylor expansion of (* (pow PI 3) (pow k 3)) in k 1539426652.413 * [misc]taylor: Taking taylor expansion of (pow PI 3) in k 1539426652.413 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.413 * [misc]backup-simplify: Simplify PI into PI 1539426652.413 * [misc]taylor: Taking taylor expansion of (pow k 3) in k 1539426652.413 * [misc]taylor: Taking taylor expansion of k in k 1539426652.413 * [misc]backup-simplify: Simplify 0 into 0 1539426652.413 * [misc]backup-simplify: Simplify 1 into 1 1539426652.413 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1539426652.414 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426652.415 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1539426652.416 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0))) into 0 1539426652.417 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0))) into 0 1539426652.417 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.417 * [misc]backup-simplify: Simplify 0 into 0 1539426652.417 * [misc]backup-simplify: Simplify 0 into 0 1539426652.417 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1539426652.417 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.418 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow PI 2) (pow k 2))) 2) (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 3) (pow k 3))))))) (* 2 0)) into (* +nan.0 (* (pow PI 4) (pow k 4))) 1539426652.418 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426652.420 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.421 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.429 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 1539426652.430 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.430 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.430 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.430 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426652.431 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k)))))) into 0 1539426652.431 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.432 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.433 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 1539426652.438 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.440 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426652.441 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 1539426652.443 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))))) 1539426652.444 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))))) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4))))) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.444 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.444 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426652.444 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426652.444 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426652.444 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.444 * [misc]backup-simplify: Simplify 2 into 2 1539426652.444 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.444 * [misc]backup-simplify: Simplify PI into PI 1539426652.444 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.445 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.445 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.445 * [misc]taylor: Taking taylor expansion of n in k 1539426652.445 * [misc]backup-simplify: Simplify n into n 1539426652.445 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.445 * [misc]taylor: Taking taylor expansion of k in k 1539426652.445 * [misc]backup-simplify: Simplify 0 into 0 1539426652.445 * [misc]backup-simplify: Simplify 1 into 1 1539426652.445 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426652.445 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426652.446 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426652.446 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426652.447 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426652.447 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 4) (pow k 4))) in k 1539426652.447 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.447 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.447 * [misc]backup-simplify: Simplify 2 into 2 1539426652.447 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.448 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.448 * [misc]taylor: Taking taylor expansion of (* (pow PI 4) (pow k 4)) in k 1539426652.448 * [misc]taylor: Taking taylor expansion of (pow PI 4) in k 1539426652.448 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.448 * [misc]backup-simplify: Simplify PI into PI 1539426652.448 * [misc]taylor: Taking taylor expansion of (pow k 4) in k 1539426652.448 * [misc]taylor: Taking taylor expansion of k in k 1539426652.448 * [misc]backup-simplify: Simplify 0 into 0 1539426652.448 * [misc]backup-simplify: Simplify 1 into 1 1539426652.448 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426652.448 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426652.449 * [misc]backup-simplify: Simplify (* (pow PI 2) 1) into (pow PI 2) 1539426652.450 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539426652.451 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) 1539426652.452 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) into (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) 1539426652.453 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) 1539426652.454 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) 1539426652.455 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539426652.455 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426652.457 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426652.459 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0)))) into 0 1539426652.461 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0)))) into 0 1539426652.461 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.461 * [misc]backup-simplify: Simplify 0 into 0 1539426652.461 * [misc]backup-simplify: Simplify 0 into 0 1539426652.462 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k))))) into 0 1539426652.462 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.464 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 4) (pow k 4))))) (* 2 (* (* +nan.0 (* (pow PI 2) (pow k 2))) (* +nan.0 (* (pow PI 3) (pow k 3))))))) (* 2 0)) into (* +nan.0 (* (pow PI 5) (pow k 5))) 1539426652.464 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426652.466 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.469 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.490 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 1539426652.490 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.490 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.490 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.490 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.491 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426652.492 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))))) into 0 1539426652.492 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.492 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.494 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 1539426652.502 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426652.503 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426652.504 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))))))) into 0 1539426652.507 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 5) (pow k 5)))) (+ (* 0 (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0)))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))))) 1539426652.507 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))))) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5))))) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.507 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.507 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426652.507 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426652.507 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426652.507 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.507 * [misc]backup-simplify: Simplify 2 into 2 1539426652.507 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.507 * [misc]backup-simplify: Simplify PI into PI 1539426652.508 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.508 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.508 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.508 * [misc]taylor: Taking taylor expansion of n in k 1539426652.508 * [misc]backup-simplify: Simplify n into n 1539426652.508 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.508 * [misc]taylor: Taking taylor expansion of k in k 1539426652.508 * [misc]backup-simplify: Simplify 0 into 0 1539426652.508 * [misc]backup-simplify: Simplify 1 into 1 1539426652.508 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426652.509 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426652.509 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426652.510 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426652.510 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426652.510 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 5) (pow k 5))) in k 1539426652.510 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.511 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.511 * [misc]backup-simplify: Simplify 2 into 2 1539426652.511 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.511 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.511 * [misc]taylor: Taking taylor expansion of (* (pow PI 5) (pow k 5)) in k 1539426652.511 * [misc]taylor: Taking taylor expansion of (pow PI 5) in k 1539426652.511 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.511 * [misc]backup-simplify: Simplify PI into PI 1539426652.511 * [misc]taylor: Taking taylor expansion of (pow k 5) in k 1539426652.511 * [misc]taylor: Taking taylor expansion of k in k 1539426652.511 * [misc]backup-simplify: Simplify 0 into 0 1539426652.511 * [misc]backup-simplify: Simplify 1 into 1 1539426652.511 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426652.512 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426652.513 * [misc]backup-simplify: Simplify (+ (* (pow PI 2) 0) (* 0 1)) into 0 1539426652.514 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539426652.516 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (* (sqrt 2) (pow PI 2)))) into 0 1539426652.517 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into 0 1539426652.517 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.517 * [misc]backup-simplify: Simplify 0 into 0 1539426652.519 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539426652.520 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426652.522 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426652.525 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0))))) into 0 1539426652.526 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0))))) into 0 1539426652.527 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.527 * [misc]backup-simplify: Simplify 0 into 0 1539426652.527 * [misc]backup-simplify: Simplify 0 into 0 1539426652.528 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))))) into 0 1539426652.529 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.531 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow PI 3) (pow k 3))) 2) (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 5) (pow k 5))))) (* 2 (* (* +nan.0 (* (pow PI 2) (pow k 2))) (* +nan.0 (* (pow PI 4) (pow k 4))))))) (* 2 0)) into (* +nan.0 (* (pow PI 6) (pow k 6))) 1539426652.531 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426652.534 * [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 1539426652.537 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.557 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 1539426652.558 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.558 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.558 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.558 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.558 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.558 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426652.559 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k)))))))) into 0 1539426652.559 * [misc]backup-simplify: Simplify (- 0) into 0 1539426652.559 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.560 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 1539426652.571 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.573 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426652.574 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))))) into 0 1539426652.577 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 6) (pow k 6)))) (+ (* 0 (* +nan.0 (* (pow PI 5) (pow k 5)))) (+ (* 0 (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))))) 1539426652.577 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))))) in k 1539426652.577 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6))))) in k 1539426652.578 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.578 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.578 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))) in k 1539426652.578 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426652.578 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426652.578 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426652.578 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426652.578 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426652.578 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426652.578 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426652.578 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426652.578 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.578 * [misc]backup-simplify: Simplify 2 into 2 1539426652.578 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.578 * [misc]backup-simplify: Simplify PI into PI 1539426652.578 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.579 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.579 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.579 * [misc]taylor: Taking taylor expansion of n in k 1539426652.579 * [misc]backup-simplify: Simplify n into n 1539426652.579 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.579 * [misc]taylor: Taking taylor expansion of k in k 1539426652.579 * [misc]backup-simplify: Simplify 0 into 0 1539426652.579 * [misc]backup-simplify: Simplify 1 into 1 1539426652.579 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426652.579 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426652.580 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426652.580 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426652.581 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426652.581 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 6) (pow k 6))) in k 1539426652.581 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426652.581 * [misc]taylor: Taking taylor expansion of 2 in k 1539426652.581 * [misc]backup-simplify: Simplify 2 into 2 1539426652.581 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426652.582 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426652.582 * [misc]taylor: Taking taylor expansion of (* (pow PI 6) (pow k 6)) in k 1539426652.582 * [misc]taylor: Taking taylor expansion of (pow PI 6) in k 1539426652.582 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.582 * [misc]backup-simplify: Simplify PI into PI 1539426652.582 * [misc]taylor: Taking taylor expansion of (pow k 6) in k 1539426652.582 * [misc]taylor: Taking taylor expansion of k in k 1539426652.582 * [misc]backup-simplify: Simplify 0 into 0 1539426652.582 * [misc]backup-simplify: Simplify 1 into 1 1539426652.582 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426652.583 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539426652.583 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426652.583 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426652.584 * [misc]backup-simplify: Simplify (* (pow PI 3) 1) into (pow PI 3) 1539426652.585 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539426652.586 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) 1539426652.587 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))) into (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))) 1539426652.588 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) 1539426652.589 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) 1539426652.594 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (pow PI 3))))) (* (pow (/ 1 k) 3) (pow (/ 1 n) 2))) (+ (* (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (pow PI 2))))) (* (pow (/ 1 k) 2) (/ 1 n))) (* (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) PI)))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 2))) (* n (pow k 2)))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 3))) (* (pow n 2) (pow k 3)))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) PI)) k))))))) 1539426652.594 * [misc]backup-simplify: Simplify (/ (* (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (- (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) into (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) 1539426652.594 * [misc]approximate: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) in (n k) around 0 1539426652.594 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) in k 1539426652.594 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in k 1539426652.594 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1539426652.595 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1539426652.595 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1539426652.595 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426652.595 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426652.595 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.595 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426652.595 * [misc]taylor: Taking taylor expansion of k in k 1539426652.595 * [misc]backup-simplify: Simplify 0 into 0 1539426652.595 * [misc]backup-simplify: Simplify 1 into 1 1539426652.595 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426652.595 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539426652.595 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426652.595 * [misc]taylor: Taking taylor expansion of -2 in k 1539426652.595 * [misc]backup-simplify: Simplify -2 into -2 1539426652.595 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426652.595 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.595 * [misc]backup-simplify: Simplify PI into PI 1539426652.595 * [misc]taylor: Taking taylor expansion of n in k 1539426652.595 * [misc]backup-simplify: Simplify n into n 1539426652.595 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426652.595 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426652.595 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539426652.596 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426652.596 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539426652.596 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1539426652.596 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in k 1539426652.596 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in k 1539426652.596 * [misc]taylor: Taking taylor expansion of (* PI -2) in k 1539426652.596 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.596 * [misc]backup-simplify: Simplify PI into PI 1539426652.596 * [misc]taylor: Taking taylor expansion of -2 in k 1539426652.596 * [misc]backup-simplify: Simplify -2 into -2 1539426652.596 * [misc]taylor: Taking taylor expansion of n in k 1539426652.596 * [misc]backup-simplify: Simplify n into n 1539426652.597 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426652.597 * [misc]backup-simplify: Simplify (/ (* -2 PI) n) into (* -2 (/ PI n)) 1539426652.597 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539426652.597 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 1539426652.598 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (* -2 (/ PI n)) (/ 0 n)))) into 0 1539426652.598 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539426652.598 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426652.598 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426652.598 * [misc]taylor: Taking taylor expansion of -1 in k 1539426652.598 * [misc]backup-simplify: Simplify -1 into -1 1539426652.598 * [misc]taylor: Taking taylor expansion of k in k 1539426652.598 * [misc]backup-simplify: Simplify 0 into 0 1539426652.598 * [misc]backup-simplify: Simplify 1 into 1 1539426652.598 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426652.598 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.599 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426652.599 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) into (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1539426652.599 * [misc]backup-simplify: Simplify (/ (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) +nan.0) into (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) 1539426652.599 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) in n 1539426652.599 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in n 1539426652.599 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1539426652.599 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1539426652.600 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1539426652.600 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426652.600 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.600 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.600 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426652.600 * [misc]taylor: Taking taylor expansion of k in n 1539426652.600 * [misc]backup-simplify: Simplify k into k 1539426652.600 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426652.600 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426652.600 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426652.600 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.600 * [misc]backup-simplify: Simplify -2 into -2 1539426652.600 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.600 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.600 * [misc]backup-simplify: Simplify PI into PI 1539426652.600 * [misc]taylor: Taking taylor expansion of n in n 1539426652.600 * [misc]backup-simplify: Simplify 0 into 0 1539426652.600 * [misc]backup-simplify: Simplify 1 into 1 1539426652.600 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.601 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.601 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426652.601 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426652.602 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.602 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426652.603 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426652.603 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in n 1539426652.603 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in n 1539426652.603 * [misc]taylor: Taking taylor expansion of (* PI -2) in n 1539426652.603 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.603 * [misc]backup-simplify: Simplify PI into PI 1539426652.603 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.603 * [misc]backup-simplify: Simplify -2 into -2 1539426652.603 * [misc]taylor: Taking taylor expansion of n in n 1539426652.603 * [misc]backup-simplify: Simplify 0 into 0 1539426652.603 * [misc]backup-simplify: Simplify 1 into 1 1539426652.603 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426652.604 * [misc]backup-simplify: Simplify (/ (* -2 PI) 1) into (* -2 PI) 1539426652.604 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.605 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426652.605 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539426652.605 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539426652.605 * [misc]taylor: Taking taylor expansion of -1 in n 1539426652.605 * [misc]backup-simplify: Simplify -1 into -1 1539426652.605 * [misc]taylor: Taking taylor expansion of k in n 1539426652.605 * [misc]backup-simplify: Simplify k into k 1539426652.605 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539426652.605 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539426652.605 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539426652.605 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539426652.606 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 1539426652.607 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.608 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426652.610 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426652.610 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426652.611 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426652.611 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.612 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426652.613 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426652.614 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426652.615 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) into (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) 1539426652.615 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) in n 1539426652.615 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in n 1539426652.615 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1539426652.615 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1539426652.615 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1539426652.615 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426652.615 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.615 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.615 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426652.615 * [misc]taylor: Taking taylor expansion of k in n 1539426652.615 * [misc]backup-simplify: Simplify k into k 1539426652.615 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426652.616 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426652.616 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426652.616 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.616 * [misc]backup-simplify: Simplify -2 into -2 1539426652.616 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.616 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.616 * [misc]backup-simplify: Simplify PI into PI 1539426652.616 * [misc]taylor: Taking taylor expansion of n in n 1539426652.616 * [misc]backup-simplify: Simplify 0 into 0 1539426652.616 * [misc]backup-simplify: Simplify 1 into 1 1539426652.616 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.616 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.617 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426652.617 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426652.617 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.618 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426652.619 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426652.619 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in n 1539426652.619 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in n 1539426652.619 * [misc]taylor: Taking taylor expansion of (* PI -2) in n 1539426652.619 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.619 * [misc]backup-simplify: Simplify PI into PI 1539426652.619 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.619 * [misc]backup-simplify: Simplify -2 into -2 1539426652.619 * [misc]taylor: Taking taylor expansion of n in n 1539426652.619 * [misc]backup-simplify: Simplify 0 into 0 1539426652.619 * [misc]backup-simplify: Simplify 1 into 1 1539426652.619 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426652.620 * [misc]backup-simplify: Simplify (/ (* -2 PI) 1) into (* -2 PI) 1539426652.620 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.620 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426652.620 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539426652.620 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539426652.620 * [misc]taylor: Taking taylor expansion of -1 in n 1539426652.621 * [misc]backup-simplify: Simplify -1 into -1 1539426652.621 * [misc]taylor: Taking taylor expansion of k in n 1539426652.621 * [misc]backup-simplify: Simplify k into k 1539426652.621 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539426652.621 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539426652.622 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539426652.622 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539426652.623 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 1539426652.625 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.625 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426652.628 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426652.628 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426652.628 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426652.629 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.629 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426652.631 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426652.632 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426652.633 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) into (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) 1539426652.633 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.633 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.633 * [misc]taylor: Taking taylor expansion of (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.633 * [misc]backup-simplify: Simplify PI into PI 1539426652.633 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426652.633 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.633 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539426652.633 * [misc]taylor: Taking taylor expansion of -2 in k 1539426652.633 * [misc]backup-simplify: Simplify -2 into -2 1539426652.633 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.633 * [misc]backup-simplify: Simplify PI into PI 1539426652.634 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.635 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426652.635 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.635 * [misc]taylor: Taking taylor expansion of n in k 1539426652.635 * [misc]backup-simplify: Simplify n into n 1539426652.635 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.635 * [misc]taylor: Taking taylor expansion of k in k 1539426652.635 * [misc]backup-simplify: Simplify 0 into 0 1539426652.635 * [misc]backup-simplify: Simplify 1 into 1 1539426652.635 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426652.635 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539426652.636 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539426652.636 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539426652.637 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426652.637 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426652.637 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426652.637 * [misc]taylor: Taking taylor expansion of -1 in k 1539426652.637 * [misc]backup-simplify: Simplify -1 into -1 1539426652.637 * [misc]taylor: Taking taylor expansion of k in k 1539426652.637 * [misc]backup-simplify: Simplify 0 into 0 1539426652.637 * [misc]backup-simplify: Simplify 1 into 1 1539426652.637 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426652.638 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.638 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426652.639 * [misc]backup-simplify: Simplify (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539426652.639 * [misc]backup-simplify: Simplify (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) +nan.0) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426652.640 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426652.641 * [misc]backup-simplify: Simplify (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426652.641 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 1539426652.643 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* -2 PI) (/ 0 1)))) into 0 1539426652.644 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539426652.645 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.646 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426652.651 * [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 1539426652.651 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426652.652 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539426652.652 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.653 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1539426652.656 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.658 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426652.660 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) (+ (* (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))))) into (- (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))))) 1539426652.660 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))))) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426652.660 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426652.660 * [misc]taylor: Taking taylor expansion of (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.660 * [misc]backup-simplify: Simplify PI into PI 1539426652.660 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426652.660 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.660 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539426652.660 * [misc]taylor: Taking taylor expansion of -2 in k 1539426652.660 * [misc]backup-simplify: Simplify -2 into -2 1539426652.660 * [misc]taylor: Taking taylor expansion of PI in k 1539426652.660 * [misc]backup-simplify: Simplify PI into PI 1539426652.661 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.661 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426652.661 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426652.661 * [misc]taylor: Taking taylor expansion of n in k 1539426652.661 * [misc]backup-simplify: Simplify n into n 1539426652.661 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426652.661 * [misc]taylor: Taking taylor expansion of k in k 1539426652.661 * [misc]backup-simplify: Simplify 0 into 0 1539426652.661 * [misc]backup-simplify: Simplify 1 into 1 1539426652.661 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426652.662 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539426652.662 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539426652.663 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539426652.664 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426652.664 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426652.664 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426652.664 * [misc]taylor: Taking taylor expansion of -1 in k 1539426652.664 * [misc]backup-simplify: Simplify -1 into -1 1539426652.664 * [misc]taylor: Taking taylor expansion of k in k 1539426652.664 * [misc]backup-simplify: Simplify 0 into 0 1539426652.664 * [misc]backup-simplify: Simplify 1 into 1 1539426652.664 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426652.664 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426652.665 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426652.665 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426652.666 * [misc]backup-simplify: Simplify (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539426652.667 * [misc]backup-simplify: Simplify (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) +nan.0) into (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426652.667 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426652.668 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426652.669 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426652.670 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into 0 1539426652.671 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539426652.672 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539426652.673 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426652.674 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* 0 (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426652.675 * [misc]backup-simplify: Simplify (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426652.678 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (+ (* (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* 1 (/ 1 (- n)))) (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI)) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow PI 2)) n))))))) 1539426652.678 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1) 1539426652.678 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) 1/2) into (pow (* 2 (* n PI)) 1/2) 1539426652.678 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) 1/2) in (n) around 0 1539426652.678 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) 1/2) in n 1539426652.678 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* 2 (* n PI))))) in n 1539426652.678 * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* 2 (* n PI)))) in n 1539426652.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.678 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426652.678 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426652.678 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.678 * [misc]backup-simplify: Simplify 2 into 2 1539426652.678 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.679 * [misc]taylor: Taking taylor expansion of n in n 1539426652.679 * [misc]backup-simplify: Simplify 0 into 0 1539426652.679 * [misc]backup-simplify: Simplify 1 into 1 1539426652.679 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.679 * [misc]backup-simplify: Simplify PI into PI 1539426652.679 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426652.679 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426652.680 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426652.680 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426652.681 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.682 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.682 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1539426652.683 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539426652.683 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) 1/2) in n 1539426652.683 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* 2 (* n PI))))) in n 1539426652.683 * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* 2 (* n PI)))) in n 1539426652.683 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.683 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.683 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426652.683 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426652.683 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.683 * [misc]backup-simplify: Simplify 2 into 2 1539426652.683 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426652.683 * [misc]taylor: Taking taylor expansion of n in n 1539426652.683 * [misc]backup-simplify: Simplify 0 into 0 1539426652.683 * [misc]backup-simplify: Simplify 1 into 1 1539426652.683 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.683 * [misc]backup-simplify: Simplify PI into PI 1539426652.683 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426652.684 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426652.684 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426652.685 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426652.685 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.686 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.687 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1539426652.687 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539426652.688 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539426652.689 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426652.690 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426652.693 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426652.694 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.694 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539426652.696 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426652.696 * [misc]backup-simplify: Simplify 0 into 0 1539426652.697 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.698 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426652.701 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1539426652.701 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.702 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539426652.703 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.703 * [misc]backup-simplify: Simplify 0 into 0 1539426652.704 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.705 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426652.710 * [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 1539426652.710 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.711 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1539426652.713 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426652.713 * [misc]backup-simplify: Simplify 0 into 0 1539426652.715 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.716 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539426652.723 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 1539426652.724 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.725 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))) into 0 1539426652.731 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.731 * [misc]backup-simplify: Simplify 0 into 0 1539426652.734 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.738 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539426652.755 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 1539426652.755 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.756 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))))) into 0 1539426652.762 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426652.762 * [misc]backup-simplify: Simplify 0 into 0 1539426652.764 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539426652.767 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539426652.788 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 1539426652.789 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426652.790 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))))) into 0 1539426652.804 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.804 * [misc]backup-simplify: Simplify 0 into 0 1539426652.805 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539426652.805 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 n) 2)) 1/2) into (pow (* 2 (/ PI n)) 1/2) 1539426652.805 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) 1/2) in (n) around 0 1539426652.805 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) 1/2) in n 1539426652.805 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* 2 (/ PI n))))) in n 1539426652.805 * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* 2 (/ PI n)))) in n 1539426652.805 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.805 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.805 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426652.805 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426652.805 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.805 * [misc]backup-simplify: Simplify 2 into 2 1539426652.805 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.805 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.805 * [misc]backup-simplify: Simplify PI into PI 1539426652.805 * [misc]taylor: Taking taylor expansion of n in n 1539426652.805 * [misc]backup-simplify: Simplify 0 into 0 1539426652.805 * [misc]backup-simplify: Simplify 1 into 1 1539426652.806 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.806 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.806 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.807 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.807 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539426652.808 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 1539426652.808 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) 1/2) in n 1539426652.808 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* 2 (/ PI n))))) in n 1539426652.808 * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* 2 (/ PI n)))) in n 1539426652.808 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.808 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.808 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426652.808 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426652.808 * [misc]taylor: Taking taylor expansion of 2 in n 1539426652.808 * [misc]backup-simplify: Simplify 2 into 2 1539426652.808 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.808 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.808 * [misc]backup-simplify: Simplify PI into PI 1539426652.808 * [misc]taylor: Taking taylor expansion of n in n 1539426652.808 * [misc]backup-simplify: Simplify 0 into 0 1539426652.808 * [misc]backup-simplify: Simplify 1 into 1 1539426652.808 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.808 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426652.809 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426652.809 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.809 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539426652.810 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 1539426652.810 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 1539426652.811 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.811 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426652.813 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426652.813 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.814 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539426652.815 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426652.815 * [misc]backup-simplify: Simplify 0 into 0 1539426652.816 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.816 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426652.819 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1539426652.819 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.820 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539426652.821 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.821 * [misc]backup-simplify: Simplify 0 into 0 1539426652.822 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.823 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.828 * [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 1539426652.828 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.829 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539426652.831 * [misc]backup-simplify: Simplify (* (exp (* 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 1539426652.831 * [misc]backup-simplify: Simplify 0 into 0 1539426652.833 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.835 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.848 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 1539426652.848 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.849 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 1539426652.852 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.852 * [misc]backup-simplify: Simplify 0 into 0 1539426652.853 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.855 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.867 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 1539426652.867 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.868 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 1539426652.873 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426652.873 * [misc]backup-simplify: Simplify 0 into 0 1539426652.875 * [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 1539426652.877 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426652.901 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 1539426652.901 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426652.903 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 1539426652.915 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.915 * [misc]backup-simplify: Simplify 0 into 0 1539426652.916 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) 1539426652.916 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 (- n)) 2)) 1/2) into (pow (* -2 (/ PI n)) 1/2) 1539426652.916 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) 1/2) in (n) around 0 1539426652.916 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) 1/2) in n 1539426652.916 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* -2 (/ PI n))))) in n 1539426652.916 * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* -2 (/ PI n)))) in n 1539426652.916 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.916 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.916 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426652.916 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426652.916 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.916 * [misc]backup-simplify: Simplify -2 into -2 1539426652.916 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.916 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.916 * [misc]backup-simplify: Simplify PI into PI 1539426652.917 * [misc]taylor: Taking taylor expansion of n in n 1539426652.917 * [misc]backup-simplify: Simplify 0 into 0 1539426652.917 * [misc]backup-simplify: Simplify 1 into 1 1539426652.917 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.917 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.918 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426652.918 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.919 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539426652.919 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) 1539426652.919 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) 1/2) in n 1539426652.919 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* -2 (/ PI n))))) in n 1539426652.919 * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* -2 (/ PI n)))) in n 1539426652.919 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426652.919 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426652.919 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426652.919 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426652.919 * [misc]taylor: Taking taylor expansion of -2 in n 1539426652.919 * [misc]backup-simplify: Simplify -2 into -2 1539426652.920 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426652.920 * [misc]taylor: Taking taylor expansion of PI in n 1539426652.920 * [misc]backup-simplify: Simplify PI into PI 1539426652.920 * [misc]taylor: Taking taylor expansion of n in n 1539426652.920 * [misc]backup-simplify: Simplify 0 into 0 1539426652.920 * [misc]backup-simplify: Simplify 1 into 1 1539426652.920 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426652.920 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426652.921 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426652.921 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.922 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539426652.922 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) 1539426652.923 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) 1539426652.924 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426652.924 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426652.927 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426652.928 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.928 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426652.930 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426652.930 * [misc]backup-simplify: Simplify 0 into 0 1539426652.931 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.932 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426652.937 * [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 1539426652.937 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.938 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1539426652.940 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.940 * [misc]backup-simplify: Simplify 0 into 0 1539426652.942 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.943 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426652.951 * [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 1539426652.951 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.953 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1539426652.956 * [misc]backup-simplify: Simplify (* (exp (* 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 1539426652.956 * [misc]backup-simplify: Simplify 0 into 0 1539426652.958 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.960 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426652.967 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0 1539426652.968 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.968 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0 1539426652.972 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426652.972 * [misc]backup-simplify: Simplify 0 into 0 1539426652.973 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426652.975 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426652.986 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0 1539426652.987 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426652.988 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0 1539426652.997 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426652.997 * [misc]backup-simplify: Simplify 0 into 0 1539426653.000 * [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 1539426653.004 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426653.037 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0 1539426653.037 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426653.039 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0 1539426653.052 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426653.053 * [misc]backup-simplify: Simplify 0 into 0 1539426653.053 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) 1539426653.053 * * * [misc]progress: simplifying candidates 1539426653.054 * * * * [misc]progress: [ 1 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 2 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 3 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 4 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 5 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 6 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 7 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 8 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 9 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 10 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 11 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 12 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 13 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 14 / 82 ] simplifiying candidate # 1539426653.054 * * * * [misc]progress: [ 15 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 16 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 17 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 18 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 19 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 20 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 21 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 22 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 23 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 24 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 25 / 82 ] simplifiying candidate # 1539426653.055 * * * * [misc]progress: [ 26 / 82 ] simplifiying candidate # 1539426653.056 * [enter]simplify: Simplifying (- (+ (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (- (/ k 2)))) (log (sqrt k))) 1539426653.056 * * [misc]simplify: iters left: 6 (16 enodes) 1539426653.061 * * [misc]simplify: iters left: 5 (37 enodes) 1539426653.075 * * [misc]simplify: iters left: 4 (91 enodes) 1539426653.115 * * [misc]simplify: iters left: 3 (254 enodes) 1539426653.289 * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1539426653.289 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1539426653.289 * * * * [misc]progress: [ 27 / 82 ] simplifiying candidate # 1539426653.290 * [enter]simplify: Simplifying (- (+ (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (- (/ k 2)))) (log (sqrt k))) 1539426653.290 * * [misc]simplify: iters left: 6 (16 enodes) 1539426653.295 * * [misc]simplify: iters left: 5 (37 enodes) 1539426653.309 * * [misc]simplify: iters left: 4 (91 enodes) 1539426653.350 * * [misc]simplify: iters left: 3 (254 enodes) 1539426653.495 * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1539426653.495 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1539426653.495 * * * * [misc]progress: [ 28 / 82 ] simplifiying candidate # 1539426653.495 * [enter]simplify: Simplifying (- (+ (* (log (* PI (* n 2))) 1/2) (log (pow (* PI (* n 2)) (- (/ k 2))))) (log (sqrt k))) 1539426653.495 * * [misc]simplify: iters left: 6 (17 enodes) 1539426653.501 * * [misc]simplify: iters left: 5 (34 enodes) 1539426653.512 * * [misc]simplify: iters left: 4 (79 enodes) 1539426653.545 * * [misc]simplify: iters left: 3 (220 enodes) 1539426653.682 * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1539426653.682 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1539426653.682 * * * * [misc]progress: [ 29 / 82 ] simplifiying candidate # 1539426653.683 * [enter]simplify: Simplifying (- (+ (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (- (/ k 2)))) (log (sqrt k))) 1539426653.683 * * [misc]simplify: iters left: 6 (16 enodes) 1539426653.688 * * [misc]simplify: iters left: 5 (37 enodes) 1539426653.697 * * [misc]simplify: iters left: 4 (91 enodes) 1539426653.717 * * [misc]simplify: iters left: 3 (254 enodes) 1539426653.839 * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1539426653.839 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1539426653.839 * * * * [misc]progress: [ 30 / 82 ] simplifiying candidate # 1539426653.839 * [enter]simplify: Simplifying (- (+ (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (- (/ k 2)))) (log (sqrt k))) 1539426653.839 * * [misc]simplify: iters left: 6 (16 enodes) 1539426653.842 * * [misc]simplify: iters left: 5 (37 enodes) 1539426653.854 * * [misc]simplify: iters left: 4 (91 enodes) 1539426653.878 * * [misc]simplify: iters left: 3 (254 enodes) 1539426654.019 * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1539426654.019 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1539426654.019 * * * * [misc]progress: [ 31 / 82 ] simplifiying candidate # 1539426654.019 * [enter]simplify: Simplifying (- (+ (* (log (* PI (* n 2))) 1/2) (log (pow (* PI (* n 2)) (- (/ k 2))))) (log (sqrt k))) 1539426654.020 * * [misc]simplify: iters left: 6 (17 enodes) 1539426654.025 * * [misc]simplify: iters left: 5 (34 enodes) 1539426654.037 * * [misc]simplify: iters left: 4 (79 enodes) 1539426654.070 * * [misc]simplify: iters left: 3 (220 enodes) 1539426654.160 * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) 1539426654.160 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) 1539426654.160 * * * * [misc]progress: [ 32 / 82 ] simplifiying candidate # 1539426654.160 * [enter]simplify: Simplifying (- (+ (log (pow (* PI (* n 2)) 1/2)) (* (log (* PI (* n 2))) (- (/ k 2)))) (log (sqrt k))) 1539426654.160 * * [misc]simplify: iters left: 6 (17 enodes) 1539426654.166 * * [misc]simplify: iters left: 5 (36 enodes) 1539426654.176 * * [misc]simplify: iters left: 4 (89 enodes) 1539426654.197 * * [misc]simplify: iters left: 3 (250 enodes) 1539426654.309 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1539426654.309 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1539426654.309 * * * * [misc]progress: [ 33 / 82 ] simplifiying candidate # 1539426654.309 * [enter]simplify: Simplifying (- (+ (log (pow (* PI (* n 2)) 1/2)) (* (log (* PI (* n 2))) (- (/ k 2)))) (log (sqrt k))) 1539426654.309 * * [misc]simplify: iters left: 6 (17 enodes) 1539426654.312 * * [misc]simplify: iters left: 5 (36 enodes) 1539426654.318 * * [misc]simplify: iters left: 4 (89 enodes) 1539426654.339 * * [misc]simplify: iters left: 3 (250 enodes) 1539426654.443 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1539426654.443 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1539426654.443 * * * * [misc]progress: [ 34 / 82 ] simplifiying candidate # 1539426654.443 * [enter]simplify: Simplifying (- (+ (log (pow (* PI (* n 2)) 1/2)) (log (pow (* PI (* n 2)) (- (/ k 2))))) (log (sqrt k))) 1539426654.444 * * [misc]simplify: iters left: 6 (17 enodes) 1539426654.449 * * [misc]simplify: iters left: 5 (32 enodes) 1539426654.458 * * [misc]simplify: iters left: 4 (67 enodes) 1539426654.486 * * [misc]simplify: iters left: 3 (166 enodes) 1539426654.559 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1539426654.559 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1539426654.559 * * * * [misc]progress: [ 35 / 82 ] simplifiying candidate # 1539426654.559 * [enter]simplify: Simplifying (- (log (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))) (log (sqrt k))) 1539426654.559 * * [misc]simplify: iters left: 6 (16 enodes) 1539426654.562 * * [misc]simplify: iters left: 5 (29 enodes) 1539426654.568 * * [misc]simplify: iters left: 4 (44 enodes) 1539426654.575 * * [misc]simplify: iters left: 3 (81 enodes) 1539426654.599 * * [misc]simplify: iters left: 2 (219 enodes) 1539426655.077 * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) 1539426655.077 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) 1539426655.077 * * * * [misc]progress: [ 36 / 82 ] simplifiying candidate # 1539426655.077 * * * * [misc]progress: [ 37 / 82 ] simplifiying candidate # 1539426655.078 * * * * [misc]progress: [ 38 / 82 ] simplifiying candidate # 1539426655.078 * [enter]simplify: Simplifying (/ (* (* (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) 1/2)) (* (* (pow (* PI (* n 2)) (- (/ k 2))) (pow (* PI (* n 2)) (- (/ k 2)))) (pow (* PI (* n 2)) (- (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1539426655.078 * * [misc]simplify: iters left: 6 (20 enodes) 1539426655.081 * * [misc]simplify: iters left: 5 (42 enodes) 1539426655.095 * * [misc]simplify: iters left: 4 (131 enodes) 1539426655.155 * * [misc]simplify: iters left: 3 (470 enodes) 1539426655.557 * [exit]simplify: Simplified to (* (pow (pow (* (* 2 n) PI) (/ (- k) 2)) 3) (* (/ (* (* 2 n) PI) (* k (sqrt k))) (sqrt (* (* 2 n) PI)))) 1539426655.557 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (pow (pow (* (* 2 n) PI) (/ (- k) 2)) 3) (* (/ (* (* 2 n) PI) (* k (sqrt k))) (sqrt (* (* 2 n) PI)))))) 1539426655.558 * * * * [misc]progress: [ 39 / 82 ] simplifiying candidate # 1539426655.558 * [enter]simplify: Simplifying (/ (* (* (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1539426655.558 * * [misc]simplify: iters left: 6 (18 enodes) 1539426655.561 * * [misc]simplify: iters left: 5 (41 enodes) 1539426655.573 * * [misc]simplify: iters left: 4 (112 enodes) 1539426655.607 * * [misc]simplify: iters left: 3 (360 enodes) 1539426655.955 * [exit]simplify: Simplified to (* (/ (* (pow (* (* 2 n) PI) (/ (- k) 2)) (sqrt (* (* 2 n) PI))) (/ (sqrt k) (pow (* (* 2 n) PI) (/ (- k) 2)))) (/ (* (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ (- k) 2))) k)) 1539426655.955 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (* (pow (* (* 2 n) PI) (/ (- k) 2)) (sqrt (* (* 2 n) PI))) (/ (sqrt k) (pow (* (* 2 n) PI) (/ (- k) 2)))) (/ (* (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ (- k) 2))) k)))) 1539426655.955 * * * * [misc]progress: [ 40 / 82 ] simplifiying candidate # 1539426655.956 * * * * [misc]progress: [ 41 / 82 ] simplifiying candidate # 1539426655.956 * * * * [misc]progress: [ 42 / 82 ] simplifiying candidate # 1539426655.956 * * * * [misc]progress: [ 43 / 82 ] simplifiying candidate # 1539426655.956 * * * * [misc]progress: [ 44 / 82 ] simplifiying candidate # 1539426655.956 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426655.956 * * [misc]simplify: iters left: 6 (12 enodes) 1539426655.960 * * [misc]simplify: iters left: 5 (19 enodes) 1539426655.965 * * [misc]simplify: iters left: 4 (25 enodes) 1539426655.972 * * [misc]simplify: iters left: 3 (26 enodes) 1539426655.978 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539426655.978 * [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))))) 1539426655.978 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1539426655.978 * * [misc]simplify: iters left: 6 (12 enodes) 1539426655.982 * * [misc]simplify: iters left: 5 (18 enodes) 1539426655.987 * * [misc]simplify: iters left: 4 (24 enodes) 1539426655.994 * * [misc]simplify: iters left: 3 (25 enodes) 1539426656.000 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1539426656.000 * [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))))) 1539426656.000 * * * * [misc]progress: [ 45 / 82 ] simplifiying candidate # 1539426656.000 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1539426656.000 * * [misc]simplify: iters left: 6 (11 enodes) 1539426656.002 * * [misc]simplify: iters left: 5 (16 enodes) 1539426656.004 * * [misc]simplify: iters left: 4 (22 enodes) 1539426656.007 * * [misc]simplify: iters left: 3 (24 enodes) 1539426656.010 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1539426656.010 * [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))))) 1539426656.010 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1539426656.010 * * [misc]simplify: iters left: 6 (12 enodes) 1539426656.012 * * [misc]simplify: iters left: 5 (18 enodes) 1539426656.014 * * [misc]simplify: iters left: 4 (24 enodes) 1539426656.017 * * [misc]simplify: iters left: 3 (25 enodes) 1539426656.020 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1539426656.020 * [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))))) 1539426656.020 * * * * [misc]progress: [ 46 / 82 ] simplifiying candidate # 1539426656.021 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1539426656.021 * * [misc]simplify: iters left: 6 (9 enodes) 1539426656.022 * * [misc]simplify: iters left: 5 (16 enodes) 1539426656.024 * * [misc]simplify: iters left: 4 (24 enodes) 1539426656.027 * * [misc]simplify: iters left: 3 (26 enodes) 1539426656.030 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1539426656.030 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426656.030 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1539426656.030 * * [misc]simplify: iters left: 6 (11 enodes) 1539426656.032 * * [misc]simplify: iters left: 5 (17 enodes) 1539426656.034 * * [misc]simplify: iters left: 4 (23 enodes) 1539426656.037 * * [misc]simplify: iters left: 3 (24 enodes) 1539426656.041 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1539426656.041 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1539426656.041 * * * * [misc]progress: [ 47 / 82 ] simplifiying candidate # 1539426656.041 * * * * [misc]progress: [ 48 / 82 ] simplifiying candidate # 1539426656.041 * * * * [misc]progress: [ 49 / 82 ] simplifiying candidate # 1539426656.041 * * * * [misc]progress: [ 50 / 82 ] simplifiying candidate # 1539426656.041 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1539426656.041 * * [misc]simplify: iters left: 2 (3 enodes) 1539426656.041 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1539426656.041 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) 1539426656.042 * * * * [misc]progress: [ 51 / 82 ] simplifiying candidate # 1539426656.042 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1539426656.042 * * [misc]simplify: iters left: 2 (3 enodes) 1539426656.042 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1539426656.042 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1539426656.042 * * * * [misc]progress: [ 52 / 82 ] simplifiying candidate # 1539426656.042 * [enter]simplify: Simplifying (sqrt k) 1539426656.042 * * [misc]simplify: iters left: 1 (2 enodes) 1539426656.043 * [exit]simplify: Simplified to (sqrt k) 1539426656.043 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) 1) (sqrt k))) 1539426656.043 * * * * [misc]progress: [ 53 / 82 ] simplifiying candidate # 1539426656.043 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1539426656.043 * * [misc]simplify: iters left: 5 (7 enodes) 1539426656.044 * * [misc]simplify: iters left: 4 (12 enodes) 1539426656.045 * * [misc]simplify: iters left: 3 (18 enodes) 1539426656.048 * * [misc]simplify: iters left: 2 (20 enodes) 1539426656.050 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539426656.050 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426656.050 * * * * [misc]progress: [ 54 / 82 ] simplifiying candidate # 1539426656.050 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1539426656.050 * * [misc]simplify: iters left: 5 (7 enodes) 1539426656.051 * * [misc]simplify: iters left: 4 (12 enodes) 1539426656.053 * * [misc]simplify: iters left: 3 (18 enodes) 1539426656.055 * * [misc]simplify: iters left: 2 (20 enodes) 1539426656.060 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539426656.060 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539426656.060 * * * * [misc]progress: [ 55 / 82 ] simplifiying candidate # 1539426656.060 * [enter]simplify: Simplifying (* (pow (* PI (* n 2)) 1/2) 1) 1539426656.060 * * [misc]simplify: iters left: 6 (9 enodes) 1539426656.063 * * [misc]simplify: iters left: 5 (17 enodes) 1539426656.068 * * [misc]simplify: iters left: 4 (26 enodes) 1539426656.073 * * [misc]simplify: iters left: 3 (27 enodes) 1539426656.078 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539426656.078 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539426656.078 * * * * [misc]progress: [ 56 / 82 ] simplifiying candidate # 1539426656.079 * [enter]simplify: Simplifying (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) 0)) 1539426656.079 * * [misc]simplify: iters left: 6 (10 enodes) 1539426656.082 * * [misc]simplify: iters left: 5 (17 enodes) 1539426656.086 * * [misc]simplify: iters left: 4 (24 enodes) 1539426656.092 * * [misc]simplify: iters left: 3 (29 enodes) 1539426656.095 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539426656.095 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539426656.095 * * * * [misc]progress: [ 57 / 82 ] simplifiying candidate # 1539426656.095 * * * * [misc]progress: [ 58 / 82 ] simplifiying candidate # 1539426656.095 * * * * [misc]progress: [ 59 / 82 ] simplifiying candidate # 1539426656.095 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) 1/2) 1539426656.095 * * [misc]simplify: iters left: 6 (8 enodes) 1539426656.096 * * [misc]simplify: iters left: 5 (16 enodes) 1539426656.099 * * [misc]simplify: iters left: 4 (33 enodes) 1539426656.105 * * [misc]simplify: iters left: 3 (62 enodes) 1539426656.114 * * [misc]simplify: iters left: 2 (93 enodes) 1539426656.137 * * [misc]simplify: iters left: 1 (115 enodes) 1539426656.153 * [exit]simplify: Simplified to (fma 1/2 (log (* 2 n)) (* 1/2 (log PI))) 1539426656.153 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (exp (fma 1/2 (log (* 2 n)) (* 1/2 (log PI)))) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.154 * * * * [misc]progress: [ 60 / 82 ] simplifiying candidate # 1539426656.154 * * * * [misc]progress: [ 61 / 82 ] simplifiying candidate # 1539426656.154 * [enter]simplify: Simplifying (* PI (* n 2)) 1539426656.154 * * [misc]simplify: iters left: 4 (5 enodes) 1539426656.155 * * [misc]simplify: iters left: 3 (9 enodes) 1539426656.156 * * [misc]simplify: iters left: 2 (15 enodes) 1539426656.158 * * [misc]simplify: iters left: 1 (17 enodes) 1539426656.160 * [exit]simplify: Simplified to (* (* 2 n) PI) 1539426656.160 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (pow (* (* 2 n) PI) (* 1 1/2)) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.160 * * * * [misc]progress: [ 62 / 82 ] simplifiying candidate # 1539426656.160 * [enter]simplify: Simplifying (pow PI 1/2) 1539426656.160 * * [misc]simplify: iters left: 1 (3 enodes) 1539426656.160 * [exit]simplify: Simplified to (sqrt PI) 1539426656.160 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (* (sqrt PI) (pow (* n 2) 1/2)) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.160 * * * * [misc]progress: [ 63 / 82 ] simplifiying candidate # 1539426656.160 * * * * [misc]progress: [ 64 / 82 ] simplifiying candidate # 1539426656.160 * * * * [misc]progress: [ 65 / 82 ] simplifiying candidate # 1539426656.160 * * * * [misc]progress: [ 66 / 82 ] simplifiying candidate # 1539426656.161 * * * * [misc]progress: [ 67 / 82 ] simplifiying candidate # 1539426656.161 * * * * [misc]progress: [ 68 / 82 ] simplifiying candidate # 1539426656.161 * * * * [misc]progress: [ 69 / 82 ] simplifiying candidate # 1539426656.161 * * * * [misc]progress: [ 70 / 82 ] simplifiying candidate # 1539426656.161 * * * * [misc]progress: [ 71 / 82 ] simplifiying candidate # 1539426656.161 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426656.161 * * [misc]simplify: iters left: 4 (5 enodes) 1539426656.162 * * [misc]simplify: iters left: 3 (9 enodes) 1539426656.163 * * [misc]simplify: iters left: 2 (15 enodes) 1539426656.165 * * [misc]simplify: iters left: 1 (17 enodes) 1539426656.167 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426656.167 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1539426656.167 * * * * [misc]progress: [ 72 / 82 ] simplifiying candidate # 1539426656.167 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426656.167 * * [misc]simplify: iters left: 4 (5 enodes) 1539426656.168 * * [misc]simplify: iters left: 3 (9 enodes) 1539426656.169 * * [misc]simplify: iters left: 2 (15 enodes) 1539426656.171 * * [misc]simplify: iters left: 1 (17 enodes) 1539426656.173 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426656.173 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1539426656.173 * * * * [misc]progress: [ 73 / 82 ] simplifiying candidate # 1539426656.173 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426656.173 * * [misc]simplify: iters left: 4 (5 enodes) 1539426656.174 * * [misc]simplify: iters left: 3 (9 enodes) 1539426656.176 * * [misc]simplify: iters left: 2 (15 enodes) 1539426656.177 * * [misc]simplify: iters left: 1 (17 enodes) 1539426656.179 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426656.180 * [misc]simplify: Simplified (2 1 2 1) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1539426656.180 * * * * [misc]progress: [ 74 / 82 ] simplifiying candidate # 1539426656.180 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426656.180 * * [misc]simplify: iters left: 4 (5 enodes) 1539426656.182 * * [misc]simplify: iters left: 3 (9 enodes) 1539426656.184 * * [misc]simplify: iters left: 2 (15 enodes) 1539426656.188 * * [misc]simplify: iters left: 1 (17 enodes) 1539426656.192 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426656.192 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.192 * * * * [misc]progress: [ 75 / 82 ] simplifiying candidate # 1539426656.192 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426656.192 * * [misc]simplify: iters left: 4 (5 enodes) 1539426656.194 * * [misc]simplify: iters left: 3 (9 enodes) 1539426656.197 * * [misc]simplify: iters left: 2 (15 enodes) 1539426656.200 * * [misc]simplify: iters left: 1 (17 enodes) 1539426656.204 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426656.204 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.204 * * * * [misc]progress: [ 76 / 82 ] simplifiying candidate # 1539426656.205 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426656.205 * * [misc]simplify: iters left: 4 (5 enodes) 1539426656.206 * * [misc]simplify: iters left: 3 (9 enodes) 1539426656.209 * * [misc]simplify: iters left: 2 (15 enodes) 1539426656.213 * * [misc]simplify: iters left: 1 (17 enodes) 1539426656.216 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426656.217 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (* (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.217 * * * * [misc]progress: [ 77 / 82 ] simplifiying candidate # 1539426656.217 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log n)))) k)) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log (* 2 PI))))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) 1539426656.217 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426656.217 * * * * [misc]progress: [ 78 / 82 ] simplifiying candidate # 1539426656.217 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 2))) (* n (pow k 2)))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 3))) (* (pow n 2) (pow k 3)))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) PI)) k))))))) 1539426656.217 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426656.217 * * * * [misc]progress: [ 79 / 82 ] simplifiying candidate # 1539426656.218 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI)) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow PI 2)) n))))))) 1539426656.218 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426656.218 * * * * [misc]progress: [ 80 / 82 ] simplifiying candidate # 1539426656.218 * [enter]simplify: Simplifying (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539426656.218 * * [misc]simplify: iters left: 6 (10 enodes) 1539426656.222 * * [misc]simplify: iters left: 5 (24 enodes) 1539426656.231 * * [misc]simplify: iters left: 4 (45 enodes) 1539426656.245 * * [misc]simplify: iters left: 3 (91 enodes) 1539426656.276 * * [misc]simplify: iters left: 2 (155 enodes) 1539426656.296 * * [misc]simplify: iters left: 1 (189 enodes) 1539426656.317 * [exit]simplify: Simplified to (sqrt (* 2 (* PI n))) 1539426656.317 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (* 2 (* PI n))) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.318 * * * * [misc]progress: [ 81 / 82 ] simplifiying candidate # 1539426656.318 * [enter]simplify: Simplifying (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) 1539426656.318 * * [misc]simplify: iters left: 6 (12 enodes) 1539426656.323 * * [misc]simplify: iters left: 5 (27 enodes) 1539426656.327 * * [misc]simplify: iters left: 4 (39 enodes) 1539426656.333 * * [misc]simplify: iters left: 3 (73 enodes) 1539426656.348 * * [misc]simplify: iters left: 2 (158 enodes) 1539426656.424 * * [misc]simplify: iters left: 1 (399 enodes) 1539426656.829 * [exit]simplify: Simplified to (sqrt (* (* n PI) 2)) 1539426656.829 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (* (* n PI) 2)) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.829 * * * * [misc]progress: [ 82 / 82 ] simplifiying candidate # 1539426656.829 * [enter]simplify: Simplifying (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) 1539426656.829 * * [misc]simplify: iters left: 6 (12 enodes) 1539426656.834 * * [misc]simplify: iters left: 5 (24 enodes) 1539426656.842 * * [misc]simplify: iters left: 4 (40 enodes) 1539426656.857 * * [misc]simplify: iters left: 3 (89 enodes) 1539426656.895 * * [misc]simplify: iters left: 2 (242 enodes) 1539426656.995 * [exit]simplify: Simplified to (* (sqrt (* PI -2)) (pow (/ -1 n) -1/2)) 1539426656.995 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (* (sqrt (* PI -2)) (pow (/ -1 n) -1/2)) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426656.996 * * * [misc]progress: adding candidates to table 1539426657.969 * * [misc]progress: iteration 3 / 4 1539426657.969 * * * [misc]progress: picking best candidate 1539426658.005 * * * * [misc]pick: Picked # 1539426658.005 * * * [misc]progress: localizing error 1539426658.024 * * * [misc]progress: generating rewritten candidates 1539426658.024 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2) 1539426658.035 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1) 1539426658.037 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1 1) 1539426658.040 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1) 1539426658.041 * * * [misc]progress: generating series expansions 1539426658.041 * * * * [misc]progress: [ 1 / 4 ] generating series at (2) 1539426658.042 * [misc]backup-simplify: Simplify (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) into (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) 1539426658.042 * [misc]approximate: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in (n k) around 0 1539426658.042 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in k 1539426658.042 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in k 1539426658.042 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.042 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.042 * [misc]backup-simplify: Simplify 2 into 2 1539426658.042 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.042 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.042 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1539426658.042 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539426658.042 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539426658.042 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1539426658.042 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426658.042 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426658.042 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.042 * [misc]taylor: Taking taylor expansion of k in k 1539426658.043 * [misc]backup-simplify: Simplify 0 into 0 1539426658.043 * [misc]backup-simplify: Simplify 1 into 1 1539426658.043 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539426658.043 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539426658.043 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.043 * [misc]backup-simplify: Simplify 2 into 2 1539426658.043 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426658.043 * [misc]taylor: Taking taylor expansion of n in k 1539426658.043 * [misc]backup-simplify: Simplify n into n 1539426658.043 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.043 * [misc]backup-simplify: Simplify PI into PI 1539426658.043 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426658.043 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539426658.043 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539426658.043 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426658.043 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.043 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539426658.043 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.043 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539426658.044 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539426658.044 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539426658.044 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539426658.044 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426658.044 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1539426658.044 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426658.044 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1539426658.044 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in k 1539426658.045 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426658.045 * [misc]taylor: Taking taylor expansion of n in k 1539426658.045 * [misc]backup-simplify: Simplify n into n 1539426658.045 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.045 * [misc]backup-simplify: Simplify PI into PI 1539426658.045 * [misc]taylor: Taking taylor expansion of k in k 1539426658.045 * [misc]backup-simplify: Simplify 0 into 0 1539426658.045 * [misc]backup-simplify: Simplify 1 into 1 1539426658.045 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426658.045 * [misc]backup-simplify: Simplify (/ (* n PI) 1) into (* n PI) 1539426658.045 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.045 * [misc]backup-simplify: Simplify (/ (* n PI) (* 2 (sqrt 0))) into (* +nan.0 (* n PI)) 1539426658.045 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.045 * [misc]backup-simplify: Simplify 2 into 2 1539426658.045 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.045 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.045 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426658.045 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.045 * [misc]taylor: Taking taylor expansion of k in n 1539426658.045 * [misc]backup-simplify: Simplify k into k 1539426658.045 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426658.045 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.045 * [misc]backup-simplify: Simplify 2 into 2 1539426658.046 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.046 * [misc]taylor: Taking taylor expansion of n in n 1539426658.046 * [misc]backup-simplify: Simplify 0 into 0 1539426658.046 * [misc]backup-simplify: Simplify 1 into 1 1539426658.046 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.046 * [misc]backup-simplify: Simplify PI into PI 1539426658.046 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426658.046 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426658.046 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426658.047 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426658.047 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.047 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426658.047 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426658.048 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426658.048 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539426658.049 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539426658.049 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1539426658.049 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1539426658.049 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.049 * [misc]taylor: Taking taylor expansion of n in n 1539426658.049 * [misc]backup-simplify: Simplify 0 into 0 1539426658.049 * [misc]backup-simplify: Simplify 1 into 1 1539426658.049 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.049 * [misc]backup-simplify: Simplify PI into PI 1539426658.049 * [misc]taylor: Taking taylor expansion of k in n 1539426658.049 * [misc]backup-simplify: Simplify k into k 1539426658.049 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426658.050 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426658.050 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1539426658.050 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.050 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1539426658.050 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in n 1539426658.050 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.051 * [misc]backup-simplify: Simplify 2 into 2 1539426658.051 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.051 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.051 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426658.051 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.051 * [misc]taylor: Taking taylor expansion of k in n 1539426658.051 * [misc]backup-simplify: Simplify k into k 1539426658.051 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.051 * [misc]backup-simplify: Simplify 2 into 2 1539426658.051 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.051 * [misc]taylor: Taking taylor expansion of n in n 1539426658.051 * [misc]backup-simplify: Simplify 0 into 0 1539426658.051 * [misc]backup-simplify: Simplify 1 into 1 1539426658.051 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.051 * [misc]backup-simplify: Simplify PI into PI 1539426658.052 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426658.052 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426658.053 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426658.053 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426658.054 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.054 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426658.054 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426658.054 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426658.055 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539426658.056 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539426658.056 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1539426658.056 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1539426658.056 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.056 * [misc]taylor: Taking taylor expansion of n in n 1539426658.056 * [misc]backup-simplify: Simplify 0 into 0 1539426658.056 * [misc]backup-simplify: Simplify 1 into 1 1539426658.056 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.056 * [misc]backup-simplify: Simplify PI into PI 1539426658.056 * [misc]taylor: Taking taylor expansion of k in n 1539426658.056 * [misc]backup-simplify: Simplify k into k 1539426658.056 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426658.057 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426658.057 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1539426658.057 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.057 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1539426658.058 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1539426658.059 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 0) into 0 1539426658.059 * [misc]taylor: Taking taylor expansion of 0 in k 1539426658.059 * [misc]backup-simplify: Simplify 0 into 0 1539426658.059 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426658.060 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426658.061 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426658.064 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426658.064 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1539426658.064 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.065 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426658.065 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539426658.067 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426658.068 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) into 0 1539426658.069 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) (* +nan.0 (/ PI k))) (* 0 0)) into (- (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k))) 1539426658.069 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k))) in k 1539426658.069 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k)) in k 1539426658.069 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.069 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.069 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) k) in k 1539426658.069 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) in k 1539426658.069 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.069 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.069 * [misc]backup-simplify: Simplify 2 into 2 1539426658.069 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.069 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.069 * [misc]taylor: Taking taylor expansion of (* PI (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k 1539426658.070 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.070 * [misc]backup-simplify: Simplify PI into PI 1539426658.070 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1539426658.070 * [misc]taylor: Taking taylor expansion of (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1539426658.070 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426658.070 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426658.070 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1539426658.070 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539426658.070 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.070 * [misc]taylor: Taking taylor expansion of n in k 1539426658.070 * [misc]backup-simplify: Simplify n into n 1539426658.070 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.070 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426658.070 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426658.070 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.070 * [misc]backup-simplify: Simplify 2 into 2 1539426658.070 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.070 * [misc]backup-simplify: Simplify PI into PI 1539426658.070 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.071 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.071 * [misc]taylor: Taking taylor expansion of k in k 1539426658.071 * [misc]backup-simplify: Simplify 0 into 0 1539426658.071 * [misc]backup-simplify: Simplify 1 into 1 1539426658.071 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426658.072 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539426658.072 * [misc]backup-simplify: Simplify (* -1/2 0) into 0 1539426658.072 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539426658.073 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426658.074 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426658.074 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426658.075 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1539426658.075 * [misc]backup-simplify: Simplify (+ (* -1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1539426658.075 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426658.075 * [misc]taylor: Taking taylor expansion of k in k 1539426658.075 * [misc]backup-simplify: Simplify 0 into 0 1539426658.075 * [misc]backup-simplify: Simplify 1 into 1 1539426658.075 * [misc]backup-simplify: Simplify (* PI 1) into PI 1539426658.076 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1539426658.076 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) PI) 1) into (* (sqrt 2) PI) 1539426658.076 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) PI)) into (* +nan.0 (* (sqrt 2) PI)) 1539426658.077 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426658.078 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426658.078 * [misc]backup-simplify: Simplify 0 into 0 1539426658.078 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426658.078 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)))) into 0 1539426658.079 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow PI 2) (pow k 2))) 1539426658.079 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426658.080 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.081 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426658.083 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1539426658.083 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.084 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1539426658.084 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.084 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426658.085 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539426658.086 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426658.087 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426658.087 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into 0 1539426658.088 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) (* +nan.0 (/ (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (/ PI k))) (* 0 0))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)))) 1539426658.088 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)))) in k 1539426658.088 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2))) in k 1539426658.088 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.088 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.088 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) (pow k 2)) in k 1539426658.088 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) in k 1539426658.088 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.088 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.088 * [misc]backup-simplify: Simplify 2 into 2 1539426658.088 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.089 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.089 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.089 * [misc]backup-simplify: Simplify PI into PI 1539426658.089 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426658.089 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426658.089 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of n in k 1539426658.089 * [misc]backup-simplify: Simplify n into n 1539426658.089 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.089 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426658.089 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.089 * [misc]backup-simplify: Simplify 2 into 2 1539426658.089 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.089 * [misc]backup-simplify: Simplify PI into PI 1539426658.089 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.089 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.089 * [misc]taylor: Taking taylor expansion of k in k 1539426658.089 * [misc]backup-simplify: Simplify 0 into 0 1539426658.089 * [misc]backup-simplify: Simplify 1 into 1 1539426658.090 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426658.090 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539426658.090 * [misc]backup-simplify: Simplify (* -1/2 0) into 0 1539426658.091 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539426658.091 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426658.093 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426658.093 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426658.093 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1539426658.094 * [misc]backup-simplify: Simplify (+ (* -1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1539426658.094 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426658.094 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1539426658.094 * [misc]taylor: Taking taylor expansion of k in k 1539426658.094 * [misc]backup-simplify: Simplify 0 into 0 1539426658.094 * [misc]backup-simplify: Simplify 1 into 1 1539426658.094 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426658.095 * [misc]backup-simplify: Simplify (* (pow PI 2) 1) into (pow PI 2) 1539426658.095 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539426658.095 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426658.096 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 2)) 1) into (* (sqrt 2) (pow PI 2)) 1539426658.097 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1539426658.097 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426658.098 * [misc]backup-simplify: Simplify (+ (* (pow PI 2) (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* 0 1)) into (- (+ (* 1/2 (* (pow PI 2) (log (* 2 PI)))) (* 1/2 (* (pow PI 2) (log n))))) 1539426658.099 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (- (+ (* 1/2 (* (pow PI 2) (log (* 2 PI)))) (* 1/2 (* (pow PI 2) (log n)))))) (* 0 (pow PI 2))) into (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1539426658.100 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426658.104 * [misc]backup-simplify: Simplify (- (/ (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1) (+ (* (* (sqrt 2) (pow PI 2)) (/ 0 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1539426658.108 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n))))))) (* 0 (* (sqrt 2) (pow PI 2)))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1539426658.110 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1539426658.113 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) 1539426658.114 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1539426658.115 * [misc]backup-simplify: Simplify (+ (* PI (* -1 (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))) (* 0 1)) into (- (+ (* 1/2 (* PI (log (* 2 PI)))) (* 1/2 (* PI (log n))))) 1539426658.117 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (- (+ (* 1/2 (* PI (log (* 2 PI)))) (* 1/2 (* PI (log n)))))) (* 0 PI)) into (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1539426658.120 * [misc]backup-simplify: Simplify (- (/ (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1) (+ (* (* (sqrt 2) PI) (/ 0 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1539426658.123 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* 0 (* (sqrt 2) PI))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426658.128 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426658.130 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426658.138 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* 1 n)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (- (* +nan.0 (* (sqrt 2) (* (pow PI 2) (log n))))))) (* (/ 1 k) (pow n 2))) (* (- (* +nan.0 (* (sqrt 2) PI))) (* (/ 1 k) n)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log n)))) k)) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log (* 2 PI))))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) 1539426658.138 * [misc]backup-simplify: Simplify (* (sqrt (* (* PI 2) (/ 1 n))) (/ (pow (* PI (* (/ 1 n) 2)) (- (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) 1539426658.138 * [misc]approximate: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in (n k) around 0 1539426658.139 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.139 * [misc]backup-simplify: Simplify 2 into 2 1539426658.139 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.139 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.139 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426658.139 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.139 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426658.139 * [misc]taylor: Taking taylor expansion of k in k 1539426658.139 * [misc]backup-simplify: Simplify 0 into 0 1539426658.139 * [misc]backup-simplify: Simplify 1 into 1 1539426658.140 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426658.140 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539426658.140 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539426658.140 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.140 * [misc]backup-simplify: Simplify 2 into 2 1539426658.140 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426658.140 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.140 * [misc]backup-simplify: Simplify PI into PI 1539426658.140 * [misc]taylor: Taking taylor expansion of n in k 1539426658.140 * [misc]backup-simplify: Simplify n into n 1539426658.140 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426658.140 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539426658.140 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539426658.140 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426658.140 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426658.141 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539426658.141 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1539426658.141 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in k 1539426658.141 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in k 1539426658.141 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539426658.141 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.141 * [misc]backup-simplify: Simplify PI into PI 1539426658.141 * [misc]taylor: Taking taylor expansion of k in k 1539426658.141 * [misc]backup-simplify: Simplify 0 into 0 1539426658.141 * [misc]backup-simplify: Simplify 1 into 1 1539426658.141 * [misc]taylor: Taking taylor expansion of n in k 1539426658.141 * [misc]backup-simplify: Simplify n into n 1539426658.141 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539426658.142 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539426658.142 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426658.142 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.142 * [misc]backup-simplify: Simplify (/ (/ PI n) (* 2 (sqrt 0))) into (* +nan.0 (/ PI n)) 1539426658.142 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in n 1539426658.142 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in n 1539426658.143 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426658.143 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.143 * [misc]backup-simplify: Simplify 2 into 2 1539426658.143 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.143 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.143 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1539426658.143 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426658.143 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426658.143 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1539426658.143 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426658.143 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426658.143 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.143 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426658.143 * [misc]taylor: Taking taylor expansion of k in n 1539426658.144 * [misc]backup-simplify: Simplify k into k 1539426658.144 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426658.144 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426658.144 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426658.144 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.144 * [misc]backup-simplify: Simplify 2 into 2 1539426658.144 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.144 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.144 * [misc]backup-simplify: Simplify PI into PI 1539426658.144 * [misc]taylor: Taking taylor expansion of n in n 1539426658.144 * [misc]backup-simplify: Simplify 0 into 0 1539426658.144 * [misc]backup-simplify: Simplify 1 into 1 1539426658.144 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.145 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.145 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.145 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426658.145 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426658.146 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426658.147 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426658.147 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426658.147 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1539426658.147 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1539426658.147 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539426658.147 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.147 * [misc]backup-simplify: Simplify PI into PI 1539426658.147 * [misc]taylor: Taking taylor expansion of k in n 1539426658.147 * [misc]backup-simplify: Simplify k into k 1539426658.147 * [misc]taylor: Taking taylor expansion of n in n 1539426658.147 * [misc]backup-simplify: Simplify 0 into 0 1539426658.147 * [misc]backup-simplify: Simplify 1 into 1 1539426658.147 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539426658.148 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1539426658.148 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.148 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1539426658.148 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in n 1539426658.148 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in n 1539426658.148 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426658.148 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.148 * [misc]backup-simplify: Simplify 2 into 2 1539426658.148 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.148 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.149 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426658.149 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.149 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of k in n 1539426658.149 * [misc]backup-simplify: Simplify k into k 1539426658.149 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426658.149 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.149 * [misc]backup-simplify: Simplify 2 into 2 1539426658.149 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.149 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.149 * [misc]backup-simplify: Simplify PI into PI 1539426658.149 * [misc]taylor: Taking taylor expansion of n in n 1539426658.149 * [misc]backup-simplify: Simplify 0 into 0 1539426658.149 * [misc]backup-simplify: Simplify 1 into 1 1539426658.149 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.150 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.150 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.150 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426658.150 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426658.151 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426658.152 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426658.152 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426658.152 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1539426658.152 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1539426658.152 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539426658.152 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.152 * [misc]backup-simplify: Simplify PI into PI 1539426658.152 * [misc]taylor: Taking taylor expansion of k in n 1539426658.152 * [misc]backup-simplify: Simplify k into k 1539426658.152 * [misc]taylor: Taking taylor expansion of n in n 1539426658.152 * [misc]backup-simplify: Simplify 0 into 0 1539426658.152 * [misc]backup-simplify: Simplify 1 into 1 1539426658.153 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539426658.153 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1539426658.153 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.153 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1539426658.154 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 1539426658.155 * [misc]backup-simplify: Simplify (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 0) into 0 1539426658.155 * [misc]taylor: Taking taylor expansion of 0 in k 1539426658.155 * [misc]backup-simplify: Simplify 0 into 0 1539426658.155 * [misc]backup-simplify: Simplify 0 into 0 1539426658.155 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426658.156 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.157 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426658.159 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426658.159 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426658.160 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426658.160 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.160 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426658.161 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539426658.163 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426658.163 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 1539426658.164 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* PI k))) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))))) 1539426658.164 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))))) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k)))) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.165 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.165 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* PI k))) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426658.165 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426658.165 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426658.165 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.165 * [misc]backup-simplify: Simplify 2 into 2 1539426658.165 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.165 * [misc]backup-simplify: Simplify PI into PI 1539426658.165 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.166 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.166 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.166 * [misc]taylor: Taking taylor expansion of n in k 1539426658.166 * [misc]backup-simplify: Simplify n into n 1539426658.166 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.166 * [misc]taylor: Taking taylor expansion of k in k 1539426658.166 * [misc]backup-simplify: Simplify 0 into 0 1539426658.166 * [misc]backup-simplify: Simplify 1 into 1 1539426658.166 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426658.166 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426658.167 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426658.168 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426658.168 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426658.168 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* PI k)) in k 1539426658.168 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.168 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.168 * [misc]backup-simplify: Simplify 2 into 2 1539426658.168 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.169 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.169 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539426658.169 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.169 * [misc]backup-simplify: Simplify PI into PI 1539426658.169 * [misc]taylor: Taking taylor expansion of k in k 1539426658.169 * [misc]backup-simplify: Simplify 0 into 0 1539426658.169 * [misc]backup-simplify: Simplify 1 into 1 1539426658.169 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539426658.169 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426658.170 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) into 0 1539426658.170 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1539426658.170 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.170 * [misc]backup-simplify: Simplify 0 into 0 1539426658.170 * [misc]backup-simplify: Simplify 0 into 0 1539426658.170 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 k)) into 0 1539426658.171 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)))) into 0 1539426658.171 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow PI 2) (pow k 2))) 1539426658.171 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426658.173 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.174 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426658.179 * [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 1539426658.179 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.179 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426658.180 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539426658.180 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.181 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426658.181 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539426658.184 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426658.185 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426658.186 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1539426658.187 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))))) 1539426658.187 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))))) in k 1539426658.187 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2))))) in k 1539426658.187 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.188 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.188 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 2) (pow k 2)))) in k 1539426658.188 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426658.188 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426658.188 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426658.188 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426658.188 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426658.188 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426658.188 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426658.188 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426658.188 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.188 * [misc]backup-simplify: Simplify 2 into 2 1539426658.188 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.188 * [misc]backup-simplify: Simplify PI into PI 1539426658.188 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.189 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.189 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.189 * [misc]taylor: Taking taylor expansion of n in k 1539426658.189 * [misc]backup-simplify: Simplify n into n 1539426658.189 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.189 * [misc]taylor: Taking taylor expansion of k in k 1539426658.189 * [misc]backup-simplify: Simplify 0 into 0 1539426658.189 * [misc]backup-simplify: Simplify 1 into 1 1539426658.189 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426658.189 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426658.190 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426658.191 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426658.191 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426658.191 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 2) (pow k 2))) in k 1539426658.191 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.191 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.191 * [misc]backup-simplify: Simplify 2 into 2 1539426658.191 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.192 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.192 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (pow k 2)) in k 1539426658.192 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539426658.192 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.192 * [misc]backup-simplify: Simplify PI into PI 1539426658.192 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1539426658.192 * [misc]taylor: Taking taylor expansion of k in k 1539426658.192 * [misc]backup-simplify: Simplify 0 into 0 1539426658.192 * [misc]backup-simplify: Simplify 1 into 1 1539426658.193 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539426658.193 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539426658.195 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (* 0 0)) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) 1539426658.196 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1539426658.197 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1539426658.198 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1539426658.198 * [misc]backup-simplify: Simplify 0 into 0 1539426658.199 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 k))) into 0 1539426658.199 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.200 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 2) (pow k 2))))))) (* 2 0)) into (* +nan.0 (* (pow PI 3) (pow k 3))) 1539426658.200 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426658.202 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.204 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.212 * [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 1539426658.212 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.212 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.213 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426658.213 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1539426658.213 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.214 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426658.215 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539426658.217 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426658.217 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426658.218 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539426658.219 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))))) 1539426658.219 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))))) in k 1539426658.219 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3))))) in k 1539426658.219 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.219 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.219 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 3) (pow k 3)))) in k 1539426658.219 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426658.219 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426658.219 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426658.219 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426658.219 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426658.219 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426658.220 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426658.220 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426658.220 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.220 * [misc]backup-simplify: Simplify 2 into 2 1539426658.220 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.220 * [misc]backup-simplify: Simplify PI into PI 1539426658.220 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.220 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.220 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.220 * [misc]taylor: Taking taylor expansion of n in k 1539426658.220 * [misc]backup-simplify: Simplify n into n 1539426658.220 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.220 * [misc]taylor: Taking taylor expansion of k in k 1539426658.220 * [misc]backup-simplify: Simplify 0 into 0 1539426658.220 * [misc]backup-simplify: Simplify 1 into 1 1539426658.220 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426658.221 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426658.221 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426658.221 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426658.222 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426658.222 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 3) (pow k 3))) in k 1539426658.222 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.222 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.222 * [misc]backup-simplify: Simplify 2 into 2 1539426658.222 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.222 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.222 * [misc]taylor: Taking taylor expansion of (* (pow PI 3) (pow k 3)) in k 1539426658.222 * [misc]taylor: Taking taylor expansion of (pow PI 3) in k 1539426658.222 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.222 * [misc]backup-simplify: Simplify PI into PI 1539426658.222 * [misc]taylor: Taking taylor expansion of (pow k 3) in k 1539426658.222 * [misc]taylor: Taking taylor expansion of k in k 1539426658.222 * [misc]backup-simplify: Simplify 0 into 0 1539426658.222 * [misc]backup-simplify: Simplify 1 into 1 1539426658.223 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1539426658.223 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426658.224 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1539426658.225 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0))) into 0 1539426658.226 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0))) into 0 1539426658.226 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.226 * [misc]backup-simplify: Simplify 0 into 0 1539426658.226 * [misc]backup-simplify: Simplify 0 into 0 1539426658.227 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1539426658.227 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.228 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow PI 2) (pow k 2))) 2) (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 3) (pow k 3))))))) (* 2 0)) into (* +nan.0 (* (pow PI 4) (pow k 4))) 1539426658.228 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426658.229 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.230 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426658.237 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 1539426658.238 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.238 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.238 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.238 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426658.238 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k)))))) into 0 1539426658.239 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.239 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426658.240 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 1539426658.243 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426658.244 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426658.245 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 1539426658.247 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))))) 1539426658.247 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))))) in k 1539426658.247 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4))))) in k 1539426658.248 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.248 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.248 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 4) (pow k 4)))) in k 1539426658.248 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426658.248 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426658.248 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426658.248 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426658.248 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426658.248 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426658.248 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426658.248 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426658.248 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.248 * [misc]backup-simplify: Simplify 2 into 2 1539426658.248 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.248 * [misc]backup-simplify: Simplify PI into PI 1539426658.248 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.249 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.249 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.249 * [misc]taylor: Taking taylor expansion of n in k 1539426658.249 * [misc]backup-simplify: Simplify n into n 1539426658.249 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.249 * [misc]taylor: Taking taylor expansion of k in k 1539426658.249 * [misc]backup-simplify: Simplify 0 into 0 1539426658.249 * [misc]backup-simplify: Simplify 1 into 1 1539426658.249 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426658.249 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426658.250 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426658.250 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426658.251 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426658.251 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 4) (pow k 4))) in k 1539426658.251 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.251 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.251 * [misc]backup-simplify: Simplify 2 into 2 1539426658.251 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.251 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.251 * [misc]taylor: Taking taylor expansion of (* (pow PI 4) (pow k 4)) in k 1539426658.251 * [misc]taylor: Taking taylor expansion of (pow PI 4) in k 1539426658.252 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.252 * [misc]backup-simplify: Simplify PI into PI 1539426658.252 * [misc]taylor: Taking taylor expansion of (pow k 4) in k 1539426658.252 * [misc]taylor: Taking taylor expansion of k in k 1539426658.252 * [misc]backup-simplify: Simplify 0 into 0 1539426658.252 * [misc]backup-simplify: Simplify 1 into 1 1539426658.252 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426658.252 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426658.253 * [misc]backup-simplify: Simplify (* (pow PI 2) 1) into (pow PI 2) 1539426658.253 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539426658.254 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) 1539426658.255 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) into (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) 1539426658.256 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) 1539426658.258 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) 1539426658.258 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539426658.259 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426658.260 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426658.263 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0)))) into 0 1539426658.264 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0)))) into 0 1539426658.264 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.264 * [misc]backup-simplify: Simplify 0 into 0 1539426658.264 * [misc]backup-simplify: Simplify 0 into 0 1539426658.265 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k))))) into 0 1539426658.265 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.266 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 4) (pow k 4))))) (* 2 (* (* +nan.0 (* (pow PI 2) (pow k 2))) (* +nan.0 (* (pow PI 3) (pow k 3))))))) (* 2 0)) into (* +nan.0 (* (pow PI 5) (pow k 5))) 1539426658.266 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426658.268 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.270 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426658.281 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 1539426658.281 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.281 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.281 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.282 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.282 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426658.282 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))))) into 0 1539426658.282 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.283 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426658.283 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 1539426658.288 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426658.289 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426658.290 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))))))))) into 0 1539426658.291 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 5) (pow k 5)))) (+ (* 0 (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0)))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))))) 1539426658.291 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))))) in k 1539426658.291 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5))))) in k 1539426658.291 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.291 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.291 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 5) (pow k 5)))) in k 1539426658.291 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426658.291 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426658.291 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426658.291 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426658.291 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426658.291 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426658.291 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426658.292 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426658.292 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.292 * [misc]backup-simplify: Simplify 2 into 2 1539426658.292 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.292 * [misc]backup-simplify: Simplify PI into PI 1539426658.292 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.292 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.292 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.292 * [misc]taylor: Taking taylor expansion of n in k 1539426658.292 * [misc]backup-simplify: Simplify n into n 1539426658.292 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.292 * [misc]taylor: Taking taylor expansion of k in k 1539426658.293 * [misc]backup-simplify: Simplify 0 into 0 1539426658.293 * [misc]backup-simplify: Simplify 1 into 1 1539426658.293 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426658.293 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426658.294 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426658.294 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426658.295 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426658.295 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 5) (pow k 5))) in k 1539426658.295 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.295 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.295 * [misc]backup-simplify: Simplify 2 into 2 1539426658.295 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.295 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.295 * [misc]taylor: Taking taylor expansion of (* (pow PI 5) (pow k 5)) in k 1539426658.295 * [misc]taylor: Taking taylor expansion of (pow PI 5) in k 1539426658.295 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.295 * [misc]backup-simplify: Simplify PI into PI 1539426658.295 * [misc]taylor: Taking taylor expansion of (pow k 5) in k 1539426658.295 * [misc]taylor: Taking taylor expansion of k in k 1539426658.295 * [misc]backup-simplify: Simplify 0 into 0 1539426658.295 * [misc]backup-simplify: Simplify 1 into 1 1539426658.296 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426658.296 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426658.297 * [misc]backup-simplify: Simplify (+ (* (pow PI 2) 0) (* 0 1)) into 0 1539426658.298 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539426658.300 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (* (sqrt 2) (pow PI 2)))) into 0 1539426658.301 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into 0 1539426658.301 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.301 * [misc]backup-simplify: Simplify 0 into 0 1539426658.302 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539426658.303 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426658.306 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426658.308 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0))))) into 0 1539426658.310 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) (* 0 0))))) into 0 1539426658.310 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.310 * [misc]backup-simplify: Simplify 0 into 0 1539426658.310 * [misc]backup-simplify: Simplify 0 into 0 1539426658.311 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))))) into 0 1539426658.312 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.313 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow PI 3) (pow k 3))) 2) (+ (* 2 (* (* +nan.0 (* PI k)) (* +nan.0 (* (pow PI 5) (pow k 5))))) (* 2 (* (* +nan.0 (* (pow PI 2) (pow k 2))) (* +nan.0 (* (pow PI 4) (pow k 4))))))) (* 2 0)) into (* +nan.0 (* (pow PI 6) (pow k 6))) 1539426658.313 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426658.315 * [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 1539426658.317 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426658.334 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 1539426658.334 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.334 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.335 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.335 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.335 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.335 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426658.335 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k)))))))) into 0 1539426658.336 * [misc]backup-simplify: Simplify (- 0) into 0 1539426658.336 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426658.337 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 1539426658.346 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426658.347 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426658.348 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))))) into 0 1539426658.351 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (* +nan.0 (* (pow PI 6) (pow k 6)))) (+ (* 0 (* +nan.0 (* (pow PI 5) (pow k 5)))) (+ (* 0 (* +nan.0 (* (pow PI 4) (pow k 4)))) (+ (* 0 (* +nan.0 (* (pow PI 3) (pow k 3)))) (+ (* 0 (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))))) 1539426658.351 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))))) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6))))) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.351 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.351 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (* (pow PI 6) (pow k 6)))) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539426658.351 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426658.351 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539426658.351 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.351 * [misc]backup-simplify: Simplify 2 into 2 1539426658.352 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.352 * [misc]backup-simplify: Simplify PI into PI 1539426658.352 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.352 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426658.352 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.352 * [misc]taylor: Taking taylor expansion of n in k 1539426658.352 * [misc]backup-simplify: Simplify n into n 1539426658.352 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.352 * [misc]taylor: Taking taylor expansion of k in k 1539426658.352 * [misc]backup-simplify: Simplify 0 into 0 1539426658.352 * [misc]backup-simplify: Simplify 1 into 1 1539426658.352 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426658.353 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539426658.353 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539426658.354 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539426658.354 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426658.354 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 6) (pow k 6))) in k 1539426658.354 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426658.354 * [misc]taylor: Taking taylor expansion of 2 in k 1539426658.355 * [misc]backup-simplify: Simplify 2 into 2 1539426658.355 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.355 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.355 * [misc]taylor: Taking taylor expansion of (* (pow PI 6) (pow k 6)) in k 1539426658.355 * [misc]taylor: Taking taylor expansion of (pow PI 6) in k 1539426658.355 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.355 * [misc]backup-simplify: Simplify PI into PI 1539426658.355 * [misc]taylor: Taking taylor expansion of (pow k 6) in k 1539426658.355 * [misc]taylor: Taking taylor expansion of k in k 1539426658.355 * [misc]backup-simplify: Simplify 0 into 0 1539426658.355 * [misc]backup-simplify: Simplify 1 into 1 1539426658.356 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426658.356 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539426658.356 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426658.356 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426658.357 * [misc]backup-simplify: Simplify (* (pow PI 3) 1) into (pow PI 3) 1539426658.357 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539426658.358 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) 1539426658.359 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))) into (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))) 1539426658.360 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) 1539426658.361 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) 1539426658.366 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (pow PI 3))))) (* (pow (/ 1 k) 3) (pow (/ 1 n) 2))) (+ (* (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (pow PI 2))))) (* (pow (/ 1 k) 2) (/ 1 n))) (* (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) PI)))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 2))) (* n (pow k 2)))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 3))) (* (pow n 2) (pow k 3)))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) PI)) k))))))) 1539426658.367 * [misc]backup-simplify: Simplify (* (sqrt (* (* PI 2) (/ 1 (- n)))) (/ (pow (* PI (* (/ 1 (- n)) 2)) (- (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) 1539426658.367 * [misc]approximate: Taking taylor expansion of (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) in (n k) around 0 1539426658.367 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) in k 1539426658.367 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) in k 1539426658.367 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1539426658.367 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426658.367 * [misc]taylor: Taking taylor expansion of -2 in k 1539426658.367 * [misc]backup-simplify: Simplify -2 into -2 1539426658.367 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426658.367 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.367 * [misc]backup-simplify: Simplify PI into PI 1539426658.367 * [misc]taylor: Taking taylor expansion of n in k 1539426658.367 * [misc]backup-simplify: Simplify n into n 1539426658.367 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426658.367 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426658.367 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539426658.367 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1539426658.368 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1539426658.368 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539426658.368 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1539426658.368 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1539426658.368 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1539426658.368 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426658.368 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426658.368 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.368 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426658.368 * [misc]taylor: Taking taylor expansion of k in k 1539426658.368 * [misc]backup-simplify: Simplify 0 into 0 1539426658.368 * [misc]backup-simplify: Simplify 1 into 1 1539426658.368 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426658.368 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539426658.368 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426658.368 * [misc]taylor: Taking taylor expansion of -2 in k 1539426658.368 * [misc]backup-simplify: Simplify -2 into -2 1539426658.368 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426658.368 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.368 * [misc]backup-simplify: Simplify PI into PI 1539426658.368 * [misc]taylor: Taking taylor expansion of n in k 1539426658.368 * [misc]backup-simplify: Simplify n into n 1539426658.368 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426658.369 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426658.369 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539426658.369 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426658.369 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539426658.369 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1539426658.369 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426658.369 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426658.369 * [misc]taylor: Taking taylor expansion of -1 in k 1539426658.369 * [misc]backup-simplify: Simplify -1 into -1 1539426658.369 * [misc]taylor: Taking taylor expansion of k in k 1539426658.369 * [misc]backup-simplify: Simplify 0 into 0 1539426658.369 * [misc]backup-simplify: Simplify 1 into 1 1539426658.369 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426658.369 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.370 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426658.370 * [misc]backup-simplify: Simplify (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1539426658.370 * [misc]backup-simplify: Simplify (/ (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) +nan.0) into (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) 1539426658.370 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) in n 1539426658.370 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) in n 1539426658.370 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539426658.371 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.371 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.371 * [misc]backup-simplify: Simplify -2 into -2 1539426658.371 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.371 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.371 * [misc]backup-simplify: Simplify PI into PI 1539426658.371 * [misc]taylor: Taking taylor expansion of n in n 1539426658.371 * [misc]backup-simplify: Simplify 0 into 0 1539426658.371 * [misc]backup-simplify: Simplify 1 into 1 1539426658.371 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.371 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.371 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.372 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426658.372 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1539426658.372 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1539426658.372 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1539426658.372 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426658.372 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426658.372 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.372 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426658.372 * [misc]taylor: Taking taylor expansion of k in n 1539426658.372 * [misc]backup-simplify: Simplify k into k 1539426658.372 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426658.372 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426658.372 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.372 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.372 * [misc]backup-simplify: Simplify -2 into -2 1539426658.372 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.372 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.372 * [misc]backup-simplify: Simplify PI into PI 1539426658.372 * [misc]taylor: Taking taylor expansion of n in n 1539426658.372 * [misc]backup-simplify: Simplify 0 into 0 1539426658.372 * [misc]backup-simplify: Simplify 1 into 1 1539426658.372 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.372 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.373 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426658.373 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426658.373 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426658.373 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426658.374 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426658.374 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539426658.374 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539426658.374 * [misc]taylor: Taking taylor expansion of -1 in n 1539426658.374 * [misc]backup-simplify: Simplify -1 into -1 1539426658.374 * [misc]taylor: Taking taylor expansion of k in n 1539426658.374 * [misc]backup-simplify: Simplify k into k 1539426658.374 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539426658.374 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539426658.374 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539426658.374 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539426658.374 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1539426658.375 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.376 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426658.378 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426658.378 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426658.378 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426658.379 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426658.379 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426658.380 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426658.380 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426658.381 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) into (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) 1539426658.381 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) (sqrt (/ -1 k))) in n 1539426658.381 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k)))) in n 1539426658.381 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539426658.381 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.381 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.381 * [misc]backup-simplify: Simplify -2 into -2 1539426658.381 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.381 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.381 * [misc]backup-simplify: Simplify PI into PI 1539426658.381 * [misc]taylor: Taking taylor expansion of n in n 1539426658.381 * [misc]backup-simplify: Simplify 0 into 0 1539426658.381 * [misc]backup-simplify: Simplify 1 into 1 1539426658.381 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.381 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.382 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.382 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426658.382 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1539426658.382 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1539426658.382 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1539426658.382 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426658.382 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426658.382 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.382 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426658.382 * [misc]taylor: Taking taylor expansion of k in n 1539426658.382 * [misc]backup-simplify: Simplify k into k 1539426658.382 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426658.382 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426658.382 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.382 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.382 * [misc]backup-simplify: Simplify -2 into -2 1539426658.382 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.382 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.382 * [misc]backup-simplify: Simplify PI into PI 1539426658.382 * [misc]taylor: Taking taylor expansion of n in n 1539426658.382 * [misc]backup-simplify: Simplify 0 into 0 1539426658.382 * [misc]backup-simplify: Simplify 1 into 1 1539426658.383 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.383 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.383 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426658.383 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426658.384 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426658.384 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426658.384 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426658.384 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539426658.384 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539426658.384 * [misc]taylor: Taking taylor expansion of -1 in n 1539426658.384 * [misc]backup-simplify: Simplify -1 into -1 1539426658.384 * [misc]taylor: Taking taylor expansion of k in n 1539426658.384 * [misc]backup-simplify: Simplify k into k 1539426658.385 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539426658.385 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539426658.385 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539426658.385 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539426658.385 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1539426658.386 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.386 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426658.388 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426658.388 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426658.388 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426658.388 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426658.389 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426658.390 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426658.390 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426658.391 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) into (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) 1539426658.391 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.391 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.391 * [misc]taylor: Taking taylor expansion of (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.391 * [misc]backup-simplify: Simplify PI into PI 1539426658.391 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426658.391 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.391 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539426658.391 * [misc]taylor: Taking taylor expansion of -2 in k 1539426658.391 * [misc]backup-simplify: Simplify -2 into -2 1539426658.391 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.391 * [misc]backup-simplify: Simplify PI into PI 1539426658.391 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.392 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426658.392 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.392 * [misc]taylor: Taking taylor expansion of n in k 1539426658.392 * [misc]backup-simplify: Simplify n into n 1539426658.392 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.392 * [misc]taylor: Taking taylor expansion of k in k 1539426658.392 * [misc]backup-simplify: Simplify 0 into 0 1539426658.392 * [misc]backup-simplify: Simplify 1 into 1 1539426658.392 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426658.392 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539426658.392 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539426658.393 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539426658.393 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426658.393 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426658.393 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426658.393 * [misc]taylor: Taking taylor expansion of -1 in k 1539426658.393 * [misc]backup-simplify: Simplify -1 into -1 1539426658.393 * [misc]taylor: Taking taylor expansion of k in k 1539426658.393 * [misc]backup-simplify: Simplify 0 into 0 1539426658.393 * [misc]backup-simplify: Simplify 1 into 1 1539426658.393 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426658.393 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.394 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426658.394 * [misc]backup-simplify: Simplify (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539426658.394 * [misc]backup-simplify: Simplify (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) +nan.0) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426658.395 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426658.395 * [misc]backup-simplify: Simplify (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426658.396 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.397 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426658.400 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1539426658.400 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426658.400 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539426658.400 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426658.401 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1539426658.402 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426658.403 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.403 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426658.405 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539426658.406 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (* +nan.0 PI) 0) (* (* +nan.0 (pow PI 2)) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426658.408 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) (+ (* (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))))) into (- (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))))) 1539426658.408 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))))) in k 1539426658.408 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) in k 1539426658.408 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539426658.408 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426658.408 * [misc]taylor: Taking taylor expansion of (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.409 * [misc]backup-simplify: Simplify PI into PI 1539426658.409 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426658.409 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426658.409 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539426658.409 * [misc]taylor: Taking taylor expansion of -2 in k 1539426658.409 * [misc]backup-simplify: Simplify -2 into -2 1539426658.409 * [misc]taylor: Taking taylor expansion of PI in k 1539426658.409 * [misc]backup-simplify: Simplify PI into PI 1539426658.409 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.410 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426658.410 * [misc]taylor: Taking taylor expansion of (log n) in k 1539426658.410 * [misc]taylor: Taking taylor expansion of n in k 1539426658.410 * [misc]backup-simplify: Simplify n into n 1539426658.410 * [misc]backup-simplify: Simplify (log n) into (log n) 1539426658.410 * [misc]taylor: Taking taylor expansion of k in k 1539426658.410 * [misc]backup-simplify: Simplify 0 into 0 1539426658.410 * [misc]backup-simplify: Simplify 1 into 1 1539426658.410 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539426658.410 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539426658.411 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539426658.411 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539426658.412 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426658.412 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426658.412 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426658.412 * [misc]taylor: Taking taylor expansion of -1 in k 1539426658.412 * [misc]backup-simplify: Simplify -1 into -1 1539426658.412 * [misc]taylor: Taking taylor expansion of k in k 1539426658.412 * [misc]backup-simplify: Simplify 0 into 0 1539426658.412 * [misc]backup-simplify: Simplify 1 into 1 1539426658.412 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426658.413 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.413 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426658.413 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426658.414 * [misc]backup-simplify: Simplify (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539426658.415 * [misc]backup-simplify: Simplify (/ (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) +nan.0) into (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426658.416 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426658.417 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426658.418 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426658.419 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into 0 1539426658.419 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539426658.421 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539426658.422 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426658.423 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* 0 (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426658.424 * [misc]backup-simplify: Simplify (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426658.427 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (+ (* (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* 1 (/ 1 (- n)))) (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI)) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow PI 2)) n))))))) 1539426658.427 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1) 1539426658.427 * [misc]backup-simplify: Simplify (* (* PI 2) n) into (* 2 (* n PI)) 1539426658.427 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539426658.427 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426658.427 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.427 * [misc]backup-simplify: Simplify 2 into 2 1539426658.428 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.428 * [misc]taylor: Taking taylor expansion of n in n 1539426658.428 * [misc]backup-simplify: Simplify 0 into 0 1539426658.428 * [misc]backup-simplify: Simplify 1 into 1 1539426658.428 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.428 * [misc]backup-simplify: Simplify PI into PI 1539426658.428 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426658.428 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.428 * [misc]backup-simplify: Simplify 2 into 2 1539426658.428 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.428 * [misc]taylor: Taking taylor expansion of n in n 1539426658.428 * [misc]backup-simplify: Simplify 0 into 0 1539426658.428 * [misc]backup-simplify: Simplify 1 into 1 1539426658.428 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.428 * [misc]backup-simplify: Simplify PI into PI 1539426658.428 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426658.428 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426658.428 * [misc]backup-simplify: Simplify 0 into 0 1539426658.429 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426658.430 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426658.430 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.431 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426658.432 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426658.432 * [misc]backup-simplify: Simplify 0 into 0 1539426658.434 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.435 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426658.435 * [misc]backup-simplify: Simplify 0 into 0 1539426658.437 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426658.439 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426658.439 * [misc]backup-simplify: Simplify 0 into 0 1539426658.442 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426658.444 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539426658.445 * [misc]backup-simplify: Simplify 0 into 0 1539426658.448 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426658.451 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539426658.451 * [misc]backup-simplify: Simplify 0 into 0 1539426658.456 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539426658.459 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539426658.460 * [misc]backup-simplify: Simplify 0 into 0 1539426658.460 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539426658.460 * [misc]backup-simplify: Simplify (* (* PI 2) (/ 1 n)) into (* 2 (/ PI n)) 1539426658.460 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539426658.460 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426658.460 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.460 * [misc]backup-simplify: Simplify 2 into 2 1539426658.460 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.460 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.460 * [misc]backup-simplify: Simplify PI into PI 1539426658.460 * [misc]taylor: Taking taylor expansion of n in n 1539426658.460 * [misc]backup-simplify: Simplify 0 into 0 1539426658.460 * [misc]backup-simplify: Simplify 1 into 1 1539426658.460 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.460 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426658.460 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.460 * [misc]backup-simplify: Simplify 2 into 2 1539426658.460 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.460 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.460 * [misc]backup-simplify: Simplify PI into PI 1539426658.460 * [misc]taylor: Taking taylor expansion of n in n 1539426658.460 * [misc]backup-simplify: Simplify 0 into 0 1539426658.460 * [misc]backup-simplify: Simplify 1 into 1 1539426658.461 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.461 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.461 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.462 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.462 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426658.462 * [misc]backup-simplify: Simplify 0 into 0 1539426658.463 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.463 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426658.463 * [misc]backup-simplify: Simplify 0 into 0 1539426658.464 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.465 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.465 * [misc]backup-simplify: Simplify 0 into 0 1539426658.466 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.468 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426658.468 * [misc]backup-simplify: Simplify 0 into 0 1539426658.469 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.470 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426658.470 * [misc]backup-simplify: Simplify 0 into 0 1539426658.472 * [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 1539426658.474 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426658.474 * [misc]backup-simplify: Simplify 0 into 0 1539426658.474 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539426658.474 * [misc]backup-simplify: Simplify (* (* PI 2) (/ 1 (- n))) into (* -2 (/ PI n)) 1539426658.474 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539426658.474 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.474 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.474 * [misc]backup-simplify: Simplify -2 into -2 1539426658.474 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.475 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.475 * [misc]backup-simplify: Simplify PI into PI 1539426658.475 * [misc]taylor: Taking taylor expansion of n in n 1539426658.475 * [misc]backup-simplify: Simplify 0 into 0 1539426658.475 * [misc]backup-simplify: Simplify 1 into 1 1539426658.475 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.475 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.475 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.475 * [misc]backup-simplify: Simplify -2 into -2 1539426658.475 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.475 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.475 * [misc]backup-simplify: Simplify PI into PI 1539426658.475 * [misc]taylor: Taking taylor expansion of n in n 1539426658.475 * [misc]backup-simplify: Simplify 0 into 0 1539426658.475 * [misc]backup-simplify: Simplify 1 into 1 1539426658.475 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.475 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.475 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.476 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.476 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426658.476 * [misc]backup-simplify: Simplify 0 into 0 1539426658.477 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.478 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426658.478 * [misc]backup-simplify: Simplify 0 into 0 1539426658.479 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.480 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.480 * [misc]backup-simplify: Simplify 0 into 0 1539426658.481 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.482 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426658.482 * [misc]backup-simplify: Simplify 0 into 0 1539426658.483 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.485 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426658.485 * [misc]backup-simplify: Simplify 0 into 0 1539426658.486 * [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 1539426658.488 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426658.488 * [misc]backup-simplify: Simplify 0 into 0 1539426658.488 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539426658.488 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1 1) 1539426658.488 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539426658.488 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539426658.488 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426658.489 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.489 * [misc]backup-simplify: Simplify 2 into 2 1539426658.489 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.489 * [misc]taylor: Taking taylor expansion of n in n 1539426658.489 * [misc]backup-simplify: Simplify 0 into 0 1539426658.489 * [misc]backup-simplify: Simplify 1 into 1 1539426658.489 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.489 * [misc]backup-simplify: Simplify PI into PI 1539426658.489 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426658.489 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.489 * [misc]backup-simplify: Simplify 2 into 2 1539426658.489 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.489 * [misc]taylor: Taking taylor expansion of n in n 1539426658.489 * [misc]backup-simplify: Simplify 0 into 0 1539426658.489 * [misc]backup-simplify: Simplify 1 into 1 1539426658.489 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.489 * [misc]backup-simplify: Simplify PI into PI 1539426658.489 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426658.489 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426658.489 * [misc]backup-simplify: Simplify 0 into 0 1539426658.490 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426658.490 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426658.490 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.491 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426658.491 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426658.491 * [misc]backup-simplify: Simplify 0 into 0 1539426658.492 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.494 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426658.494 * [misc]backup-simplify: Simplify 0 into 0 1539426658.496 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426658.498 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426658.498 * [misc]backup-simplify: Simplify 0 into 0 1539426658.500 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426658.503 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539426658.503 * [misc]backup-simplify: Simplify 0 into 0 1539426658.506 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426658.509 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539426658.509 * [misc]backup-simplify: Simplify 0 into 0 1539426658.513 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539426658.517 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539426658.517 * [misc]backup-simplify: Simplify 0 into 0 1539426658.517 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539426658.517 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539426658.517 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539426658.517 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426658.517 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.518 * [misc]backup-simplify: Simplify 2 into 2 1539426658.518 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.518 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.518 * [misc]backup-simplify: Simplify PI into PI 1539426658.518 * [misc]taylor: Taking taylor expansion of n in n 1539426658.518 * [misc]backup-simplify: Simplify 0 into 0 1539426658.518 * [misc]backup-simplify: Simplify 1 into 1 1539426658.518 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.518 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426658.518 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.518 * [misc]backup-simplify: Simplify 2 into 2 1539426658.518 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.518 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.518 * [misc]backup-simplify: Simplify PI into PI 1539426658.518 * [misc]taylor: Taking taylor expansion of n in n 1539426658.518 * [misc]backup-simplify: Simplify 0 into 0 1539426658.518 * [misc]backup-simplify: Simplify 1 into 1 1539426658.518 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.519 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.519 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426658.520 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.521 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426658.521 * [misc]backup-simplify: Simplify 0 into 0 1539426658.522 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.523 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426658.523 * [misc]backup-simplify: Simplify 0 into 0 1539426658.525 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.527 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.527 * [misc]backup-simplify: Simplify 0 into 0 1539426658.529 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.531 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426658.531 * [misc]backup-simplify: Simplify 0 into 0 1539426658.533 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.536 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426658.536 * [misc]backup-simplify: Simplify 0 into 0 1539426658.538 * [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 1539426658.541 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426658.541 * [misc]backup-simplify: Simplify 0 into 0 1539426658.542 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539426658.542 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539426658.542 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539426658.542 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.542 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.542 * [misc]backup-simplify: Simplify -2 into -2 1539426658.542 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.542 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.542 * [misc]backup-simplify: Simplify PI into PI 1539426658.542 * [misc]taylor: Taking taylor expansion of n in n 1539426658.542 * [misc]backup-simplify: Simplify 0 into 0 1539426658.542 * [misc]backup-simplify: Simplify 1 into 1 1539426658.542 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.542 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.543 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.543 * [misc]backup-simplify: Simplify -2 into -2 1539426658.543 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.543 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.543 * [misc]backup-simplify: Simplify PI into PI 1539426658.543 * [misc]taylor: Taking taylor expansion of n in n 1539426658.543 * [misc]backup-simplify: Simplify 0 into 0 1539426658.543 * [misc]backup-simplify: Simplify 1 into 1 1539426658.543 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.543 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.543 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.544 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.544 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426658.544 * [misc]backup-simplify: Simplify 0 into 0 1539426658.545 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.546 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426658.546 * [misc]backup-simplify: Simplify 0 into 0 1539426658.547 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.548 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.548 * [misc]backup-simplify: Simplify 0 into 0 1539426658.549 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.550 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426658.550 * [misc]backup-simplify: Simplify 0 into 0 1539426658.551 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.553 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426658.553 * [misc]backup-simplify: Simplify 0 into 0 1539426658.554 * [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 1539426658.556 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426658.556 * [misc]backup-simplify: Simplify 0 into 0 1539426658.556 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539426658.557 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1) 1539426658.557 * [misc]backup-simplify: Simplify (sqrt (* (* PI 2) n)) into (* (sqrt 2) (sqrt (* n PI))) 1539426658.557 * [misc]approximate: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in (n) around 0 1539426658.557 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1539426658.557 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426658.557 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.557 * [misc]backup-simplify: Simplify 2 into 2 1539426658.557 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.557 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.557 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1539426658.557 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.557 * [misc]taylor: Taking taylor expansion of n in n 1539426658.557 * [misc]backup-simplify: Simplify 0 into 0 1539426658.557 * [misc]backup-simplify: Simplify 1 into 1 1539426658.557 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.557 * [misc]backup-simplify: Simplify PI into PI 1539426658.557 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426658.558 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426658.558 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.558 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426658.558 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1539426658.558 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426658.558 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.558 * [misc]backup-simplify: Simplify 2 into 2 1539426658.558 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.559 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.559 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1539426658.559 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426658.559 * [misc]taylor: Taking taylor expansion of n in n 1539426658.559 * [misc]backup-simplify: Simplify 0 into 0 1539426658.559 * [misc]backup-simplify: Simplify 1 into 1 1539426658.559 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.559 * [misc]backup-simplify: Simplify PI into PI 1539426658.559 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426658.559 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426658.559 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.560 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426658.560 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426658.560 * [misc]backup-simplify: Simplify 0 into 0 1539426658.560 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426658.561 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426658.562 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426658.563 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539426658.563 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426658.565 * [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)))) 1539426658.566 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1539426658.567 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426658.568 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539426658.568 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426658.570 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 3))) (+ (* 0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1539426658.571 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1539426658.575 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) (pow n 3)) (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow n 2)) (* (- (* +nan.0 (* (sqrt 2) PI))) n))) into (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))) 1539426658.575 * [misc]backup-simplify: Simplify (sqrt (* (* PI 2) (/ 1 n))) into (* (sqrt 2) (sqrt (/ PI n))) 1539426658.575 * [misc]approximate: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in (n) around 0 1539426658.575 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 1539426658.575 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426658.575 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.576 * [misc]backup-simplify: Simplify 2 into 2 1539426658.576 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.576 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.576 * [misc]taylor: Taking taylor expansion of (sqrt (/ PI n)) in n 1539426658.576 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.576 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.576 * [misc]backup-simplify: Simplify PI into PI 1539426658.576 * [misc]taylor: Taking taylor expansion of n in n 1539426658.576 * [misc]backup-simplify: Simplify 0 into 0 1539426658.576 * [misc]backup-simplify: Simplify 1 into 1 1539426658.576 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.576 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.577 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426658.577 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 1539426658.577 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426658.577 * [misc]taylor: Taking taylor expansion of 2 in n 1539426658.577 * [misc]backup-simplify: Simplify 2 into 2 1539426658.577 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426658.577 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426658.577 * [misc]taylor: Taking taylor expansion of (sqrt (/ PI n)) in n 1539426658.577 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.577 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.577 * [misc]backup-simplify: Simplify PI into PI 1539426658.577 * [misc]taylor: Taking taylor expansion of n in n 1539426658.577 * [misc]backup-simplify: Simplify 0 into 0 1539426658.577 * [misc]backup-simplify: Simplify 1 into 1 1539426658.578 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.578 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.578 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426658.578 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426658.578 * [misc]backup-simplify: Simplify 0 into 0 1539426658.579 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426658.580 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426658.581 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.583 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539426658.584 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426658.586 * [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)))) 1539426658.587 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1539426658.589 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.591 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539426658.592 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426658.595 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 3))) (+ (* 0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1539426658.596 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1539426658.599 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) (pow (/ 1 n) 2)) (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (/ 1 n)) (- (* +nan.0 (* (sqrt 2) PI))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (pow n 2))) (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) n)) (- (* +nan.0 (* (sqrt 2) PI))))))) 1539426658.600 * [misc]backup-simplify: Simplify (sqrt (* (* PI 2) (/ 1 (- n)))) into (sqrt (* -2 (/ PI n))) 1539426658.600 * [misc]approximate: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in (n) around 0 1539426658.600 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539426658.600 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.600 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.600 * [misc]backup-simplify: Simplify -2 into -2 1539426658.600 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.600 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.600 * [misc]backup-simplify: Simplify PI into PI 1539426658.600 * [misc]taylor: Taking taylor expansion of n in n 1539426658.600 * [misc]backup-simplify: Simplify 0 into 0 1539426658.600 * [misc]backup-simplify: Simplify 1 into 1 1539426658.600 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.600 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.600 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.601 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426658.601 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539426658.601 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426658.601 * [misc]taylor: Taking taylor expansion of -2 in n 1539426658.601 * [misc]backup-simplify: Simplify -2 into -2 1539426658.601 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426658.601 * [misc]taylor: Taking taylor expansion of PI in n 1539426658.601 * [misc]backup-simplify: Simplify PI into PI 1539426658.601 * [misc]taylor: Taking taylor expansion of n in n 1539426658.601 * [misc]backup-simplify: Simplify 0 into 0 1539426658.601 * [misc]backup-simplify: Simplify 1 into 1 1539426658.601 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426658.601 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426658.601 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426658.602 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426658.602 * [misc]backup-simplify: Simplify 0 into 0 1539426658.602 * [misc]backup-simplify: Simplify (* +nan.0 PI) into (* +nan.0 PI) 1539426658.603 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426658.603 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426658.604 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539426658.604 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 2)) into (* +nan.0 (pow PI 2)) 1539426658.605 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426658.606 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426658.607 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539426658.608 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 3)) into (* +nan.0 (pow PI 3)) 1539426658.608 * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (pow PI 3)) (pow (/ 1 (- n)) 2)) (+ (* (* +nan.0 (pow PI 2)) (/ 1 (- n))) (* +nan.0 PI))) into (- (+ (* +nan.0 PI) (- (+ (* +nan.0 (/ (pow PI 3) (pow n 2))) (- (* +nan.0 (/ (pow PI 2) n))))))) 1539426658.609 * * * [misc]progress: simplifying candidates 1539426658.609 * * * * [misc]progress: [ 1 / 83 ] simplifiying candidate # 1539426658.609 * * * * [misc]progress: [ 2 / 83 ] simplifiying candidate # 1539426658.609 * * * * [misc]progress: [ 3 / 83 ] simplifiying candidate # 1539426658.609 * [enter]simplify: Simplifying (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1539426658.609 * * [misc]simplify: iters left: 6 (15 enodes) 1539426658.611 * * [misc]simplify: iters left: 5 (27 enodes) 1539426658.616 * * [misc]simplify: iters left: 4 (35 enodes) 1539426658.619 * * [misc]simplify: iters left: 3 (37 enodes) 1539426658.623 * * [misc]simplify: iters left: 2 (39 enodes) 1539426658.627 * * [misc]simplify: iters left: 1 (40 enodes) 1539426658.637 * [exit]simplify: Simplified to (* (pow (* (* PI 2) n) (- (/ k 2))) (/ (sqrt (* (* PI 2) n)) (sqrt k))) 1539426658.637 * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (* (pow (* (* PI 2) n) (- (/ k 2))) (/ (sqrt (* (* PI 2) n)) (sqrt k))) 1)) 1539426658.637 * * * * [misc]progress: [ 4 / 83 ] simplifiying candidate # 1539426658.637 * * * * [misc]progress: [ 5 / 83 ] simplifiying candidate # 1539426658.637 * [enter]simplify: Simplifying (+ (log (sqrt (* (* PI 2) n))) (- (* (log (* PI (* n 2))) (- (/ k 2))) (log (sqrt k)))) 1539426658.638 * * [misc]simplify: iters left: 6 (18 enodes) 1539426658.643 * * [misc]simplify: iters left: 5 (39 enodes) 1539426658.650 * * [misc]simplify: iters left: 4 (75 enodes) 1539426658.664 * * [misc]simplify: iters left: 3 (189 enodes) 1539426658.745 * [exit]simplify: Simplified to (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))) 1539426658.745 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))))) 1539426658.745 * * * * [misc]progress: [ 6 / 83 ] simplifiying candidate # 1539426658.745 * [enter]simplify: Simplifying (+ (log (sqrt (* (* PI 2) n))) (- (* (log (* PI (* n 2))) (- (/ k 2))) (log (sqrt k)))) 1539426658.745 * * [misc]simplify: iters left: 6 (18 enodes) 1539426658.748 * * [misc]simplify: iters left: 5 (39 enodes) 1539426658.754 * * [misc]simplify: iters left: 4 (75 enodes) 1539426658.769 * * [misc]simplify: iters left: 3 (189 enodes) 1539426658.824 * [exit]simplify: Simplified to (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))) 1539426658.824 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* PI 2) n))) (fma (/ k 2) (log (* (* PI 2) n)) (log (sqrt k)))))) 1539426658.824 * * * * [misc]progress: [ 7 / 83 ] simplifiying candidate # 1539426658.825 * [enter]simplify: Simplifying (+ (log (sqrt (* (* PI 2) n))) (- (log (pow (* PI (* n 2)) (- (/ k 2)))) (log (sqrt k)))) 1539426658.825 * * [misc]simplify: iters left: 6 (18 enodes) 1539426658.828 * * [misc]simplify: iters left: 5 (34 enodes) 1539426658.833 * * [misc]simplify: iters left: 4 (64 enodes) 1539426658.844 * * [misc]simplify: iters left: 3 (169 enodes) 1539426658.926 * [exit]simplify: Simplified to (- (log (sqrt (* (* PI 2) n))) (fma (log (* (* PI 2) n)) (/ k 2) (log (sqrt k)))) 1539426658.926 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* PI 2) n))) (fma (log (* (* PI 2) n)) (/ k 2) (log (sqrt k)))))) 1539426658.926 * * * * [misc]progress: [ 8 / 83 ] simplifiying candidate # 1539426658.926 * [enter]simplify: Simplifying (+ (log (sqrt (* (* PI 2) n))) (log (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426658.926 * * [misc]simplify: iters left: 6 (17 enodes) 1539426658.932 * * [misc]simplify: iters left: 5 (30 enodes) 1539426658.940 * * [misc]simplify: iters left: 4 (42 enodes) 1539426658.951 * * [misc]simplify: iters left: 3 (70 enodes) 1539426658.976 * * [misc]simplify: iters left: 2 (183 enodes) 1539426659.103 * [exit]simplify: Simplified to (- (log (sqrt (* 2 (* n PI)))) (fma (/ k 2) (log (* 2 (* n PI))) (log (sqrt k)))) 1539426659.104 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* 2 (* n PI)))) (fma (/ k 2) (log (* 2 (* n PI))) (log (sqrt k)))))) 1539426659.104 * * * * [misc]progress: [ 9 / 83 ] simplifiying candidate # 1539426659.104 * * * * [misc]progress: [ 10 / 83 ] simplifiying candidate # 1539426659.104 * * * * [misc]progress: [ 11 / 83 ] simplifiying candidate # 1539426659.104 * [enter]simplify: Simplifying (* (* (* (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n))) (sqrt (* (* PI 2) n))) (/ (* (* (pow (* PI (* n 2)) (- (/ k 2))) (pow (* PI (* n 2)) (- (/ k 2)))) (pow (* PI (* n 2)) (- (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1539426659.104 * * [misc]simplify: iters left: 6 (21 enodes) 1539426659.109 * * [misc]simplify: iters left: 5 (46 enodes) 1539426659.127 * * [misc]simplify: iters left: 4 (154 enodes) 1539426659.259 * [exit]simplify: Simplified to (* (/ (sqrt (* (* n PI) 2)) (/ k (* (* n PI) 2))) (* (* (pow (* (* n PI) 2) (- (/ k 2))) (pow (* (* n PI) 2) (- (/ k 2)))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))) 1539426659.259 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (sqrt (* (* n PI) 2)) (/ k (* (* n PI) 2))) (* (* (pow (* (* n PI) 2) (- (/ k 2))) (pow (* (* n PI) 2) (- (/ k 2)))) (/ (pow (* (* n PI) 2) (- (/ k 2))) (sqrt k)))))) 1539426659.259 * * * * [misc]progress: [ 12 / 83 ] simplifiying candidate # 1539426659.260 * [enter]simplify: Simplifying (* (* (* (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n))) (sqrt (* (* PI 2) n))) (* (* (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.260 * * [misc]simplify: iters left: 6 (19 enodes) 1539426659.263 * * [misc]simplify: iters left: 5 (42 enodes) 1539426659.271 * * [misc]simplify: iters left: 4 (132 enodes) 1539426659.342 * [exit]simplify: Simplified to (* (* (* (* PI (* n 2)) (sqrt (* PI (* n 2)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (* (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.342 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (* (* PI (* n 2)) (sqrt (* PI (* n 2)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (* (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))))) 1539426659.343 * * * * [misc]progress: [ 13 / 83 ] simplifiying candidate # 1539426659.343 * * * * [misc]progress: [ 14 / 83 ] simplifiying candidate # 1539426659.343 * * * * [misc]progress: [ 15 / 83 ] simplifiying candidate # 1539426659.343 * * * * [misc]progress: [ 16 / 83 ] simplifiying candidate # 1539426659.343 * * * * [misc]progress: [ 17 / 83 ] simplifiying candidate # 1539426659.343 * [enter]simplify: Simplifying (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1539426659.343 * * [misc]simplify: iters left: 6 (12 enodes) 1539426659.347 * * [misc]simplify: iters left: 5 (18 enodes) 1539426659.352 * * [misc]simplify: iters left: 4 (24 enodes) 1539426659.359 * * [misc]simplify: iters left: 3 (25 enodes) 1539426659.365 * [exit]simplify: Simplified to (cbrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1539426659.365 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (* (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1539426659.365 * * * * [misc]progress: [ 18 / 83 ] simplifiying candidate # 1539426659.365 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))) 1539426659.365 * * [misc]simplify: iters left: 6 (12 enodes) 1539426659.369 * * [misc]simplify: iters left: 5 (18 enodes) 1539426659.374 * * [misc]simplify: iters left: 4 (24 enodes) 1539426659.383 * * [misc]simplify: iters left: 3 (25 enodes) 1539426659.389 * [exit]simplify: Simplified to (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))) 1539426659.389 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (sqrt (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))) 1539426659.389 * * * * [misc]progress: [ 19 / 83 ] simplifiying candidate # 1539426659.390 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (cbrt (sqrt k))) 1539426659.390 * * [misc]simplify: iters left: 6 (10 enodes) 1539426659.393 * * [misc]simplify: iters left: 5 (13 enodes) 1539426659.396 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))) 1539426659.396 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (pow PI (- (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n 2) (/ (- k) 2)) (cbrt (sqrt k))))) 1539426659.396 * * * * [misc]progress: [ 20 / 83 ] simplifiying candidate # 1539426659.396 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt (sqrt k))) 1539426659.396 * * [misc]simplify: iters left: 6 (10 enodes) 1539426659.399 * * [misc]simplify: iters left: 5 (13 enodes) 1539426659.403 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))) 1539426659.403 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- k) 2)) (sqrt (sqrt k))))) 1539426659.403 * * * * [misc]progress: [ 21 / 83 ] simplifiying candidate # 1539426659.403 * [enter]simplify: Simplifying (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1539426659.403 * * [misc]simplify: iters left: 6 (9 enodes) 1539426659.406 * * [misc]simplify: iters left: 5 (12 enodes) 1539426659.409 * [exit]simplify: Simplified to (/ (pow (* n 2) (- (/ k 2))) (sqrt k)) 1539426659.409 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (pow PI (- (/ k 2))) 1)) (/ (pow (* n 2) (- (/ k 2))) (sqrt k)))) 1539426659.409 * * * * [misc]progress: [ 22 / 83 ] simplifiying candidate # 1539426659.409 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k))) 1539426659.410 * * [misc]simplify: iters left: 6 (13 enodes) 1539426659.414 * * [misc]simplify: iters left: 5 (19 enodes) 1539426659.419 * * [misc]simplify: iters left: 4 (25 enodes) 1539426659.426 * * [misc]simplify: iters left: 3 (26 enodes) 1539426659.432 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))) 1539426659.432 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))))) 1539426659.432 * * * * [misc]progress: [ 23 / 83 ] simplifiying candidate # 1539426659.432 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) 1539426659.433 * * [misc]simplify: iters left: 6 (13 enodes) 1539426659.436 * * [misc]simplify: iters left: 5 (19 enodes) 1539426659.442 * * [misc]simplify: iters left: 4 (25 enodes) 1539426659.448 * * [misc]simplify: iters left: 3 (26 enodes) 1539426659.455 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) 1539426659.455 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))))) 1539426659.455 * * * * [misc]progress: [ 24 / 83 ] simplifiying candidate # 1539426659.455 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)) 1539426659.456 * * [misc]simplify: iters left: 6 (12 enodes) 1539426659.459 * * [misc]simplify: iters left: 5 (18 enodes) 1539426659.465 * * [misc]simplify: iters left: 4 (24 enodes) 1539426659.471 * * [misc]simplify: iters left: 3 (25 enodes) 1539426659.477 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)) 1539426659.477 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (* (cbrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- (/ k 2))))) 1)) (/ (cbrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)))) 1539426659.477 * * * * [misc]progress: [ 25 / 83 ] simplifiying candidate # 1539426659.478 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k))) 1539426659.478 * * [misc]simplify: iters left: 6 (13 enodes) 1539426659.482 * * [misc]simplify: iters left: 5 (19 enodes) 1539426659.487 * * [misc]simplify: iters left: 4 (25 enodes) 1539426659.493 * * [misc]simplify: iters left: 3 (26 enodes) 1539426659.500 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))) 1539426659.500 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (cbrt (sqrt k))))) 1539426659.500 * * * * [misc]progress: [ 26 / 83 ] simplifiying candidate # 1539426659.500 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k))) 1539426659.501 * * [misc]simplify: iters left: 6 (13 enodes) 1539426659.505 * * [misc]simplify: iters left: 5 (19 enodes) 1539426659.510 * * [misc]simplify: iters left: 4 (25 enodes) 1539426659.517 * * [misc]simplify: iters left: 3 (26 enodes) 1539426659.523 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))) 1539426659.523 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt (sqrt k))))) 1539426659.523 * * * * [misc]progress: [ 27 / 83 ] simplifiying candidate # 1539426659.524 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)) 1539426659.524 * * [misc]simplify: iters left: 6 (12 enodes) 1539426659.528 * * [misc]simplify: iters left: 5 (18 enodes) 1539426659.533 * * [misc]simplify: iters left: 4 (24 enodes) 1539426659.539 * * [misc]simplify: iters left: 3 (25 enodes) 1539426659.545 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)) 1539426659.545 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ (sqrt (pow (* PI (* n 2)) (- (/ k 2)))) 1)) (/ (sqrt (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)))) 1539426659.545 * * * * [misc]progress: [ 28 / 83 ] simplifiying candidate # 1539426659.546 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1539426659.546 * * [misc]simplify: iters left: 6 (12 enodes) 1539426659.550 * * [misc]simplify: iters left: 5 (18 enodes) 1539426659.555 * * [misc]simplify: iters left: 4 (24 enodes) 1539426659.561 * * [misc]simplify: iters left: 3 (25 enodes) 1539426659.567 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1539426659.567 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) 1539426659.567 * * * * [misc]progress: [ 29 / 83 ] simplifiying candidate # 1539426659.568 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1539426659.568 * * [misc]simplify: iters left: 6 (12 enodes) 1539426659.571 * * [misc]simplify: iters left: 5 (18 enodes) 1539426659.577 * * [misc]simplify: iters left: 4 (24 enodes) 1539426659.583 * * [misc]simplify: iters left: 3 (25 enodes) 1539426659.589 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1539426659.589 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ 1 (sqrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) 1539426659.589 * * * * [misc]progress: [ 30 / 83 ] simplifiying candidate # 1539426659.589 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1539426659.589 * * [misc]simplify: iters left: 6 (11 enodes) 1539426659.593 * * [misc]simplify: iters left: 5 (17 enodes) 1539426659.597 * * [misc]simplify: iters left: 4 (23 enodes) 1539426659.603 * * [misc]simplify: iters left: 3 (24 enodes) 1539426659.609 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1539426659.609 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (/ 1 1)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1539426659.609 * * * * [misc]progress: [ 31 / 83 ] simplifiying candidate # 1539426659.609 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1539426659.609 * * [misc]simplify: iters left: 6 (11 enodes) 1539426659.613 * * [misc]simplify: iters left: 5 (17 enodes) 1539426659.618 * * [misc]simplify: iters left: 4 (23 enodes) 1539426659.624 * * [misc]simplify: iters left: 3 (24 enodes) 1539426659.629 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1539426659.629 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) 1) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1539426659.630 * * * * [misc]progress: [ 32 / 83 ] simplifiying candidate # 1539426659.630 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1539426659.630 * * [misc]simplify: iters left: 3 (4 enodes) 1539426659.631 * * [misc]simplify: iters left: 2 (6 enodes) 1539426659.633 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1539426659.633 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (sqrt (* (* PI 2) n)) (pow (* PI (* n 2)) (- (/ k 2)))) (/ 1 (sqrt k)))) 1539426659.633 * * * * [misc]progress: [ 33 / 83 ] simplifiying candidate # 1539426659.633 * [enter]simplify: Simplifying (* (cbrt (sqrt (* (* PI 2) n))) (cbrt (sqrt (* (* PI 2) n)))) 1539426659.633 * * [misc]simplify: iters left: 6 (8 enodes) 1539426659.636 * * [misc]simplify: iters left: 5 (12 enodes) 1539426659.639 * * [misc]simplify: iters left: 4 (18 enodes) 1539426659.644 * * [misc]simplify: iters left: 3 (20 enodes) 1539426659.648 * [exit]simplify: Simplified to (* (cbrt (sqrt (* PI (* n 2)))) (cbrt (sqrt (* PI (* n 2))))) 1539426659.648 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (sqrt (* PI (* n 2)))) (cbrt (sqrt (* PI (* n 2))))) (* (cbrt (sqrt (* (* PI 2) n))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1539426659.648 * * * * [misc]progress: [ 34 / 83 ] simplifiying candidate # 1539426659.649 * [enter]simplify: Simplifying (sqrt (* PI 2)) 1539426659.649 * * [misc]simplify: iters left: 3 (4 enodes) 1539426659.650 * * [misc]simplify: iters left: 2 (5 enodes) 1539426659.651 * [exit]simplify: Simplified to (sqrt (* PI 2)) 1539426659.651 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* PI 2)) (* (sqrt n) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1539426659.651 * * * * [misc]progress: [ 35 / 83 ] simplifiying candidate # 1539426659.651 * [enter]simplify: Simplifying (sqrt (sqrt (* (* PI 2) n))) 1539426659.651 * * [misc]simplify: iters left: 6 (7 enodes) 1539426659.653 * * [misc]simplify: iters left: 5 (11 enodes) 1539426659.656 * * [misc]simplify: iters left: 4 (17 enodes) 1539426659.661 * * [misc]simplify: iters left: 3 (19 enodes) 1539426659.666 * [exit]simplify: Simplified to (sqrt (sqrt (* (* PI 2) n))) 1539426659.666 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (* (* PI 2) n))) (* (sqrt (sqrt (* (* PI 2) n))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))) 1539426659.666 * * * * [misc]progress: [ 36 / 83 ] simplifiying candidate # 1539426659.666 * * * * [misc]progress: [ 37 / 83 ] simplifiying candidate # 1539426659.666 * [enter]simplify: Simplifying (sqrt k) 1539426659.666 * * [misc]simplify: iters left: 1 (2 enodes) 1539426659.667 * [exit]simplify: Simplified to (sqrt k) 1539426659.667 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt (* (* PI 2) n)) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k))) 1539426659.667 * * * * [misc]progress: [ 38 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 39 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 40 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 41 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 42 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 43 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 44 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 45 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 46 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 47 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 48 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 49 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 50 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 51 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 52 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 53 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 54 / 83 ] simplifiying candidate # 1539426659.668 * * * * [misc]progress: [ 55 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 56 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 57 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 58 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 59 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 60 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 61 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 62 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 63 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 64 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 65 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 66 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 67 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 68 / 83 ] simplifiying candidate # 1539426659.669 * * * * [misc]progress: [ 69 / 83 ] simplifiying candidate # 1539426659.670 * [enter]simplify: Simplifying (sqrt (* PI 2)) 1539426659.670 * * [misc]simplify: iters left: 3 (4 enodes) 1539426659.671 * * [misc]simplify: iters left: 2 (5 enodes) 1539426659.672 * [exit]simplify: Simplified to (sqrt (* PI 2)) 1539426659.672 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (sqrt (* PI 2)) (sqrt n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.672 * * * * [misc]progress: [ 70 / 83 ] simplifiying candidate # 1539426659.672 * * * * [misc]progress: [ 71 / 83 ] simplifiying candidate # 1539426659.672 * * * * [misc]progress: [ 72 / 83 ] simplifiying candidate # 1539426659.673 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log n)))) k)) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (* (pow PI 2) (log (* 2 PI))))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) 1539426659.673 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426659.673 * * * * [misc]progress: [ 73 / 83 ] simplifiying candidate # 1539426659.673 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 2))) (* n (pow k 2)))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (pow PI 3))) (* (pow n 2) (pow k 3)))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) PI)) k))))))) 1539426659.673 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426659.673 * * * * [misc]progress: [ 74 / 83 ] simplifiying candidate # 1539426659.673 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI)) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow PI 2)) n))))))) 1539426659.673 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426659.674 * * * * [misc]progress: [ 75 / 83 ] simplifiying candidate # 1539426659.674 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426659.674 * * [misc]simplify: iters left: 4 (5 enodes) 1539426659.675 * * [misc]simplify: iters left: 3 (9 enodes) 1539426659.678 * * [misc]simplify: iters left: 2 (15 enodes) 1539426659.682 * * [misc]simplify: iters left: 1 (17 enodes) 1539426659.686 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426659.686 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.686 * * * * [misc]progress: [ 76 / 83 ] simplifiying candidate # 1539426659.686 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426659.686 * * [misc]simplify: iters left: 4 (5 enodes) 1539426659.688 * * [misc]simplify: iters left: 3 (9 enodes) 1539426659.690 * * [misc]simplify: iters left: 2 (15 enodes) 1539426659.694 * * [misc]simplify: iters left: 1 (17 enodes) 1539426659.697 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426659.697 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.698 * * * * [misc]progress: [ 77 / 83 ] simplifiying candidate # 1539426659.698 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426659.698 * * [misc]simplify: iters left: 4 (5 enodes) 1539426659.699 * * [misc]simplify: iters left: 3 (9 enodes) 1539426659.702 * * [misc]simplify: iters left: 2 (15 enodes) 1539426659.705 * * [misc]simplify: iters left: 1 (17 enodes) 1539426659.709 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426659.709 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (sqrt (* (* PI n) 2)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.709 * * * * [misc]progress: [ 78 / 83 ] simplifiying candidate # 1539426659.710 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426659.710 * * [misc]simplify: iters left: 4 (5 enodes) 1539426659.711 * * [misc]simplify: iters left: 3 (9 enodes) 1539426659.714 * * [misc]simplify: iters left: 2 (15 enodes) 1539426659.718 * * [misc]simplify: iters left: 1 (17 enodes) 1539426659.722 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426659.722 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1539426659.722 * * * * [misc]progress: [ 79 / 83 ] simplifiying candidate # 1539426659.722 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426659.722 * * [misc]simplify: iters left: 4 (5 enodes) 1539426659.724 * * [misc]simplify: iters left: 3 (9 enodes) 1539426659.726 * * [misc]simplify: iters left: 2 (15 enodes) 1539426659.730 * * [misc]simplify: iters left: 1 (17 enodes) 1539426659.734 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426659.734 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1539426659.734 * * * * [misc]progress: [ 80 / 83 ] simplifiying candidate # 1539426659.734 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426659.734 * * [misc]simplify: iters left: 4 (5 enodes) 1539426659.736 * * [misc]simplify: iters left: 3 (9 enodes) 1539426659.738 * * [misc]simplify: iters left: 2 (15 enodes) 1539426659.742 * * [misc]simplify: iters left: 1 (17 enodes) 1539426659.746 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426659.746 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1539426659.746 * * * * [misc]progress: [ 81 / 83 ] simplifiying candidate # 1539426659.746 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))) 1539426659.746 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.746 * * * * [misc]progress: [ 82 / 83 ] simplifiying candidate # 1539426659.746 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (pow n 2))) (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) n)) (- (* +nan.0 (* (sqrt 2) PI))))))) 1539426659.746 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.746 * * * * [misc]progress: [ 83 / 83 ] simplifiying candidate # 1539426659.747 * [enter]simplify: Simplifying (- (+ (* +nan.0 PI) (- (+ (* +nan.0 (/ (pow PI 3) (pow n 2))) (- (* +nan.0 (/ (pow PI 2) n))))))) 1539426659.747 * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539426659.747 * * * [misc]progress: adding candidates to table 1539426660.691 * * [misc]progress: iteration 4 / 4 1539426660.691 * * * [misc]progress: picking best candidate 1539426660.740 * * * * [misc]pick: Picked # 1539426660.740 * * * [misc]progress: localizing error 1539426660.752 * * * [misc]progress: generating rewritten candidates 1539426660.752 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 2 1) 1539426660.756 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1 1) 1539426660.758 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1539426660.782 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1539426660.825 * * * [misc]progress: generating series expansions 1539426660.825 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 2 1) 1539426660.825 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539426660.825 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539426660.825 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426660.825 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.825 * [misc]backup-simplify: Simplify 2 into 2 1539426660.825 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.825 * [misc]taylor: Taking taylor expansion of n in n 1539426660.825 * [misc]backup-simplify: Simplify 0 into 0 1539426660.825 * [misc]backup-simplify: Simplify 1 into 1 1539426660.825 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.825 * [misc]backup-simplify: Simplify PI into PI 1539426660.825 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426660.825 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.825 * [misc]backup-simplify: Simplify 2 into 2 1539426660.825 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.825 * [misc]taylor: Taking taylor expansion of n in n 1539426660.825 * [misc]backup-simplify: Simplify 0 into 0 1539426660.825 * [misc]backup-simplify: Simplify 1 into 1 1539426660.825 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.825 * [misc]backup-simplify: Simplify PI into PI 1539426660.826 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426660.826 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426660.826 * [misc]backup-simplify: Simplify 0 into 0 1539426660.827 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426660.828 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426660.828 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426660.829 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426660.830 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426660.830 * [misc]backup-simplify: Simplify 0 into 0 1539426660.832 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426660.833 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426660.833 * [misc]backup-simplify: Simplify 0 into 0 1539426660.835 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426660.837 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426660.837 * [misc]backup-simplify: Simplify 0 into 0 1539426660.840 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426660.842 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539426660.842 * [misc]backup-simplify: Simplify 0 into 0 1539426660.846 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426660.849 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539426660.849 * [misc]backup-simplify: Simplify 0 into 0 1539426660.854 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539426660.858 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539426660.858 * [misc]backup-simplify: Simplify 0 into 0 1539426660.859 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539426660.859 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539426660.859 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539426660.859 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426660.859 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.859 * [misc]backup-simplify: Simplify 2 into 2 1539426660.859 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426660.859 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.859 * [misc]backup-simplify: Simplify PI into PI 1539426660.859 * [misc]taylor: Taking taylor expansion of n in n 1539426660.859 * [misc]backup-simplify: Simplify 0 into 0 1539426660.859 * [misc]backup-simplify: Simplify 1 into 1 1539426660.859 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426660.859 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426660.859 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.860 * [misc]backup-simplify: Simplify 2 into 2 1539426660.860 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426660.860 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.860 * [misc]backup-simplify: Simplify PI into PI 1539426660.860 * [misc]taylor: Taking taylor expansion of n in n 1539426660.860 * [misc]backup-simplify: Simplify 0 into 0 1539426660.860 * [misc]backup-simplify: Simplify 1 into 1 1539426660.860 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426660.860 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426660.861 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426660.862 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426660.862 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426660.862 * [misc]backup-simplify: Simplify 0 into 0 1539426660.864 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.865 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426660.865 * [misc]backup-simplify: Simplify 0 into 0 1539426660.866 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.868 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426660.868 * [misc]backup-simplify: Simplify 0 into 0 1539426660.870 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.872 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426660.872 * [misc]backup-simplify: Simplify 0 into 0 1539426660.874 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.877 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426660.877 * [misc]backup-simplify: Simplify 0 into 0 1539426660.880 * [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 1539426660.883 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426660.883 * [misc]backup-simplify: Simplify 0 into 0 1539426660.883 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539426660.883 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539426660.884 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539426660.884 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426660.884 * [misc]taylor: Taking taylor expansion of -2 in n 1539426660.884 * [misc]backup-simplify: Simplify -2 into -2 1539426660.884 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426660.884 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.884 * [misc]backup-simplify: Simplify PI into PI 1539426660.884 * [misc]taylor: Taking taylor expansion of n in n 1539426660.884 * [misc]backup-simplify: Simplify 0 into 0 1539426660.884 * [misc]backup-simplify: Simplify 1 into 1 1539426660.884 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426660.884 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426660.884 * [misc]taylor: Taking taylor expansion of -2 in n 1539426660.884 * [misc]backup-simplify: Simplify -2 into -2 1539426660.884 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426660.884 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.884 * [misc]backup-simplify: Simplify PI into PI 1539426660.884 * [misc]taylor: Taking taylor expansion of n in n 1539426660.884 * [misc]backup-simplify: Simplify 0 into 0 1539426660.884 * [misc]backup-simplify: Simplify 1 into 1 1539426660.884 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426660.884 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426660.884 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426660.885 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426660.886 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426660.886 * [misc]backup-simplify: Simplify 0 into 0 1539426660.886 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.887 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426660.887 * [misc]backup-simplify: Simplify 0 into 0 1539426660.888 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.889 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426660.889 * [misc]backup-simplify: Simplify 0 into 0 1539426660.890 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.891 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426660.891 * [misc]backup-simplify: Simplify 0 into 0 1539426660.893 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.894 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426660.894 * [misc]backup-simplify: Simplify 0 into 0 1539426660.897 * [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 1539426660.899 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426660.899 * [misc]backup-simplify: Simplify 0 into 0 1539426660.899 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539426660.899 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1 1) 1539426660.899 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539426660.899 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539426660.899 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426660.899 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.899 * [misc]backup-simplify: Simplify 2 into 2 1539426660.899 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.899 * [misc]taylor: Taking taylor expansion of n in n 1539426660.899 * [misc]backup-simplify: Simplify 0 into 0 1539426660.899 * [misc]backup-simplify: Simplify 1 into 1 1539426660.899 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.899 * [misc]backup-simplify: Simplify PI into PI 1539426660.899 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426660.899 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.899 * [misc]backup-simplify: Simplify 2 into 2 1539426660.899 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.899 * [misc]taylor: Taking taylor expansion of n in n 1539426660.899 * [misc]backup-simplify: Simplify 0 into 0 1539426660.899 * [misc]backup-simplify: Simplify 1 into 1 1539426660.899 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.899 * [misc]backup-simplify: Simplify PI into PI 1539426660.900 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426660.900 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426660.900 * [misc]backup-simplify: Simplify 0 into 0 1539426660.900 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426660.901 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426660.901 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426660.902 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426660.902 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426660.902 * [misc]backup-simplify: Simplify 0 into 0 1539426660.903 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426660.904 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539426660.904 * [misc]backup-simplify: Simplify 0 into 0 1539426660.905 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426660.906 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539426660.907 * [misc]backup-simplify: Simplify 0 into 0 1539426660.908 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426660.910 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539426660.910 * [misc]backup-simplify: Simplify 0 into 0 1539426660.912 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426660.913 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539426660.913 * [misc]backup-simplify: Simplify 0 into 0 1539426660.916 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539426660.918 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539426660.918 * [misc]backup-simplify: Simplify 0 into 0 1539426660.918 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539426660.918 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539426660.918 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539426660.918 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426660.918 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.918 * [misc]backup-simplify: Simplify 2 into 2 1539426660.918 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426660.918 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.918 * [misc]backup-simplify: Simplify PI into PI 1539426660.918 * [misc]taylor: Taking taylor expansion of n in n 1539426660.918 * [misc]backup-simplify: Simplify 0 into 0 1539426660.918 * [misc]backup-simplify: Simplify 1 into 1 1539426660.919 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426660.919 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426660.919 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.919 * [misc]backup-simplify: Simplify 2 into 2 1539426660.919 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426660.919 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.919 * [misc]backup-simplify: Simplify PI into PI 1539426660.919 * [misc]taylor: Taking taylor expansion of n in n 1539426660.919 * [misc]backup-simplify: Simplify 0 into 0 1539426660.919 * [misc]backup-simplify: Simplify 1 into 1 1539426660.919 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426660.919 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426660.919 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426660.920 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426660.920 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426660.920 * [misc]backup-simplify: Simplify 0 into 0 1539426660.921 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.922 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426660.922 * [misc]backup-simplify: Simplify 0 into 0 1539426660.923 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.924 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426660.924 * [misc]backup-simplify: Simplify 0 into 0 1539426660.925 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.926 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426660.926 * [misc]backup-simplify: Simplify 0 into 0 1539426660.927 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.929 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426660.929 * [misc]backup-simplify: Simplify 0 into 0 1539426660.930 * [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 1539426660.932 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426660.932 * [misc]backup-simplify: Simplify 0 into 0 1539426660.932 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539426660.933 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539426660.933 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539426660.933 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426660.933 * [misc]taylor: Taking taylor expansion of -2 in n 1539426660.933 * [misc]backup-simplify: Simplify -2 into -2 1539426660.933 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426660.933 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.933 * [misc]backup-simplify: Simplify PI into PI 1539426660.933 * [misc]taylor: Taking taylor expansion of n in n 1539426660.933 * [misc]backup-simplify: Simplify 0 into 0 1539426660.933 * [misc]backup-simplify: Simplify 1 into 1 1539426660.933 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426660.933 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426660.933 * [misc]taylor: Taking taylor expansion of -2 in n 1539426660.933 * [misc]backup-simplify: Simplify -2 into -2 1539426660.933 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426660.933 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.933 * [misc]backup-simplify: Simplify PI into PI 1539426660.933 * [misc]taylor: Taking taylor expansion of n in n 1539426660.933 * [misc]backup-simplify: Simplify 0 into 0 1539426660.933 * [misc]backup-simplify: Simplify 1 into 1 1539426660.933 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426660.933 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426660.934 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426660.934 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426660.935 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426660.935 * [misc]backup-simplify: Simplify 0 into 0 1539426660.935 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.936 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426660.936 * [misc]backup-simplify: Simplify 0 into 0 1539426660.937 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.938 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426660.938 * [misc]backup-simplify: Simplify 0 into 0 1539426660.939 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.941 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426660.941 * [misc]backup-simplify: Simplify 0 into 0 1539426660.943 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426660.945 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539426660.945 * [misc]backup-simplify: Simplify 0 into 0 1539426660.948 * [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 1539426660.951 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539426660.951 * [misc]backup-simplify: Simplify 0 into 0 1539426660.951 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539426660.951 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1539426660.952 * [misc]backup-simplify: Simplify (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))) into (* (/ 1 (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k))))) (sqrt (/ k (* n PI)))) 1539426660.952 * [misc]approximate: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k))))) (sqrt (/ k (* n PI)))) in (k n) around 0 1539426660.952 * [misc]taylor: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k))))) (sqrt (/ k (* n PI)))) in n 1539426660.952 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k))))) in n 1539426660.952 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in n 1539426660.952 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426660.952 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.952 * [misc]backup-simplify: Simplify 2 into 2 1539426660.952 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426660.952 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426660.952 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1539426660.952 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426660.952 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426660.953 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1539426660.953 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426660.953 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426660.953 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426660.953 * [misc]taylor: Taking taylor expansion of k in n 1539426660.953 * [misc]backup-simplify: Simplify k into k 1539426660.953 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426660.953 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426660.953 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.953 * [misc]backup-simplify: Simplify 2 into 2 1539426660.953 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.953 * [misc]taylor: Taking taylor expansion of n in n 1539426660.953 * [misc]backup-simplify: Simplify 0 into 0 1539426660.953 * [misc]backup-simplify: Simplify 1 into 1 1539426660.953 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.953 * [misc]backup-simplify: Simplify PI into PI 1539426660.953 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426660.953 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426660.954 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426660.955 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426660.955 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426660.955 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426660.955 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426660.956 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426660.956 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539426660.957 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539426660.958 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1539426660.958 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (/ 1 (* (sqrt 2) (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))))) 1539426660.958 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in n 1539426660.959 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in n 1539426660.959 * [misc]taylor: Taking taylor expansion of k in n 1539426660.959 * [misc]backup-simplify: Simplify k into k 1539426660.959 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.959 * [misc]taylor: Taking taylor expansion of n in n 1539426660.959 * [misc]backup-simplify: Simplify 0 into 0 1539426660.959 * [misc]backup-simplify: Simplify 1 into 1 1539426660.959 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.959 * [misc]backup-simplify: Simplify PI into PI 1539426660.959 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426660.960 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426660.960 * [misc]backup-simplify: Simplify (/ k PI) into (/ k PI) 1539426660.960 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426660.960 * [misc]backup-simplify: Simplify (/ (/ k PI) (* 2 (sqrt 0))) into (* +nan.0 (/ k PI)) 1539426660.960 * [misc]taylor: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k))))) (sqrt (/ k (* n PI)))) in k 1539426660.960 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k))))) in k 1539426660.960 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in k 1539426660.960 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426660.960 * [misc]taylor: Taking taylor expansion of 2 in k 1539426660.960 * [misc]backup-simplify: Simplify 2 into 2 1539426660.960 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426660.961 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426660.961 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1539426660.961 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539426660.961 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539426660.961 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1539426660.961 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426660.961 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426660.961 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426660.961 * [misc]taylor: Taking taylor expansion of k in k 1539426660.961 * [misc]backup-simplify: Simplify 0 into 0 1539426660.961 * [misc]backup-simplify: Simplify 1 into 1 1539426660.961 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539426660.961 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539426660.961 * [misc]taylor: Taking taylor expansion of 2 in k 1539426660.961 * [misc]backup-simplify: Simplify 2 into 2 1539426660.961 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426660.961 * [misc]taylor: Taking taylor expansion of n in k 1539426660.961 * [misc]backup-simplify: Simplify n into n 1539426660.961 * [misc]taylor: Taking taylor expansion of PI in k 1539426660.961 * [misc]backup-simplify: Simplify PI into PI 1539426660.961 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426660.961 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539426660.961 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539426660.961 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426660.962 * [misc]backup-simplify: Simplify (- 0) into 0 1539426660.962 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539426660.962 * [misc]backup-simplify: Simplify (- 0) into 0 1539426660.962 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539426660.962 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539426660.963 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539426660.963 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539426660.963 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426660.964 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1539426660.964 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426660.964 * [misc]backup-simplify: Simplify (* (sqrt 2) 1) into (sqrt 2) 1539426660.964 * [misc]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 1539426660.964 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in k 1539426660.964 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in k 1539426660.964 * [misc]taylor: Taking taylor expansion of k in k 1539426660.964 * [misc]backup-simplify: Simplify 0 into 0 1539426660.965 * [misc]backup-simplify: Simplify 1 into 1 1539426660.965 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426660.965 * [misc]taylor: Taking taylor expansion of n in k 1539426660.965 * [misc]backup-simplify: Simplify n into n 1539426660.965 * [misc]taylor: Taking taylor expansion of PI in k 1539426660.965 * [misc]backup-simplify: Simplify PI into PI 1539426660.965 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426660.965 * [misc]backup-simplify: Simplify (/ 1 (* n PI)) into (/ 1 (* n PI)) 1539426660.965 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426660.965 * [misc]backup-simplify: Simplify (/ (/ 1 (* n PI)) (* 2 (sqrt 0))) into (/ +nan.0 (* n PI)) 1539426660.965 * [misc]taylor: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k))))) (sqrt (/ k (* n PI)))) in k 1539426660.965 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k))))) in k 1539426660.965 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in k 1539426660.965 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426660.965 * [misc]taylor: Taking taylor expansion of 2 in k 1539426660.965 * [misc]backup-simplify: Simplify 2 into 2 1539426660.965 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426660.966 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426660.966 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1539426660.966 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539426660.966 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539426660.966 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1539426660.966 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426660.966 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426660.966 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426660.966 * [misc]taylor: Taking taylor expansion of k in k 1539426660.966 * [misc]backup-simplify: Simplify 0 into 0 1539426660.966 * [misc]backup-simplify: Simplify 1 into 1 1539426660.966 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539426660.966 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539426660.966 * [misc]taylor: Taking taylor expansion of 2 in k 1539426660.966 * [misc]backup-simplify: Simplify 2 into 2 1539426660.966 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426660.966 * [misc]taylor: Taking taylor expansion of n in k 1539426660.966 * [misc]backup-simplify: Simplify n into n 1539426660.966 * [misc]taylor: Taking taylor expansion of PI in k 1539426660.966 * [misc]backup-simplify: Simplify PI into PI 1539426660.966 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426660.966 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539426660.966 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539426660.967 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426660.967 * [misc]backup-simplify: Simplify (- 0) into 0 1539426660.967 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539426660.967 * [misc]backup-simplify: Simplify (- 0) into 0 1539426660.967 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539426660.967 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539426660.968 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539426660.968 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539426660.969 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426660.969 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1539426660.969 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426660.969 * [misc]backup-simplify: Simplify (* (sqrt 2) 1) into (sqrt 2) 1539426660.970 * [misc]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 1539426660.970 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in k 1539426660.970 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in k 1539426660.970 * [misc]taylor: Taking taylor expansion of k in k 1539426660.970 * [misc]backup-simplify: Simplify 0 into 0 1539426660.970 * [misc]backup-simplify: Simplify 1 into 1 1539426660.970 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426660.970 * [misc]taylor: Taking taylor expansion of n in k 1539426660.970 * [misc]backup-simplify: Simplify n into n 1539426660.970 * [misc]taylor: Taking taylor expansion of PI in k 1539426660.970 * [misc]backup-simplify: Simplify PI into PI 1539426660.970 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426660.970 * [misc]backup-simplify: Simplify (/ 1 (* n PI)) into (/ 1 (* n PI)) 1539426660.970 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426660.970 * [misc]backup-simplify: Simplify (/ (/ 1 (* n PI)) (* 2 (sqrt 0))) into (/ +nan.0 (* n PI)) 1539426660.971 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 1539426660.971 * [misc]taylor: Taking taylor expansion of 0 in n 1539426660.971 * [misc]backup-simplify: Simplify 0 into 0 1539426660.971 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (log (* 2 (* n PI)))) 1539426660.971 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* -1/2 (log (* 2 (* n PI))))) (* 0 1)) into (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) 1539426660.972 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) (sqrt 2))))) into (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) 1539426660.973 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (/ +nan.0 (* n PI))) (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) 0)) into (- (* +nan.0 (/ 1 (* (sqrt 2) (* n PI))))) 1539426660.973 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (sqrt 2) (* n PI))))) in n 1539426660.973 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* n PI)))) in n 1539426660.973 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426660.973 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426660.973 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* n PI))) in n 1539426660.973 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539426660.973 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426660.973 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.973 * [misc]backup-simplify: Simplify 2 into 2 1539426660.973 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426660.973 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426660.973 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.973 * [misc]taylor: Taking taylor expansion of n in n 1539426660.973 * [misc]backup-simplify: Simplify 0 into 0 1539426660.974 * [misc]backup-simplify: Simplify 1 into 1 1539426660.974 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.974 * [misc]backup-simplify: Simplify PI into PI 1539426660.974 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426660.974 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426660.975 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426660.975 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539426660.976 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) PI)) into (/ 1 (* (sqrt 2) PI)) 1539426660.977 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (* (sqrt 2) PI))) into (/ +nan.0 (* (sqrt 2) PI)) 1539426660.978 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 1539426660.979 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 1539426660.979 * [misc]backup-simplify: Simplify 0 into 0 1539426660.979 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539426660.980 * [misc]backup-simplify: Simplify (- (/ 0 (* n PI)) (+ (* (/ 1 (* n PI)) (/ 0 (* n PI))))) into 0 1539426660.980 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 (* n PI)) 2) (+)) (* 2 0)) into (/ +nan.0 (* (pow n 2) (pow PI 2))) 1539426660.980 * [misc]backup-simplify: Simplify (- 0) into 0 1539426660.981 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1539426660.981 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1539426660.983 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1539426660.983 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426660.983 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1539426660.983 * [misc]backup-simplify: Simplify (- 0) into 0 1539426660.984 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1539426660.985 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (pow (log (* 2 (* n PI))) 2)) 1539426660.986 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426660.987 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* 1/8 (pow (log (* 2 (* n PI))) 2))) (+ (* 0 (* -1/2 (log (* 2 (* n PI))))) (* 0 1))) into (* 1/8 (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) 1539426660.988 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ (* 1/8 (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) (sqrt 2))) (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) (/ (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) (sqrt 2))))) into (* 1/8 (/ (pow (log (* 2 (* n PI))) 2) (sqrt 2))) 1539426660.990 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (/ +nan.0 (* (pow n 2) (pow PI 2)))) (+ (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) (/ +nan.0 (* n PI))) (* (* 1/8 (/ (pow (log (* 2 (* n PI))) 2) (sqrt 2))) 0))) into (- (+ (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))))))) 1539426660.990 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))))))) in n 1539426660.990 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI)))))) in n 1539426660.990 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1539426660.990 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426660.990 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426660.990 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1539426660.990 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1539426660.990 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426660.990 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.990 * [misc]backup-simplify: Simplify 2 into 2 1539426660.990 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426660.991 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426660.991 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539426660.991 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539426660.991 * [misc]taylor: Taking taylor expansion of n in n 1539426660.991 * [misc]backup-simplify: Simplify 0 into 0 1539426660.991 * [misc]backup-simplify: Simplify 1 into 1 1539426660.991 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539426660.991 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.991 * [misc]backup-simplify: Simplify PI into PI 1539426660.991 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426660.991 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426660.992 * [misc]backup-simplify: Simplify (* 1 (pow PI 2)) into (pow PI 2) 1539426660.993 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539426660.993 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (pow PI 2))) into (/ 1 (* (sqrt 2) (pow PI 2))) 1539426660.993 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))))) in n 1539426660.993 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI)))) in n 1539426660.994 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426660.994 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426660.994 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))) in n 1539426660.994 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426660.994 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426660.994 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.994 * [misc]backup-simplify: Simplify 2 into 2 1539426660.994 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.994 * [misc]taylor: Taking taylor expansion of n in n 1539426660.994 * [misc]backup-simplify: Simplify 0 into 0 1539426660.994 * [misc]backup-simplify: Simplify 1 into 1 1539426660.994 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.994 * [misc]backup-simplify: Simplify PI into PI 1539426660.994 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426660.994 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426660.995 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426660.995 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426660.996 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426660.996 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539426660.996 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426660.996 * [misc]taylor: Taking taylor expansion of 2 in n 1539426660.996 * [misc]backup-simplify: Simplify 2 into 2 1539426660.996 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426660.996 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426660.996 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426660.996 * [misc]taylor: Taking taylor expansion of n in n 1539426660.996 * [misc]backup-simplify: Simplify 0 into 0 1539426660.996 * [misc]backup-simplify: Simplify 1 into 1 1539426660.996 * [misc]taylor: Taking taylor expansion of PI in n 1539426660.996 * [misc]backup-simplify: Simplify PI into PI 1539426660.997 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426660.997 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426660.997 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426660.998 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426660.999 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539426661.000 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.000 * [misc]backup-simplify: Simplify (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI)) into (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI)) 1539426661.001 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426661.001 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426661.003 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 2))) into 0 1539426661.004 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539426661.007 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) (pow PI 2))) (/ 0 (* (sqrt 2) (pow PI 2)))))) into 0 1539426661.009 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (sqrt 2) (pow PI 2))))) into 0 1539426661.010 * [misc]backup-simplify: Simplify (* +nan.0 (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI))) into (* +nan.0 (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI))) 1539426661.011 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) 1539426661.013 * [misc]backup-simplify: Simplify (+ 0 (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) 1539426661.015 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) 1539426661.017 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) 1539426661.018 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426661.020 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.021 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1539426661.023 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))))) into 0 1539426661.025 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (sqrt 2) PI)))) into 0 1539426661.025 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.025 * [misc]backup-simplify: Simplify 0 into 0 1539426661.025 * [misc]backup-simplify: Simplify 0 into 0 1539426661.026 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.026 * [misc]backup-simplify: Simplify (- (/ 0 (* n PI)) (+ (* (/ 1 (* n PI)) (/ 0 (* n PI))) (* 0 (/ 0 (* n PI))))) into 0 1539426661.027 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (/ +nan.0 (* n PI)) (/ +nan.0 (* (pow n 2) (pow PI 2))))))) (* 2 0)) into (/ +nan.0 (* (pow n 3) (pow PI 3))) 1539426661.027 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.028 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426661.028 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1539426661.031 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 1539426661.031 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.031 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.032 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539426661.032 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.032 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1539426661.034 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (pow (log (* 2 (* n PI))) 3)) 1539426661.034 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.035 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* -1/48 (pow (log (* 2 (* n PI))) 3))) (+ (* 0 (* 1/8 (pow (log (* 2 (* n PI))) 2))) (+ (* 0 (* -1/2 (log (* 2 (* n PI))))) (* 0 1)))) into (- (* 1/48 (* (sqrt 2) (pow (log (* 2 (* n PI))) 3)))) 1539426661.037 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ (- (* 1/48 (* (sqrt 2) (pow (log (* 2 (* n PI))) 3)))) (sqrt 2))) (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) (/ (* 1/8 (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) (sqrt 2))) (* (* 1/8 (/ (pow (log (* 2 (* n PI))) 2) (sqrt 2))) (/ (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) (sqrt 2))))) into (* 1/48 (/ (pow (log (* 2 (* n PI))) 3) (sqrt 2))) 1539426661.040 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (/ +nan.0 (* (pow n 3) (pow PI 3)))) (+ (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) (/ +nan.0 (* (pow n 2) (pow PI 2)))) (+ (* (* 1/8 (/ (pow (log (* 2 (* n PI))) 2) (sqrt 2))) (/ +nan.0 (* n PI))) (* (* 1/48 (/ (pow (log (* 2 (* n PI))) 3) (sqrt 2))) 0)))) into (- (+ (* +nan.0 (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3))))) (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))) 1539426661.040 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3))))) (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))) in n 1539426661.040 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3))))) (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))) in n 1539426661.040 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI)))) in n 1539426661.040 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.040 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.040 * [misc]taylor: Taking taylor expansion of (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI))) in n 1539426661.040 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1539426661.040 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.040 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.040 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.040 * [misc]backup-simplify: Simplify 2 into 2 1539426661.040 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.040 * [misc]taylor: Taking taylor expansion of n in n 1539426661.040 * [misc]backup-simplify: Simplify 0 into 0 1539426661.040 * [misc]backup-simplify: Simplify 1 into 1 1539426661.040 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.040 * [misc]backup-simplify: Simplify PI into PI 1539426661.040 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.041 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.041 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.042 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.042 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.043 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.043 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539426661.043 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.043 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.043 * [misc]backup-simplify: Simplify 2 into 2 1539426661.043 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.043 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.043 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.043 * [misc]taylor: Taking taylor expansion of n in n 1539426661.043 * [misc]backup-simplify: Simplify 0 into 0 1539426661.043 * [misc]backup-simplify: Simplify 1 into 1 1539426661.043 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.043 * [misc]backup-simplify: Simplify PI into PI 1539426661.044 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.045 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.046 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1539426661.046 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.046 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426661.047 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.048 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539426661.049 * [misc]backup-simplify: Simplify (/ (pow (+ (log n) (log (* 2 PI))) 2) (* (sqrt 2) PI)) into (/ (pow (+ (log n) (log (* 2 PI))) 2) (* (sqrt 2) PI)) 1539426661.049 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3))))) (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))) in n 1539426661.049 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3))))) (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2))))))) in n 1539426661.049 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3))))) in n 1539426661.049 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.049 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.049 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) in n 1539426661.049 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 3) (pow PI 3))) in n 1539426661.049 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.049 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.049 * [misc]backup-simplify: Simplify 2 into 2 1539426661.049 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.049 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.049 * [misc]taylor: Taking taylor expansion of (* (pow n 3) (pow PI 3)) in n 1539426661.050 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539426661.050 * [misc]taylor: Taking taylor expansion of n in n 1539426661.050 * [misc]backup-simplify: Simplify 0 into 0 1539426661.050 * [misc]backup-simplify: Simplify 1 into 1 1539426661.050 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539426661.050 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.050 * [misc]backup-simplify: Simplify PI into PI 1539426661.050 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.050 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.050 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.051 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539426661.051 * [misc]backup-simplify: Simplify (* 1 (pow PI 3)) into (pow PI 3) 1539426661.052 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539426661.053 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (pow PI 3))) into (/ 1 (* (sqrt 2) (pow PI 3))) 1539426661.053 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))))) in n 1539426661.053 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1539426661.053 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.053 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.053 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1539426661.053 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.053 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.053 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.053 * [misc]backup-simplify: Simplify 2 into 2 1539426661.053 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.053 * [misc]taylor: Taking taylor expansion of n in n 1539426661.053 * [misc]backup-simplify: Simplify 0 into 0 1539426661.053 * [misc]backup-simplify: Simplify 1 into 1 1539426661.053 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.053 * [misc]backup-simplify: Simplify PI into PI 1539426661.054 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.054 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.054 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.055 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.056 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.056 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1539426661.056 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.056 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.056 * [misc]backup-simplify: Simplify 2 into 2 1539426661.056 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.056 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.056 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539426661.056 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539426661.056 * [misc]taylor: Taking taylor expansion of n in n 1539426661.056 * [misc]backup-simplify: Simplify 0 into 0 1539426661.056 * [misc]backup-simplify: Simplify 1 into 1 1539426661.056 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539426661.056 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.056 * [misc]backup-simplify: Simplify PI into PI 1539426661.057 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.057 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.057 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.058 * [misc]backup-simplify: Simplify (* 1 (pow PI 2)) into (pow PI 2) 1539426661.059 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539426661.059 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.060 * [misc]backup-simplify: Simplify (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) (pow PI 2))) into (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) (pow PI 2))) 1539426661.062 * [misc]backup-simplify: Simplify (* +nan.0 (/ (pow (+ (log n) (log (* 2 PI))) 2) (* (sqrt 2) PI))) into (* +nan.0 (/ (pow (+ (log n) (log (* 2 PI))) 2) (* (sqrt 2) PI))) 1539426661.063 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.064 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426661.065 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 (pow PI 2)))) into 0 1539426661.065 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426661.066 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426661.067 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (pow PI 2))) into 0 1539426661.067 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539426661.067 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539426661.069 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (pow PI 3)))) into 0 1539426661.070 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 3))) into 0 1539426661.071 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.072 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (pow PI 3)))) into 0 1539426661.073 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 3))) into 0 1539426661.076 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) (pow PI 3))) (/ 0 (* (sqrt 2) (pow PI 3)))))) into 0 1539426661.080 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) (pow PI 3))) (/ 0 (* (sqrt 2) (pow PI 3)))) (* 0 (/ 0 (* (sqrt 2) (pow PI 3)))))) into 0 1539426661.082 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (/ 1 (* (sqrt 2) (pow PI 3)))))) into 0 1539426661.083 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426661.083 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426661.085 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426661.085 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426661.085 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426661.086 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 2))) into 0 1539426661.086 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539426661.088 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) (pow PI 2))) (+ (* (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) (pow PI 2))) (/ 0 (* (sqrt 2) (pow PI 2)))))) into 0 1539426661.089 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) (pow PI 2))))) into 0 1539426661.089 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.089 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426661.089 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.090 * [misc]backup-simplify: Simplify (+ (* +nan.0 (/ (pow (+ (log n) (log (* 2 PI))) 2) (* (sqrt 2) PI))) 0) into (- (+ (* +nan.0 (/ (pow (log n) 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (* (sqrt 2) PI)))))))) 1539426661.093 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (pow (log n) 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (/ (pow (log n) 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (* (sqrt 2) PI)))))))) 1539426661.095 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (pow (log n) 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (/ (pow (log n) 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (* (sqrt 2) PI)))))))) 1539426661.100 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (pow (log n) 2) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (* (sqrt 2) PI))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (* (sqrt 2) PI)))))))) (* (/ 1 n) (pow k 3))) (+ (* (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) (* (/ 1 n) (pow k 2))) (* (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) (* (/ 1 n) k)))) into (- (+ (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ k (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (* (pow (log n) 2) (pow k 3)) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (* (pow k 3) (pow (log (* 2 PI)) 2)) (* (sqrt 2) (* n PI)))) (- (* +nan.0 (/ (* (pow k 3) (* (log n) (log (* 2 PI)))) (* (sqrt 2) (* n PI))))))))))))))) 1539426661.100 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 k)) (* (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (- (/ (/ 1 k) 2))))) into (* (/ 1 (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))))) (sqrt (/ n (* PI k)))) 1539426661.100 * [misc]approximate: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))))) (sqrt (/ n (* PI k)))) in (k n) around 0 1539426661.100 * [misc]taylor: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))))) (sqrt (/ n (* PI k)))) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))))) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.101 * [misc]backup-simplify: Simplify 2 into 2 1539426661.101 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.101 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.101 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.101 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.101 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of k in n 1539426661.101 * [misc]backup-simplify: Simplify k into k 1539426661.101 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426661.101 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.101 * [misc]backup-simplify: Simplify 2 into 2 1539426661.101 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.101 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.101 * [misc]backup-simplify: Simplify PI into PI 1539426661.101 * [misc]taylor: Taking taylor expansion of n in n 1539426661.101 * [misc]backup-simplify: Simplify 0 into 0 1539426661.101 * [misc]backup-simplify: Simplify 1 into 1 1539426661.101 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.102 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.102 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.102 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426661.102 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426661.103 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.103 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.103 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.104 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 1539426661.104 * [misc]backup-simplify: Simplify (/ 1 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))) into (/ 1 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))) 1539426661.104 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in n 1539426661.104 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in n 1539426661.104 * [misc]taylor: Taking taylor expansion of n in n 1539426661.104 * [misc]backup-simplify: Simplify 0 into 0 1539426661.104 * [misc]backup-simplify: Simplify 1 into 1 1539426661.104 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539426661.104 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.104 * [misc]backup-simplify: Simplify PI into PI 1539426661.105 * [misc]taylor: Taking taylor expansion of k in n 1539426661.105 * [misc]backup-simplify: Simplify k into k 1539426661.105 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539426661.105 * [misc]backup-simplify: Simplify (/ 1 (* PI k)) into (/ 1 (* PI k)) 1539426661.105 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.105 * [misc]backup-simplify: Simplify (/ (/ 1 (* PI k)) (* 2 (sqrt 0))) into (/ +nan.0 (* PI k)) 1539426661.105 * [misc]taylor: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))))) (sqrt (/ n (* PI k)))) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))))) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.105 * [misc]backup-simplify: Simplify 2 into 2 1539426661.105 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.105 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.105 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.105 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.105 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426661.105 * [misc]taylor: Taking taylor expansion of k in k 1539426661.105 * [misc]backup-simplify: Simplify 0 into 0 1539426661.105 * [misc]backup-simplify: Simplify 1 into 1 1539426661.106 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426661.106 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539426661.106 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539426661.106 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.106 * [misc]backup-simplify: Simplify 2 into 2 1539426661.106 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426661.106 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.106 * [misc]backup-simplify: Simplify PI into PI 1539426661.106 * [misc]taylor: Taking taylor expansion of n in k 1539426661.106 * [misc]backup-simplify: Simplify n into n 1539426661.106 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.106 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539426661.106 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539426661.106 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426661.106 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.106 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539426661.106 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1539426661.106 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 1539426661.107 * [misc]backup-simplify: Simplify (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) into (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) 1539426661.107 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in k 1539426661.107 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in k 1539426661.107 * [misc]taylor: Taking taylor expansion of n in k 1539426661.107 * [misc]backup-simplify: Simplify n into n 1539426661.107 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539426661.107 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.107 * [misc]backup-simplify: Simplify PI into PI 1539426661.107 * [misc]taylor: Taking taylor expansion of k in k 1539426661.107 * [misc]backup-simplify: Simplify 0 into 0 1539426661.107 * [misc]backup-simplify: Simplify 1 into 1 1539426661.107 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539426661.107 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539426661.107 * [misc]backup-simplify: Simplify (/ n PI) into (/ n PI) 1539426661.107 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.108 * [misc]backup-simplify: Simplify (/ (/ n PI) (* 2 (sqrt 0))) into (* +nan.0 (/ n PI)) 1539426661.108 * [misc]taylor: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))))) (sqrt (/ n (* PI k)))) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))))) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.108 * [misc]backup-simplify: Simplify 2 into 2 1539426661.108 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.108 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.108 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.108 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.108 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of k in k 1539426661.108 * [misc]backup-simplify: Simplify 0 into 0 1539426661.108 * [misc]backup-simplify: Simplify 1 into 1 1539426661.108 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426661.108 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.108 * [misc]backup-simplify: Simplify 2 into 2 1539426661.108 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426661.108 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.108 * [misc]backup-simplify: Simplify PI into PI 1539426661.108 * [misc]taylor: Taking taylor expansion of n in k 1539426661.108 * [misc]backup-simplify: Simplify n into n 1539426661.108 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.108 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539426661.109 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539426661.109 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426661.109 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.109 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539426661.109 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1539426661.109 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 1539426661.109 * [misc]backup-simplify: Simplify (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) into (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) 1539426661.109 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in k 1539426661.109 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in k 1539426661.109 * [misc]taylor: Taking taylor expansion of n in k 1539426661.109 * [misc]backup-simplify: Simplify n into n 1539426661.109 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539426661.109 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.109 * [misc]backup-simplify: Simplify PI into PI 1539426661.109 * [misc]taylor: Taking taylor expansion of k in k 1539426661.109 * [misc]backup-simplify: Simplify 0 into 0 1539426661.110 * [misc]backup-simplify: Simplify 1 into 1 1539426661.110 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539426661.110 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539426661.110 * [misc]backup-simplify: Simplify (/ n PI) into (/ n PI) 1539426661.110 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.110 * [misc]backup-simplify: Simplify (/ (/ n PI) (* 2 (sqrt 0))) into (* +nan.0 (/ n PI)) 1539426661.111 * [misc]backup-simplify: Simplify (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) 0) into 0 1539426661.111 * [misc]taylor: Taking taylor expansion of 0 in n 1539426661.111 * [misc]backup-simplify: Simplify 0 into 0 1539426661.111 * [misc]backup-simplify: Simplify 0 into 0 1539426661.111 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))))) into 0 1539426661.111 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))))) into 0 1539426661.112 * [misc]backup-simplify: Simplify (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (* +nan.0 (/ n PI))) (* 0 0)) into (- (* +nan.0 (/ n (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI))))) 1539426661.112 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ n (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI))))) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ n (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI)))) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.112 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.112 * [misc]taylor: Taking taylor expansion of (/ n (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI))) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of n in n 1539426661.112 * [misc]backup-simplify: Simplify 0 into 0 1539426661.112 * [misc]backup-simplify: Simplify 1 into 1 1539426661.112 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI)) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.112 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.112 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.112 * [misc]backup-simplify: Simplify 2 into 2 1539426661.112 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.112 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.112 * [misc]backup-simplify: Simplify PI into PI 1539426661.112 * [misc]taylor: Taking taylor expansion of n in n 1539426661.112 * [misc]backup-simplify: Simplify 0 into 0 1539426661.112 * [misc]backup-simplify: Simplify 1 into 1 1539426661.112 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.112 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.113 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.113 * [misc]taylor: Taking taylor expansion of k in n 1539426661.113 * [misc]backup-simplify: Simplify k into k 1539426661.113 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.114 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.114 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.115 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.115 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.115 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) PI) in n 1539426661.115 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.115 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.115 * [misc]backup-simplify: Simplify 2 into 2 1539426661.115 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.115 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.115 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.115 * [misc]backup-simplify: Simplify PI into PI 1539426661.116 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1539426661.117 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)) 1539426661.117 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) into (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) 1539426661.118 * [misc]backup-simplify: Simplify 0 into 0 1539426661.118 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1539426661.119 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)))) into 0 1539426661.119 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ n PI)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow n 2) (pow PI 2))) 1539426661.120 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.121 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 1539426661.122 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))))) into 0 1539426661.123 * [misc]backup-simplify: Simplify (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (* +nan.0 (/ (pow n 2) (pow PI 2)))) (+ (* 0 (* +nan.0 (/ n PI))) (* 0 0))) into (- (* +nan.0 (/ (pow n 2) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2)))))) 1539426661.123 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (pow n 2) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2)))))) in n 1539426661.123 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow n 2) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2))))) in n 1539426661.123 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.123 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.123 * [misc]taylor: Taking taylor expansion of (/ (pow n 2) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2)))) in n 1539426661.123 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539426661.123 * [misc]taylor: Taking taylor expansion of n in n 1539426661.123 * [misc]backup-simplify: Simplify 0 into 0 1539426661.123 * [misc]backup-simplify: Simplify 1 into 1 1539426661.123 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2))) in n 1539426661.123 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.123 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.123 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.123 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.123 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.124 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.124 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.124 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.124 * [misc]backup-simplify: Simplify 2 into 2 1539426661.124 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.124 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.124 * [misc]backup-simplify: Simplify PI into PI 1539426661.124 * [misc]taylor: Taking taylor expansion of n in n 1539426661.124 * [misc]backup-simplify: Simplify 0 into 0 1539426661.124 * [misc]backup-simplify: Simplify 1 into 1 1539426661.124 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.124 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.125 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.125 * [misc]taylor: Taking taylor expansion of k in n 1539426661.125 * [misc]backup-simplify: Simplify k into k 1539426661.125 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.126 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.127 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.127 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.128 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.128 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in n 1539426661.128 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.128 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.128 * [misc]backup-simplify: Simplify 2 into 2 1539426661.128 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.128 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.128 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539426661.128 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.128 * [misc]backup-simplify: Simplify PI into PI 1539426661.128 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.129 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.129 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539426661.131 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) 1539426661.132 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) into (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) 1539426661.132 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) into (/ +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) 1539426661.133 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))))) 1539426661.134 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))))) 1539426661.134 * [misc]backup-simplify: Simplify 0 into 0 1539426661.135 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539426661.136 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539426661.137 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (/ n PI)) (* +nan.0 (/ (pow n 2) (pow PI 2))))))) (* 2 0)) into (* +nan.0 (/ (pow n 3) (pow PI 3))) 1539426661.137 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.138 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0 1539426661.139 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))))) into 0 1539426661.141 * [misc]backup-simplify: Simplify (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (* +nan.0 (/ (pow n 3) (pow PI 3)))) (+ (* 0 (* +nan.0 (/ (pow n 2) (pow PI 2)))) (+ (* 0 (* +nan.0 (/ n PI))) (* 0 0)))) into (- (* +nan.0 (/ (pow n 3) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3)))))) 1539426661.141 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (pow n 3) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3)))))) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow n 3) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3))))) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.141 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.141 * [misc]taylor: Taking taylor expansion of (/ (pow n 3) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3)))) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of n in n 1539426661.141 * [misc]backup-simplify: Simplify 0 into 0 1539426661.141 * [misc]backup-simplify: Simplify 1 into 1 1539426661.141 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3))) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.141 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.141 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.141 * [misc]backup-simplify: Simplify 2 into 2 1539426661.141 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.141 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.141 * [misc]backup-simplify: Simplify PI into PI 1539426661.141 * [misc]taylor: Taking taylor expansion of n in n 1539426661.141 * [misc]backup-simplify: Simplify 0 into 0 1539426661.141 * [misc]backup-simplify: Simplify 1 into 1 1539426661.141 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.142 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.142 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.142 * [misc]taylor: Taking taylor expansion of k in n 1539426661.142 * [misc]backup-simplify: Simplify k into k 1539426661.143 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.144 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.144 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.145 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.145 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.145 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 3)) in n 1539426661.145 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.145 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.145 * [misc]backup-simplify: Simplify 2 into 2 1539426661.145 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.146 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.146 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539426661.146 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.146 * [misc]backup-simplify: Simplify PI into PI 1539426661.146 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.146 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.146 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.147 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539426661.148 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539426661.149 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) 1539426661.150 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))) into (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))) 1539426661.150 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 PI)) into 0 1539426661.151 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.152 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426661.156 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426661.156 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.157 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539426661.159 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.160 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (* (sqrt 2) PI))) into 0 1539426661.162 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) (+ (* (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))))) into 0 1539426661.163 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))))) into 0 1539426661.163 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.163 * [misc]backup-simplify: Simplify 0 into 0 1539426661.163 * [misc]backup-simplify: Simplify 0 into 0 1539426661.164 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539426661.166 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539426661.167 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ (pow n 2) (pow PI 2))) 2) (+ (* 2 (* (* +nan.0 (/ n PI)) (* +nan.0 (/ (pow n 3) (pow PI 3))))))) (* 2 0)) into (* +nan.0 (/ (pow n 4) (pow PI 4))) 1539426661.169 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.169 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 1539426661.171 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))))) into 0 1539426661.173 * [misc]backup-simplify: Simplify (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (* +nan.0 (/ (pow n 4) (pow PI 4)))) (+ (* 0 (* +nan.0 (/ (pow n 3) (pow PI 3)))) (+ (* 0 (* +nan.0 (/ (pow n 2) (pow PI 2)))) (+ (* 0 (* +nan.0 (/ n PI))) (* 0 0))))) into (- (* +nan.0 (/ (pow n 4) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 4)))))) 1539426661.173 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (pow n 4) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 4)))))) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow n 4) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 4))))) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.173 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.173 * [misc]taylor: Taking taylor expansion of (/ (pow n 4) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 4)))) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of (pow n 4) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of n in n 1539426661.173 * [misc]backup-simplify: Simplify 0 into 0 1539426661.173 * [misc]backup-simplify: Simplify 1 into 1 1539426661.173 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 4))) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.173 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.173 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.173 * [misc]backup-simplify: Simplify 2 into 2 1539426661.173 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.173 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.173 * [misc]backup-simplify: Simplify PI into PI 1539426661.173 * [misc]taylor: Taking taylor expansion of n in n 1539426661.173 * [misc]backup-simplify: Simplify 0 into 0 1539426661.173 * [misc]backup-simplify: Simplify 1 into 1 1539426661.174 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.174 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.174 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.174 * [misc]taylor: Taking taylor expansion of k in n 1539426661.174 * [misc]backup-simplify: Simplify k into k 1539426661.175 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.176 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.176 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.177 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.177 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.177 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 4)) in n 1539426661.177 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.177 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.177 * [misc]backup-simplify: Simplify 2 into 2 1539426661.178 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.178 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.178 * [misc]taylor: Taking taylor expansion of (pow PI 4) in n 1539426661.178 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.178 * [misc]backup-simplify: Simplify PI into PI 1539426661.178 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.178 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.178 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.179 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1539426661.180 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 4)) into (* (sqrt 2) (pow PI 4)) 1539426661.181 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 4))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 4))) 1539426661.182 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 4)))) into (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 4)))) 1539426661.183 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into (/ +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2)))) 1539426661.185 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))))) 1539426661.186 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))))) 1539426661.187 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.188 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.189 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.190 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.195 * [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 1539426661.196 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426661.197 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))) into 0 1539426661.199 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426661.200 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (* 0 (* (sqrt 2) PI)))) into 0 1539426661.203 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) (+ (* (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) (* 0 (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))))) into 0 1539426661.204 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))))) into 0 1539426661.205 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.205 * [misc]backup-simplify: Simplify 0 into 0 1539426661.205 * [misc]backup-simplify: Simplify 0 into 0 1539426661.206 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 1539426661.208 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539426661.209 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (/ n PI)) (* +nan.0 (/ (pow n 4) (pow PI 4))))) (* 2 (* (* +nan.0 (/ (pow n 2) (pow PI 2))) (* +nan.0 (/ (pow n 3) (pow PI 3))))))) (* 2 0)) into (* +nan.0 (/ (pow n 5) (pow PI 5))) 1539426661.210 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.211 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))))))))) into 0 1539426661.213 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))))) into 0 1539426661.215 * [misc]backup-simplify: Simplify (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (* +nan.0 (/ (pow n 5) (pow PI 5)))) (+ (* 0 (* +nan.0 (/ (pow n 4) (pow PI 4)))) (+ (* 0 (* +nan.0 (/ (pow n 3) (pow PI 3)))) (+ (* 0 (* +nan.0 (/ (pow n 2) (pow PI 2)))) (+ (* 0 (* +nan.0 (/ n PI))) (* 0 0)))))) into (- (* +nan.0 (/ (pow n 5) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 5)))))) 1539426661.215 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (pow n 5) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 5)))))) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow n 5) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 5))))) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.215 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.215 * [misc]taylor: Taking taylor expansion of (/ (pow n 5) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 5)))) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of (pow n 5) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of n in n 1539426661.215 * [misc]backup-simplify: Simplify 0 into 0 1539426661.215 * [misc]backup-simplify: Simplify 1 into 1 1539426661.215 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 5))) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.215 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.215 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.215 * [misc]backup-simplify: Simplify 2 into 2 1539426661.215 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.215 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.215 * [misc]backup-simplify: Simplify PI into PI 1539426661.215 * [misc]taylor: Taking taylor expansion of n in n 1539426661.215 * [misc]backup-simplify: Simplify 0 into 0 1539426661.215 * [misc]backup-simplify: Simplify 1 into 1 1539426661.216 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.216 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.216 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.216 * [misc]taylor: Taking taylor expansion of k in n 1539426661.216 * [misc]backup-simplify: Simplify k into k 1539426661.217 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.218 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.219 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.219 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.220 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.220 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 5)) in n 1539426661.220 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.220 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.220 * [misc]backup-simplify: Simplify 2 into 2 1539426661.220 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.220 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.220 * [misc]taylor: Taking taylor expansion of (pow PI 5) in n 1539426661.220 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.220 * [misc]backup-simplify: Simplify PI into PI 1539426661.221 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.221 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.221 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.221 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.222 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1539426661.222 * [misc]backup-simplify: Simplify (* PI (pow PI 4)) into (pow PI 5) 1539426661.223 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 5)) into (* (sqrt 2) (pow PI 5)) 1539426661.224 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 5))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 5))) 1539426661.225 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 5)))) into (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 5)))) 1539426661.225 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426661.226 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426661.227 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539426661.228 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.229 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426661.231 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426661.232 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.233 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539426661.234 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.236 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (* (sqrt 2) (pow PI 2)))) into 0 1539426661.239 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) (+ (* (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))) (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))))) into 0 1539426661.240 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))))) into 0 1539426661.240 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.240 * [misc]backup-simplify: Simplify 0 into 0 1539426661.241 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.242 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426661.244 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.245 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426661.253 * [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 1539426661.253 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426661.254 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 1539426661.258 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1539426661.260 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt 2) PI))))) into 0 1539426661.264 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) (+ (* (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) (* 0 (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) (* 0 (/ 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))))) into 0 1539426661.265 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))))))) into 0 1539426661.265 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.265 * [misc]backup-simplify: Simplify 0 into 0 1539426661.265 * [misc]backup-simplify: Simplify 0 into 0 1539426661.267 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 1539426661.269 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539426661.271 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ (pow n 3) (pow PI 3))) 2) (+ (* 2 (* (* +nan.0 (/ n PI)) (* +nan.0 (/ (pow n 5) (pow PI 5))))) (* 2 (* (* +nan.0 (/ (pow n 2) (pow PI 2))) (* +nan.0 (/ (pow n 4) (pow PI 4))))))) (* 2 0)) into (* +nan.0 (/ (pow n 6) (pow PI 6))) 1539426661.272 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.273 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k)))))))))) into 0 1539426661.276 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))) (* 0 (/ 0 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)))))) into 0 1539426661.278 * [misc]backup-simplify: Simplify (+ (* (/ 1 (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2))) (* +nan.0 (/ (pow n 6) (pow PI 6)))) (+ (* 0 (* +nan.0 (/ (pow n 5) (pow PI 5)))) (+ (* 0 (* +nan.0 (/ (pow n 4) (pow PI 4)))) (+ (* 0 (* +nan.0 (/ (pow n 3) (pow PI 3)))) (+ (* 0 (* +nan.0 (/ (pow n 2) (pow PI 2)))) (+ (* 0 (* +nan.0 (/ n PI))) (* 0 0))))))) into (- (* +nan.0 (/ (pow n 6) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 6)))))) 1539426661.279 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (pow n 6) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 6)))))) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow n 6) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 6))))) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.279 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.279 * [misc]taylor: Taking taylor expansion of (/ (pow n 6) (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 6)))) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of (pow n 6) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of n in n 1539426661.279 * [misc]backup-simplify: Simplify 0 into 0 1539426661.279 * [misc]backup-simplify: Simplify 1 into 1 1539426661.279 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 6))) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.279 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.279 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.279 * [misc]backup-simplify: Simplify 2 into 2 1539426661.279 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.279 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.279 * [misc]backup-simplify: Simplify PI into PI 1539426661.279 * [misc]taylor: Taking taylor expansion of n in n 1539426661.279 * [misc]backup-simplify: Simplify 0 into 0 1539426661.279 * [misc]backup-simplify: Simplify 1 into 1 1539426661.279 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.280 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.280 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.280 * [misc]taylor: Taking taylor expansion of k in n 1539426661.280 * [misc]backup-simplify: Simplify k into k 1539426661.281 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.282 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.282 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.283 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.283 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.283 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 6)) in n 1539426661.283 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.283 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.283 * [misc]backup-simplify: Simplify 2 into 2 1539426661.283 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.284 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.284 * [misc]taylor: Taking taylor expansion of (pow PI 6) in n 1539426661.284 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.284 * [misc]backup-simplify: Simplify PI into PI 1539426661.284 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.284 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.284 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.285 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.285 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539426661.286 * [misc]backup-simplify: Simplify (* (pow PI 3) (pow PI 3)) into (pow PI 6) 1539426661.286 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 6)) into (* (sqrt 2) (pow PI 6)) 1539426661.288 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 6))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 6))) 1539426661.289 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 6)))) into (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 6)))) 1539426661.290 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))))) into (/ +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3)))) 1539426661.291 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))))) 1539426661.292 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))))) 1539426661.296 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (pow PI 3)))))) (* (pow (/ 1 n) 3) (pow (/ 1 k) 2))) (+ (* (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (pow PI 2)))))) (* (pow (/ 1 n) 2) (/ 1 k))) (* (- (* +nan.0 (/ 1 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) PI))))) (* (/ 1 n) 1)))) into (- (+ (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 3) (* (pow PI 3) (pow k 2))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI))))) (- (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 2) (* (pow PI 2) k))))))))))) 1539426661.296 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 (- k))) (* (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (- (/ (/ 1 (- k)) 2))))) into (/ (sqrt (/ -1 k)) (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n)))) 1539426661.296 * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n)))) in (k n) around 0 1539426661.296 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n)))) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of -1 in n 1539426661.297 * [misc]backup-simplify: Simplify -1 into -1 1539426661.297 * [misc]taylor: Taking taylor expansion of k in n 1539426661.297 * [misc]backup-simplify: Simplify k into k 1539426661.297 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539426661.297 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539426661.297 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539426661.297 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539426661.297 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.297 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.297 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of k in n 1539426661.297 * [misc]backup-simplify: Simplify k into k 1539426661.297 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426661.297 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426661.297 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.298 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.298 * [misc]backup-simplify: Simplify -2 into -2 1539426661.298 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.298 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.298 * [misc]backup-simplify: Simplify PI into PI 1539426661.298 * [misc]taylor: Taking taylor expansion of n in n 1539426661.298 * [misc]backup-simplify: Simplify 0 into 0 1539426661.298 * [misc]backup-simplify: Simplify 1 into 1 1539426661.298 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.298 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.299 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426661.299 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426661.300 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.300 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426661.301 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426661.301 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in n 1539426661.301 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in n 1539426661.301 * [misc]taylor: Taking taylor expansion of (* PI -2) in n 1539426661.301 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.301 * [misc]backup-simplify: Simplify PI into PI 1539426661.301 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.301 * [misc]backup-simplify: Simplify -2 into -2 1539426661.301 * [misc]taylor: Taking taylor expansion of n in n 1539426661.301 * [misc]backup-simplify: Simplify 0 into 0 1539426661.301 * [misc]backup-simplify: Simplify 1 into 1 1539426661.301 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426661.302 * [misc]backup-simplify: Simplify (/ (* -2 PI) 1) into (* -2 PI) 1539426661.302 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.302 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426661.303 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 1539426661.304 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.305 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426661.307 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426661.308 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426661.308 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426661.308 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.308 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426661.310 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.311 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.311 * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (* +nan.0 (/ (sqrt (/ -1 k)) (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.311 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n)))) in k 1539426661.311 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426661.311 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426661.311 * [misc]taylor: Taking taylor expansion of -1 in k 1539426661.311 * [misc]backup-simplify: Simplify -1 into -1 1539426661.311 * [misc]taylor: Taking taylor expansion of k in k 1539426661.311 * [misc]backup-simplify: Simplify 0 into 0 1539426661.311 * [misc]backup-simplify: Simplify 1 into 1 1539426661.312 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426661.312 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.312 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426661.312 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.312 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.312 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of k in k 1539426661.312 * [misc]backup-simplify: Simplify 0 into 0 1539426661.312 * [misc]backup-simplify: Simplify 1 into 1 1539426661.312 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426661.312 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of -2 in k 1539426661.312 * [misc]backup-simplify: Simplify -2 into -2 1539426661.312 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426661.312 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.312 * [misc]backup-simplify: Simplify PI into PI 1539426661.312 * [misc]taylor: Taking taylor expansion of n in k 1539426661.312 * [misc]backup-simplify: Simplify n into n 1539426661.312 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.312 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426661.313 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539426661.313 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426661.313 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539426661.313 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1539426661.313 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in k 1539426661.313 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in k 1539426661.313 * [misc]taylor: Taking taylor expansion of (* PI -2) in k 1539426661.313 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.313 * [misc]backup-simplify: Simplify PI into PI 1539426661.313 * [misc]taylor: Taking taylor expansion of -2 in k 1539426661.313 * [misc]backup-simplify: Simplify -2 into -2 1539426661.313 * [misc]taylor: Taking taylor expansion of n in k 1539426661.313 * [misc]backup-simplify: Simplify n into n 1539426661.313 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426661.313 * [misc]backup-simplify: Simplify (/ (* -2 PI) n) into (* -2 (/ PI n)) 1539426661.313 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539426661.314 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 1539426661.314 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (* -2 (/ PI n)) (/ 0 n)))) into 0 1539426661.314 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539426661.314 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) into (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1539426661.314 * [misc]backup-simplify: Simplify (/ +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) into (/ +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) 1539426661.314 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n)))) in k 1539426661.314 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426661.314 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426661.314 * [misc]taylor: Taking taylor expansion of -1 in k 1539426661.314 * [misc]backup-simplify: Simplify -1 into -1 1539426661.314 * [misc]taylor: Taking taylor expansion of k in k 1539426661.314 * [misc]backup-simplify: Simplify 0 into 0 1539426661.314 * [misc]backup-simplify: Simplify 1 into 1 1539426661.314 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426661.315 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.315 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426661.315 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.315 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.315 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of k in k 1539426661.315 * [misc]backup-simplify: Simplify 0 into 0 1539426661.315 * [misc]backup-simplify: Simplify 1 into 1 1539426661.315 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426661.315 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of -2 in k 1539426661.315 * [misc]backup-simplify: Simplify -2 into -2 1539426661.315 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426661.315 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.315 * [misc]backup-simplify: Simplify PI into PI 1539426661.315 * [misc]taylor: Taking taylor expansion of n in k 1539426661.315 * [misc]backup-simplify: Simplify n into n 1539426661.315 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.315 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426661.315 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539426661.316 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426661.316 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539426661.316 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1539426661.316 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in k 1539426661.316 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in k 1539426661.316 * [misc]taylor: Taking taylor expansion of (* PI -2) in k 1539426661.316 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.316 * [misc]backup-simplify: Simplify PI into PI 1539426661.316 * [misc]taylor: Taking taylor expansion of -2 in k 1539426661.316 * [misc]backup-simplify: Simplify -2 into -2 1539426661.316 * [misc]taylor: Taking taylor expansion of n in k 1539426661.316 * [misc]backup-simplify: Simplify n into n 1539426661.316 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426661.316 * [misc]backup-simplify: Simplify (/ (* -2 PI) n) into (* -2 (/ PI n)) 1539426661.316 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539426661.317 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 1539426661.317 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (* -2 (/ PI n)) (/ 0 n)))) into 0 1539426661.317 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539426661.317 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) into (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1539426661.317 * [misc]backup-simplify: Simplify (/ +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) into (/ +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) 1539426661.317 * [misc]taylor: Taking taylor expansion of (/ +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) in n 1539426661.317 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.317 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.317 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) in n 1539426661.317 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539426661.317 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.317 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.317 * [misc]backup-simplify: Simplify -2 into -2 1539426661.317 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.317 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.317 * [misc]backup-simplify: Simplify PI into PI 1539426661.317 * [misc]taylor: Taking taylor expansion of n in n 1539426661.317 * [misc]backup-simplify: Simplify 0 into 0 1539426661.317 * [misc]backup-simplify: Simplify 1 into 1 1539426661.318 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.318 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.318 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.318 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426661.318 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) in n 1539426661.318 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* -2 (/ PI n))) k)) in n 1539426661.318 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.318 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.318 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1539426661.318 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426661.318 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.318 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.318 * [misc]backup-simplify: Simplify -2 into -2 1539426661.318 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.318 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.318 * [misc]backup-simplify: Simplify PI into PI 1539426661.318 * [misc]taylor: Taking taylor expansion of n in n 1539426661.318 * [misc]backup-simplify: Simplify 0 into 0 1539426661.318 * [misc]backup-simplify: Simplify 1 into 1 1539426661.319 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.319 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.319 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426661.319 * [misc]taylor: Taking taylor expansion of k in n 1539426661.319 * [misc]backup-simplify: Simplify k into k 1539426661.320 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.320 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.320 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) 1539426661.321 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426661.321 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426661.321 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1539426661.322 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.322 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426661.324 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426661.324 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.325 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 1539426661.326 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.326 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.327 * [misc]backup-simplify: Simplify (/ +nan.0 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426661.328 * [misc]backup-simplify: Simplify (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426661.328 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539426661.329 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539426661.329 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 0) (* 0 (sqrt (* -2 (/ PI n))))) into 0 1539426661.329 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) (+ (* (/ +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) (/ 0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))))))) into (- (* +nan.0 (/ 1 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))))) 1539426661.329 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))))) in n 1539426661.329 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))))) in n 1539426661.329 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.329 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.329 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) in n 1539426661.329 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) in n 1539426661.329 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539426661.329 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.329 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.329 * [misc]backup-simplify: Simplify -2 into -2 1539426661.329 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.329 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.329 * [misc]backup-simplify: Simplify PI into PI 1539426661.329 * [misc]taylor: Taking taylor expansion of n in n 1539426661.329 * [misc]backup-simplify: Simplify 0 into 0 1539426661.329 * [misc]backup-simplify: Simplify 1 into 1 1539426661.330 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.330 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.330 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.330 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426661.330 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) in n 1539426661.330 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* -2 (/ PI n))) k)) in n 1539426661.330 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.330 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.330 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1539426661.330 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426661.330 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.330 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.330 * [misc]backup-simplify: Simplify -2 into -2 1539426661.330 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.330 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.330 * [misc]backup-simplify: Simplify PI into PI 1539426661.330 * [misc]taylor: Taking taylor expansion of n in n 1539426661.330 * [misc]backup-simplify: Simplify 0 into 0 1539426661.331 * [misc]backup-simplify: Simplify 1 into 1 1539426661.331 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.331 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.331 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426661.331 * [misc]taylor: Taking taylor expansion of k in n 1539426661.331 * [misc]backup-simplify: Simplify k into k 1539426661.332 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.332 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.332 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) 1539426661.333 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426661.333 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426661.333 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1539426661.334 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.334 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426661.337 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426661.337 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.338 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 1539426661.340 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.341 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.341 * [misc]backup-simplify: Simplify (/ 1 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426661.342 * [misc]backup-simplify: Simplify (* +nan.0 (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539426661.343 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ 1 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) 1539426661.343 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (/ 1 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) 1539426661.345 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.346 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.351 * [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 1539426661.351 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426661.352 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1539426661.354 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426661.356 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.356 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426661.358 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539426661.359 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (* +nan.0 PI) 0) (* (* +nan.0 (pow PI 2)) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.362 * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (+ (* (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.363 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.365 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- n)) 1)) (+ (* (- (* +nan.0 (/ 1 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) n))) (- (+ (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI))) (- (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (* PI k))))))))) 1539426661.366 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1539426661.366 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))))) into (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) 1539426661.366 * [misc]approximate: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in (k n) around 0 1539426661.366 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in n 1539426661.366 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in n 1539426661.366 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.366 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.366 * [misc]backup-simplify: Simplify 2 into 2 1539426661.366 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.367 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.367 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in n 1539426661.367 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539426661.367 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539426661.367 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in n 1539426661.367 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539426661.367 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.367 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.367 * [misc]taylor: Taking taylor expansion of k in n 1539426661.367 * [misc]backup-simplify: Simplify k into k 1539426661.367 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.367 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.367 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.367 * [misc]backup-simplify: Simplify 2 into 2 1539426661.367 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.367 * [misc]taylor: Taking taylor expansion of n in n 1539426661.367 * [misc]backup-simplify: Simplify 0 into 0 1539426661.367 * [misc]backup-simplify: Simplify 1 into 1 1539426661.367 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.367 * [misc]backup-simplify: Simplify PI into PI 1539426661.368 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.368 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.369 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.369 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.370 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.370 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539426661.370 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539426661.370 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.371 * [misc]backup-simplify: Simplify (* (- (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* -1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539426661.372 * [misc]backup-simplify: Simplify (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* -1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539426661.372 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1539426661.372 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1539426661.372 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.372 * [misc]taylor: Taking taylor expansion of n in n 1539426661.372 * [misc]backup-simplify: Simplify 0 into 0 1539426661.372 * [misc]backup-simplify: Simplify 1 into 1 1539426661.372 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.372 * [misc]backup-simplify: Simplify PI into PI 1539426661.372 * [misc]taylor: Taking taylor expansion of k in n 1539426661.372 * [misc]backup-simplify: Simplify k into k 1539426661.372 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.373 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.373 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1539426661.373 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.373 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1539426661.373 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in k 1539426661.373 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in k 1539426661.373 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426661.373 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.373 * [misc]backup-simplify: Simplify 2 into 2 1539426661.373 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.374 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.374 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1539426661.374 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539426661.374 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539426661.374 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1539426661.374 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426661.374 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.374 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.374 * [misc]taylor: Taking taylor expansion of k in k 1539426661.374 * [misc]backup-simplify: Simplify 0 into 0 1539426661.374 * [misc]backup-simplify: Simplify 1 into 1 1539426661.374 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539426661.374 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539426661.374 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.374 * [misc]backup-simplify: Simplify 2 into 2 1539426661.374 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426661.374 * [misc]taylor: Taking taylor expansion of n in k 1539426661.374 * [misc]backup-simplify: Simplify n into n 1539426661.374 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.374 * [misc]backup-simplify: Simplify PI into PI 1539426661.374 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426661.374 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539426661.374 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539426661.375 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426661.375 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.375 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539426661.375 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.375 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539426661.376 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539426661.376 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539426661.377 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539426661.377 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.377 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1539426661.377 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426661.377 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1539426661.377 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in k 1539426661.377 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426661.377 * [misc]taylor: Taking taylor expansion of n in k 1539426661.377 * [misc]backup-simplify: Simplify n into n 1539426661.377 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.377 * [misc]backup-simplify: Simplify PI into PI 1539426661.377 * [misc]taylor: Taking taylor expansion of k in k 1539426661.377 * [misc]backup-simplify: Simplify 0 into 0 1539426661.377 * [misc]backup-simplify: Simplify 1 into 1 1539426661.377 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426661.377 * [misc]backup-simplify: Simplify (/ (* n PI) 1) into (* n PI) 1539426661.378 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.378 * [misc]backup-simplify: Simplify (/ (* n PI) (* 2 (sqrt 0))) into (* +nan.0 (* n PI)) 1539426661.378 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) (sqrt (/ (* n PI) k))) in k 1539426661.378 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (* n PI)) (- (* 1/2 k)))) in k 1539426661.378 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426661.378 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.378 * [misc]backup-simplify: Simplify 2 into 2 1539426661.378 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.378 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.378 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- (* 1/2 k))) in k 1539426661.378 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539426661.378 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539426661.378 * [misc]taylor: Taking taylor expansion of (- (* 1/2 k)) in k 1539426661.378 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539426661.379 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.379 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.379 * [misc]taylor: Taking taylor expansion of k in k 1539426661.379 * [misc]backup-simplify: Simplify 0 into 0 1539426661.379 * [misc]backup-simplify: Simplify 1 into 1 1539426661.379 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539426661.379 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539426661.379 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.379 * [misc]backup-simplify: Simplify 2 into 2 1539426661.379 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426661.379 * [misc]taylor: Taking taylor expansion of n in k 1539426661.379 * [misc]backup-simplify: Simplify n into n 1539426661.379 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.379 * [misc]backup-simplify: Simplify PI into PI 1539426661.379 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426661.379 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539426661.379 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539426661.380 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539426661.380 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.380 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539426661.380 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.380 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539426661.381 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539426661.381 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539426661.382 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539426661.382 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.382 * [misc]backup-simplify: Simplify (+ (* 0 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1539426661.382 * [misc]backup-simplify: Simplify (exp 0) into 1 1539426661.382 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1539426661.382 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in k 1539426661.382 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539426661.382 * [misc]taylor: Taking taylor expansion of n in k 1539426661.382 * [misc]backup-simplify: Simplify n into n 1539426661.382 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.382 * [misc]backup-simplify: Simplify PI into PI 1539426661.382 * [misc]taylor: Taking taylor expansion of k in k 1539426661.382 * [misc]backup-simplify: Simplify 0 into 0 1539426661.382 * [misc]backup-simplify: Simplify 1 into 1 1539426661.382 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539426661.382 * [misc]backup-simplify: Simplify (/ (* n PI) 1) into (* n PI) 1539426661.383 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.383 * [misc]backup-simplify: Simplify (/ (* n PI) (* 2 (sqrt 0))) into (* +nan.0 (* n PI)) 1539426661.383 * [misc]backup-simplify: Simplify (* (sqrt 2) 1) into (sqrt 2) 1539426661.383 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426661.383 * [misc]taylor: Taking taylor expansion of 0 in n 1539426661.383 * [misc]backup-simplify: Simplify 0 into 0 1539426661.383 * [misc]backup-simplify: Simplify 0 into 0 1539426661.384 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (log (* 2 (* n PI)))) 1539426661.384 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* -1/2 (log (* 2 (* n PI))))) (* 0 1)) into (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) 1539426661.385 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (* n PI))) (* (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (* n PI)))) 1539426661.385 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (* n PI)))) in n 1539426661.385 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* n PI))) in n 1539426661.385 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.385 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.385 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539426661.385 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.385 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.385 * [misc]backup-simplify: Simplify 2 into 2 1539426661.385 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.385 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.385 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.385 * [misc]taylor: Taking taylor expansion of n in n 1539426661.385 * [misc]backup-simplify: Simplify 0 into 0 1539426661.385 * [misc]backup-simplify: Simplify 1 into 1 1539426661.385 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.385 * [misc]backup-simplify: Simplify PI into PI 1539426661.386 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.386 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426661.386 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1539426661.386 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.386 * [misc]backup-simplify: Simplify 0 into 0 1539426661.386 * [misc]backup-simplify: Simplify 0 into 0 1539426661.387 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539426661.387 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* n PI) (/ 0 1)))) into 0 1539426661.388 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* n PI)) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow n 2) (pow PI 2))) 1539426661.388 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.388 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.389 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1539426661.390 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 1539426661.390 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.391 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1539426661.391 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.391 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1539426661.392 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (pow (log (* 2 (* n PI))) 2)) 1539426661.393 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.394 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* 1/8 (pow (log (* 2 (* n PI))) 2))) (+ (* 0 (* -1/2 (log (* 2 (* n PI))))) (* 0 1))) into (* 1/8 (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) 1539426661.395 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (* (pow n 2) (pow PI 2)))) (+ (* (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) (* +nan.0 (* n PI))) (* (* 1/8 (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* n PI)))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))) 1539426661.395 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* n PI)))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))) in n 1539426661.395 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* n PI)))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))) in n 1539426661.395 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* n PI)))) in n 1539426661.396 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.396 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.396 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (* n PI))) in n 1539426661.396 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.396 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.396 * [misc]backup-simplify: Simplify 2 into 2 1539426661.396 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.396 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.396 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (* n PI)) in n 1539426661.396 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.396 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.396 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.396 * [misc]backup-simplify: Simplify 2 into 2 1539426661.396 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.396 * [misc]taylor: Taking taylor expansion of n in n 1539426661.396 * [misc]backup-simplify: Simplify 0 into 0 1539426661.396 * [misc]backup-simplify: Simplify 1 into 1 1539426661.396 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.396 * [misc]backup-simplify: Simplify PI into PI 1539426661.397 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.397 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.397 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.398 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.398 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.399 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.399 * [misc]taylor: Taking taylor expansion of n in n 1539426661.399 * [misc]backup-simplify: Simplify 0 into 0 1539426661.399 * [misc]backup-simplify: Simplify 1 into 1 1539426661.399 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.399 * [misc]backup-simplify: Simplify PI into PI 1539426661.399 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1539426661.399 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1539426661.399 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.399 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.399 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1539426661.399 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.399 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.399 * [misc]backup-simplify: Simplify 2 into 2 1539426661.399 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.399 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.399 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539426661.399 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539426661.399 * [misc]taylor: Taking taylor expansion of n in n 1539426661.399 * [misc]backup-simplify: Simplify 0 into 0 1539426661.399 * [misc]backup-simplify: Simplify 1 into 1 1539426661.399 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539426661.399 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.399 * [misc]backup-simplify: Simplify PI into PI 1539426661.400 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.400 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.401 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539426661.401 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426661.401 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1539426661.401 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426661.402 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.402 * [misc]backup-simplify: Simplify 0 into 0 1539426661.402 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.403 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539426661.404 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* (sqrt 2) PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426661.405 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426661.406 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539426661.406 * [misc]backup-simplify: Simplify 0 into 0 1539426661.407 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.408 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* n PI) (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.408 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (* n PI)) (* +nan.0 (* (pow n 2) (pow PI 2))))))) (* 2 0)) into (* +nan.0 (* (pow n 3) (pow PI 3))) 1539426661.409 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.410 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426661.410 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1539426661.413 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 1539426661.413 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.413 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.413 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539426661.414 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.414 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1539426661.416 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (pow (log (* 2 (* n PI))) 3)) 1539426661.416 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.417 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* -1/48 (pow (log (* 2 (* n PI))) 3))) (+ (* 0 (* 1/8 (pow (log (* 2 (* n PI))) 2))) (+ (* 0 (* -1/2 (log (* 2 (* n PI))))) (* 0 1)))) into (- (* 1/48 (* (sqrt 2) (pow (log (* 2 (* n PI))) 3)))) 1539426661.419 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (* (pow n 3) (pow PI 3)))) (+ (* (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) (* +nan.0 (* (pow n 2) (pow PI 2)))) (+ (* (* 1/8 (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) (* +nan.0 (* n PI))) (* (- (* 1/48 (* (sqrt 2) (pow (log (* 2 (* n PI))) 3)))) 0)))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* n PI)))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2)))))))))) 1539426661.419 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* n PI)))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2)))))))))) in n 1539426661.419 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* n PI)))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2))))))))) in n 1539426661.419 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.420 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.420 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 3) (pow PI 3))) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.420 * [misc]backup-simplify: Simplify 2 into 2 1539426661.420 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.420 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.420 * [misc]taylor: Taking taylor expansion of (* (pow n 3) (pow PI 3)) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of n in n 1539426661.420 * [misc]backup-simplify: Simplify 0 into 0 1539426661.420 * [misc]backup-simplify: Simplify 1 into 1 1539426661.420 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.420 * [misc]backup-simplify: Simplify PI into PI 1539426661.420 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* n PI)))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2)))))))) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* n PI)))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2))))))) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* n PI)))) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.420 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.420 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* n PI))) in n 1539426661.420 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.421 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.421 * [misc]backup-simplify: Simplify 2 into 2 1539426661.421 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.421 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.421 * [misc]taylor: Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 2) (* n PI)) in n 1539426661.421 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1539426661.421 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.421 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.421 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.421 * [misc]backup-simplify: Simplify 2 into 2 1539426661.421 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.421 * [misc]taylor: Taking taylor expansion of n in n 1539426661.421 * [misc]backup-simplify: Simplify 0 into 0 1539426661.421 * [misc]backup-simplify: Simplify 1 into 1 1539426661.421 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.421 * [misc]backup-simplify: Simplify PI into PI 1539426661.421 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.422 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.422 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.423 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.423 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.424 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.424 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.424 * [misc]taylor: Taking taylor expansion of n in n 1539426661.424 * [misc]backup-simplify: Simplify 0 into 0 1539426661.424 * [misc]backup-simplify: Simplify 1 into 1 1539426661.424 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.424 * [misc]backup-simplify: Simplify PI into PI 1539426661.424 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2)))))) in n 1539426661.424 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2))))) in n 1539426661.424 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.424 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.424 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2)))) in n 1539426661.424 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.424 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.424 * [misc]backup-simplify: Simplify 2 into 2 1539426661.425 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.425 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.425 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (* (pow n 2) (pow PI 2))) in n 1539426661.425 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.425 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.425 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.425 * [misc]backup-simplify: Simplify 2 into 2 1539426661.425 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.425 * [misc]taylor: Taking taylor expansion of n in n 1539426661.425 * [misc]backup-simplify: Simplify 0 into 0 1539426661.425 * [misc]backup-simplify: Simplify 1 into 1 1539426661.425 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.425 * [misc]backup-simplify: Simplify PI into PI 1539426661.425 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.425 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.426 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.427 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.427 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.427 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539426661.427 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539426661.427 * [misc]taylor: Taking taylor expansion of n in n 1539426661.427 * [misc]backup-simplify: Simplify 0 into 0 1539426661.427 * [misc]backup-simplify: Simplify 1 into 1 1539426661.427 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539426661.427 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.427 * [misc]backup-simplify: Simplify PI into PI 1539426661.428 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.429 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.430 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1539426661.430 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.431 * [misc]backup-simplify: Simplify (* (pow (+ (log n) (log (* 2 PI))) 2) 0) into 0 1539426661.431 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426661.431 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1539426661.431 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426661.432 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.432 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426661.432 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.432 * [misc]backup-simplify: Simplify 0 into 0 1539426661.433 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.433 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.434 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426661.435 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426661.438 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426661.439 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) PI) (* 0 0)) into (+ (* PI (log (* 2 PI))) (* PI (log n))) 1539426661.440 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (+ (* PI (log (* 2 PI))) (* PI (log n)))) (* 0 0)) into (+ (* (sqrt 2) (* PI (log n))) (* (sqrt 2) (* PI (log (* 2 PI))))) 1539426661.441 * [misc]backup-simplify: Simplify (+ (* +nan.0 (+ (* (sqrt 2) (* PI (log n))) (* (sqrt 2) (* PI (log (* 2 PI)))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426661.442 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 0) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426661.444 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426661.445 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1539426661.446 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426661.447 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.447 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1539426661.448 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 (* (sqrt 2) PI)) (* 0 0))) into 0 1539426661.448 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.448 * [misc]backup-simplify: Simplify 0 into 0 1539426661.448 * [misc]backup-simplify: Simplify 0 into 0 1539426661.450 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539426661.450 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* n PI) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.451 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* (pow n 2) (pow PI 2))) 2) (+ (* 2 (* (* +nan.0 (* n PI)) (* +nan.0 (* (pow n 3) (pow PI 3))))))) (* 2 0)) into (* +nan.0 (* (pow n 4) (pow PI 4))) 1539426661.451 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.452 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539426661.453 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI)))))) into 0 1539426661.455 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 (* n PI)) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 (* n PI)) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 (* n PI)) 1)))) 24) into 0 1539426661.455 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.456 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.456 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.456 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539426661.456 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.456 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI)))))))) into 0 1539426661.458 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 4) 24)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2) (/ (pow 0 1) 1)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/384 (pow (log (* 2 (* n PI))) 4)) 1539426661.459 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.460 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* 1/384 (pow (log (* 2 (* n PI))) 4))) (+ (* 0 (* -1/48 (pow (log (* 2 (* n PI))) 3))) (+ (* 0 (* 1/8 (pow (log (* 2 (* n PI))) 2))) (+ (* 0 (* -1/2 (log (* 2 (* n PI))))) (* 0 1))))) into (* 1/384 (* (sqrt 2) (pow (log (* 2 (* n PI))) 4))) 1539426661.462 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (* (pow n 4) (pow PI 4)))) (+ (* (- (* 1/2 (* (sqrt 2) (log (* 2 (* n PI)))))) (* +nan.0 (* (pow n 3) (pow PI 3)))) (+ (* (* 1/8 (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) (* +nan.0 (* (pow n 2) (pow PI 2)))) (+ (* (- (* 1/48 (* (sqrt 2) (pow (log (* 2 (* n PI))) 3)))) (* +nan.0 (* n PI))) (* (* 1/384 (* (sqrt 2) (pow (log (* 2 (* n PI))) 4))) 0))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 3) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 4) (pow PI 4)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3)))))))))))) 1539426661.462 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 3) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 4) (pow PI 4)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3)))))))))))) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 3) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 4) (pow PI 4)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3))))))))))) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 3) (* n PI)))) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.462 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.462 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 3) (* n PI))) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.462 * [misc]backup-simplify: Simplify 2 into 2 1539426661.462 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.462 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.462 * [misc]taylor: Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 3) (* n PI)) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 3) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.462 * [misc]backup-simplify: Simplify 2 into 2 1539426661.462 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.462 * [misc]taylor: Taking taylor expansion of n in n 1539426661.463 * [misc]backup-simplify: Simplify 0 into 0 1539426661.463 * [misc]backup-simplify: Simplify 1 into 1 1539426661.463 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.463 * [misc]backup-simplify: Simplify PI into PI 1539426661.463 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.463 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.463 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.464 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.464 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.464 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.464 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.464 * [misc]taylor: Taking taylor expansion of n in n 1539426661.464 * [misc]backup-simplify: Simplify 0 into 0 1539426661.464 * [misc]backup-simplify: Simplify 1 into 1 1539426661.464 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.464 * [misc]backup-simplify: Simplify PI into PI 1539426661.464 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (* (pow n 4) (pow PI 4)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3)))))))))) in n 1539426661.464 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (* (pow n 4) (pow PI 4)))) (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3))))))))) in n 1539426661.464 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (pow n 4) (pow PI 4)))) in n 1539426661.464 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.465 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.465 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 4) (pow PI 4))) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.465 * [misc]backup-simplify: Simplify 2 into 2 1539426661.465 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.465 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.465 * [misc]taylor: Taking taylor expansion of (* (pow n 4) (pow PI 4)) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of (pow n 4) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of n in n 1539426661.465 * [misc]backup-simplify: Simplify 0 into 0 1539426661.465 * [misc]backup-simplify: Simplify 1 into 1 1539426661.465 * [misc]taylor: Taking taylor expansion of (pow PI 4) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.465 * [misc]backup-simplify: Simplify PI into PI 1539426661.465 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3)))))))) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3))))))) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))))) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.465 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.465 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2)))) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.465 * [misc]backup-simplify: Simplify 2 into 2 1539426661.465 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.465 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.465 * [misc]taylor: Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 2) (* (pow n 2) (pow PI 2))) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.465 * [misc]backup-simplify: Simplify 2 into 2 1539426661.465 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.465 * [misc]taylor: Taking taylor expansion of n in n 1539426661.465 * [misc]backup-simplify: Simplify 0 into 0 1539426661.466 * [misc]backup-simplify: Simplify 1 into 1 1539426661.466 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.466 * [misc]backup-simplify: Simplify PI into PI 1539426661.466 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.466 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.466 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.467 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.467 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.467 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.467 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539426661.467 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539426661.467 * [misc]taylor: Taking taylor expansion of n in n 1539426661.467 * [misc]backup-simplify: Simplify 0 into 0 1539426661.467 * [misc]backup-simplify: Simplify 1 into 1 1539426661.467 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539426661.467 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.467 * [misc]backup-simplify: Simplify PI into PI 1539426661.467 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3)))))) in n 1539426661.467 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3))))) in n 1539426661.467 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.467 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.467 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3)))) in n 1539426661.468 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.468 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.468 * [misc]backup-simplify: Simplify 2 into 2 1539426661.468 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.468 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.468 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (* (pow n 3) (pow PI 3))) in n 1539426661.468 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539426661.468 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539426661.468 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.468 * [misc]backup-simplify: Simplify 2 into 2 1539426661.468 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539426661.468 * [misc]taylor: Taking taylor expansion of n in n 1539426661.468 * [misc]backup-simplify: Simplify 0 into 0 1539426661.468 * [misc]backup-simplify: Simplify 1 into 1 1539426661.468 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.468 * [misc]backup-simplify: Simplify PI into PI 1539426661.468 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.468 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539426661.469 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.469 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539426661.469 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.469 * [misc]taylor: Taking taylor expansion of (* (pow n 3) (pow PI 3)) in n 1539426661.469 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539426661.469 * [misc]taylor: Taking taylor expansion of n in n 1539426661.469 * [misc]backup-simplify: Simplify 0 into 0 1539426661.469 * [misc]backup-simplify: Simplify 1 into 1 1539426661.469 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539426661.469 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.469 * [misc]backup-simplify: Simplify PI into PI 1539426661.470 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.470 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.471 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.471 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1539426661.472 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (pow (+ (log n) (log (* 2 PI))) 2)) into (pow (+ (log n) (log (* 2 PI))) 3) 1539426661.473 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539426661.473 * [misc]backup-simplify: Simplify (* (pow (+ (log n) (log (* 2 PI))) 3) 0) into 0 1539426661.474 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539426661.474 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1539426661.474 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539426661.474 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.474 * [misc]backup-simplify: Simplify 0 into 0 1539426661.475 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539426661.475 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.477 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539426661.478 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539426661.480 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426661.481 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539426661.482 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539426661.483 * [misc]backup-simplify: Simplify (+ (* (pow (+ (log n) (log (* 2 PI))) 2) PI) (* 0 0)) into (+ (* 2 (* PI (* (log n) (log (* 2 PI))))) (+ (* PI (pow (log (* 2 PI)) 2)) (* PI (pow (log n) 2)))) 1539426661.486 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (+ (* 2 (* PI (* (log n) (log (* 2 PI))))) (+ (* PI (pow (log (* 2 PI)) 2)) (* PI (pow (log n) 2))))) (* 0 0)) into (+ (* (sqrt 2) (* PI (pow (log n) 2))) (+ (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2))) (* 2 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI)))))))) 1539426661.489 * [misc]backup-simplify: Simplify (+ (* +nan.0 (+ (* (sqrt 2) (* PI (pow (log n) 2))) (+ (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2))) (* 2 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) 1539426661.493 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) 0) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) 1539426661.497 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI)))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) 1539426661.501 * [misc]backup-simplify: Simplify (+ 0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI)))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) 1539426661.505 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI)))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) 1539426661.509 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) 1539426661.517 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log n) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (sqrt 2) (* PI (* (log n) (log (* 2 PI))))))))))) (* n (pow k 2))) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (pow (log n) 2) (pow k 2)))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (* n (* PI (pow k 2)))))) (- (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI (* (log n) (pow k 2)))))))))))))))))) 1539426661.518 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 k)) (* (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (- (/ (/ 1 k) 2)))))) into (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) 1539426661.518 * [misc]approximate: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in (k n) around 0 1539426661.518 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in n 1539426661.518 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in n 1539426661.518 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.518 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.518 * [misc]backup-simplify: Simplify 2 into 2 1539426661.518 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.519 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.519 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.519 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.519 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of k in n 1539426661.519 * [misc]backup-simplify: Simplify k into k 1539426661.519 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426661.519 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.519 * [misc]backup-simplify: Simplify 2 into 2 1539426661.519 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.519 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.519 * [misc]backup-simplify: Simplify PI into PI 1539426661.519 * [misc]taylor: Taking taylor expansion of n in n 1539426661.519 * [misc]backup-simplify: Simplify 0 into 0 1539426661.519 * [misc]backup-simplify: Simplify 1 into 1 1539426661.520 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.520 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.520 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.520 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426661.521 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539426661.521 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.522 * [misc]backup-simplify: Simplify (* (- (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.522 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.522 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1539426661.523 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1539426661.523 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539426661.523 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.523 * [misc]backup-simplify: Simplify PI into PI 1539426661.523 * [misc]taylor: Taking taylor expansion of k in n 1539426661.523 * [misc]backup-simplify: Simplify k into k 1539426661.523 * [misc]taylor: Taking taylor expansion of n in n 1539426661.523 * [misc]backup-simplify: Simplify 0 into 0 1539426661.523 * [misc]backup-simplify: Simplify 1 into 1 1539426661.523 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539426661.523 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1539426661.523 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.523 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1539426661.523 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in k 1539426661.523 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in k 1539426661.523 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426661.523 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.523 * [misc]backup-simplify: Simplify 2 into 2 1539426661.523 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.524 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.524 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.524 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.524 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of k in k 1539426661.524 * [misc]backup-simplify: Simplify 0 into 0 1539426661.524 * [misc]backup-simplify: Simplify 1 into 1 1539426661.524 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426661.524 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.524 * [misc]backup-simplify: Simplify 2 into 2 1539426661.524 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426661.524 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.524 * [misc]backup-simplify: Simplify PI into PI 1539426661.524 * [misc]taylor: Taking taylor expansion of n in k 1539426661.524 * [misc]backup-simplify: Simplify n into n 1539426661.524 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.524 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539426661.524 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539426661.524 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426661.524 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.524 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539426661.525 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1539426661.525 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in k 1539426661.525 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in k 1539426661.525 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539426661.525 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.525 * [misc]backup-simplify: Simplify PI into PI 1539426661.525 * [misc]taylor: Taking taylor expansion of k in k 1539426661.525 * [misc]backup-simplify: Simplify 0 into 0 1539426661.525 * [misc]backup-simplify: Simplify 1 into 1 1539426661.525 * [misc]taylor: Taking taylor expansion of n in k 1539426661.525 * [misc]backup-simplify: Simplify n into n 1539426661.525 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539426661.525 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539426661.525 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.525 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.526 * [misc]backup-simplify: Simplify (/ (/ PI n) (* 2 (sqrt 0))) into (* +nan.0 (/ PI n)) 1539426661.526 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) (sqrt (/ (* PI k) n))) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k))))) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.526 * [misc]backup-simplify: Simplify 2 into 2 1539426661.526 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.526 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.526 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- (* 1/2 (/ 1 k)))) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of (- (* 1/2 (/ 1 k))) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.526 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.526 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of k in k 1539426661.526 * [misc]backup-simplify: Simplify 0 into 0 1539426661.526 * [misc]backup-simplify: Simplify 1 into 1 1539426661.526 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426661.526 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of 2 in k 1539426661.526 * [misc]backup-simplify: Simplify 2 into 2 1539426661.526 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426661.526 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.526 * [misc]backup-simplify: Simplify PI into PI 1539426661.526 * [misc]taylor: Taking taylor expansion of n in k 1539426661.526 * [misc]backup-simplify: Simplify n into n 1539426661.526 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.526 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539426661.526 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539426661.527 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426661.527 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539426661.527 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539426661.527 * [misc]backup-simplify: Simplify (exp (* (- (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) 1539426661.527 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in k 1539426661.527 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in k 1539426661.527 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539426661.527 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.527 * [misc]backup-simplify: Simplify PI into PI 1539426661.527 * [misc]taylor: Taking taylor expansion of k in k 1539426661.527 * [misc]backup-simplify: Simplify 0 into 0 1539426661.527 * [misc]backup-simplify: Simplify 1 into 1 1539426661.527 * [misc]taylor: Taking taylor expansion of n in k 1539426661.527 * [misc]backup-simplify: Simplify n into n 1539426661.527 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539426661.528 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539426661.528 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.528 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.528 * [misc]backup-simplify: Simplify (/ (/ PI n) (* 2 (sqrt 0))) into (* +nan.0 (/ PI n)) 1539426661.528 * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* -1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 1539426661.528 * [misc]backup-simplify: Simplify (* (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 0) into 0 1539426661.528 * [misc]taylor: Taking taylor expansion of 0 in n 1539426661.528 * [misc]backup-simplify: Simplify 0 into 0 1539426661.529 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))))) into 0 1539426661.529 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (* +nan.0 (/ PI n))) (* 0 0)) into (- (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI)) n))) 1539426661.529 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI)) n))) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI)) n)) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.529 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.529 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI)) n) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) PI)) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.529 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.529 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.529 * [misc]backup-simplify: Simplify 2 into 2 1539426661.529 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.529 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.529 * [misc]backup-simplify: Simplify PI into PI 1539426661.529 * [misc]taylor: Taking taylor expansion of n in n 1539426661.529 * [misc]backup-simplify: Simplify 0 into 0 1539426661.529 * [misc]backup-simplify: Simplify 1 into 1 1539426661.530 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.530 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.530 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.530 * [misc]taylor: Taking taylor expansion of k in n 1539426661.530 * [misc]backup-simplify: Simplify k into k 1539426661.530 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.531 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.531 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.532 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.532 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.532 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) PI) in n 1539426661.532 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.532 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.532 * [misc]backup-simplify: Simplify 2 into 2 1539426661.532 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.532 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.532 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.532 * [misc]backup-simplify: Simplify PI into PI 1539426661.532 * [misc]taylor: Taking taylor expansion of n in n 1539426661.532 * [misc]backup-simplify: Simplify 0 into 0 1539426661.532 * [misc]backup-simplify: Simplify 1 into 1 1539426661.533 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1539426661.533 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)) 1539426661.534 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)) 1) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)) 1539426661.534 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) into (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI))) 1539426661.535 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) 1539426661.536 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) into (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) 1539426661.536 * [misc]backup-simplify: Simplify 0 into 0 1539426661.536 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1539426661.536 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1539426661.537 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ PI n)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow PI 2) (pow n 2))) 1539426661.537 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.538 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 1539426661.538 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (* +nan.0 (/ (pow PI 2) (pow n 2)))) (+ (* 0 (* +nan.0 (/ PI n))) (* 0 0))) into (- (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2))) (pow n 2)))) 1539426661.538 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2))) (pow n 2)))) in n 1539426661.538 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2))) (pow n 2))) in n 1539426661.538 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.538 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.538 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2))) (pow n 2)) in n 1539426661.538 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 2))) in n 1539426661.538 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.538 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.538 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.538 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.538 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.539 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.539 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.539 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.539 * [misc]backup-simplify: Simplify 2 into 2 1539426661.539 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.539 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.539 * [misc]backup-simplify: Simplify PI into PI 1539426661.539 * [misc]taylor: Taking taylor expansion of n in n 1539426661.539 * [misc]backup-simplify: Simplify 0 into 0 1539426661.539 * [misc]backup-simplify: Simplify 1 into 1 1539426661.539 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.539 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.539 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.539 * [misc]taylor: Taking taylor expansion of k in n 1539426661.539 * [misc]backup-simplify: Simplify k into k 1539426661.540 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.540 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.540 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.541 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.541 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.541 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in n 1539426661.541 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.541 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.541 * [misc]backup-simplify: Simplify 2 into 2 1539426661.541 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.541 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.542 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539426661.542 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.542 * [misc]backup-simplify: Simplify PI into PI 1539426661.542 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539426661.542 * [misc]taylor: Taking taylor expansion of n in n 1539426661.542 * [misc]backup-simplify: Simplify 0 into 0 1539426661.542 * [misc]backup-simplify: Simplify 1 into 1 1539426661.542 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.542 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539426661.543 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) 1539426661.543 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.544 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) 1) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) 1539426661.544 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426661.545 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539426661.546 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.546 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426661.547 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426661.548 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.548 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539426661.549 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.550 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (* (sqrt 2) (pow PI 2)))) into 0 1539426661.550 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426661.551 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) (/ 0 1)))) into 0 1539426661.552 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))))) into 0 1539426661.552 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.552 * [misc]backup-simplify: Simplify 0 into 0 1539426661.552 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 PI)) into 0 1539426661.553 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.553 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426661.555 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426661.556 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.556 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539426661.558 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.559 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (* (sqrt 2) PI))) into 0 1539426661.560 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)) (/ 0 1)))) into 0 1539426661.561 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) PI)))) into 0 1539426661.561 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.561 * [misc]backup-simplify: Simplify 0 into 0 1539426661.561 * [misc]backup-simplify: Simplify 0 into 0 1539426661.562 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539426661.562 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)) (* 0 (/ 0 n)))) into 0 1539426661.563 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (/ PI n)) (* +nan.0 (/ (pow PI 2) (pow n 2))))))) (* 2 0)) into (* +nan.0 (/ (pow PI 3) (pow n 3))) 1539426661.563 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539426661.564 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0 1539426661.565 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (* +nan.0 (/ (pow PI 3) (pow n 3)))) (+ (* 0 (* +nan.0 (/ (pow PI 2) (pow n 2)))) (+ (* 0 (* +nan.0 (/ PI n))) (* 0 0)))) into (- (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3))) (pow n 3)))) 1539426661.565 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3))) (pow n 3)))) in n 1539426661.565 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3))) (pow n 3))) in n 1539426661.565 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.566 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.566 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3))) (pow n 3)) in n 1539426661.566 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) (* (sqrt 2) (pow PI 3))) in n 1539426661.566 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539426661.566 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539426661.566 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539426661.566 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539426661.566 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539426661.566 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539426661.566 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539426661.566 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.566 * [misc]backup-simplify: Simplify 2 into 2 1539426661.566 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.566 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.566 * [misc]backup-simplify: Simplify PI into PI 1539426661.566 * [misc]taylor: Taking taylor expansion of n in n 1539426661.566 * [misc]backup-simplify: Simplify 0 into 0 1539426661.566 * [misc]backup-simplify: Simplify 1 into 1 1539426661.566 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.566 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539426661.567 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539426661.567 * [misc]taylor: Taking taylor expansion of k in n 1539426661.567 * [misc]backup-simplify: Simplify k into k 1539426661.568 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.568 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539426661.569 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539426661.569 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539426661.570 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539426661.570 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 3)) in n 1539426661.570 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539426661.570 * [misc]taylor: Taking taylor expansion of 2 in n 1539426661.570 * [misc]backup-simplify: Simplify 2 into 2 1539426661.570 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539426661.570 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539426661.570 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539426661.570 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.570 * [misc]backup-simplify: Simplify PI into PI 1539426661.570 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539426661.570 * [misc]taylor: Taking taylor expansion of n in n 1539426661.570 * [misc]backup-simplify: Simplify 0 into 0 1539426661.571 * [misc]backup-simplify: Simplify 1 into 1 1539426661.571 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539426661.571 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539426661.572 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539426661.573 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) 1539426661.573 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.573 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539426661.574 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) 1) into (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) 1539426661.577 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.578 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539426661.579 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 (pow PI 2)))) into 0 1539426661.580 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (pow PI 2))) into 0 1539426661.581 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.582 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (pow PI 3)))) into 0 1539426661.583 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.584 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539426661.587 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539426661.588 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.589 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539426661.590 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.591 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 3))) into 0 1539426661.592 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.593 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.598 * [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 1539426661.599 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426661.599 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))) into 0 1539426661.602 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426661.604 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (* 0 (* (sqrt 2) (pow PI 3))))) into 0 1539426661.604 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539426661.604 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426661.605 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539426661.606 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 (* (sqrt 2) (pow PI 3)))) into 0 1539426661.606 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539426661.608 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) (/ 0 1)))) into 0 1539426661.609 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.610 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 3)))))) into 0 1539426661.611 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.611 * [misc]backup-simplify: Simplify 0 into 0 1539426661.612 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.613 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539426661.614 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (pow PI 2)))) into 0 1539426661.616 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.617 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.621 * [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 1539426661.622 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426661.623 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))) into 0 1539426661.625 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426661.627 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (* 0 (* (sqrt 2) (pow PI 2))))) into 0 1539426661.627 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539426661.629 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.630 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log n)) k))) (pow PI 2)))))) into 0 1539426661.630 * [misc]backup-simplify: Simplify (- 0) into 0 1539426661.630 * [misc]backup-simplify: Simplify 0 into 0 1539426661.631 * [misc]backup-simplify: Simplify (* (- (* +nan.0 (* (sqrt 2) (* (exp (* -1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) PI)))) (* (/ 1 (/ 1 n)) (/ 1 k))) into (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI))) k)) 1539426661.632 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (* (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (- (/ (/ 1 (- k)) 2)))))) into (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) 1539426661.632 * [misc]approximate: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) in (k n) around 0 1539426661.632 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.632 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.632 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of k in n 1539426661.632 * [misc]backup-simplify: Simplify k into k 1539426661.632 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539426661.632 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.632 * [misc]backup-simplify: Simplify -2 into -2 1539426661.632 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.632 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.633 * [misc]backup-simplify: Simplify PI into PI 1539426661.633 * [misc]taylor: Taking taylor expansion of n in n 1539426661.633 * [misc]backup-simplify: Simplify 0 into 0 1539426661.633 * [misc]backup-simplify: Simplify 1 into 1 1539426661.633 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.633 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.634 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426661.634 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539426661.634 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.635 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426661.635 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426661.636 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in n 1539426661.636 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in n 1539426661.636 * [misc]taylor: Taking taylor expansion of (* PI -2) in n 1539426661.636 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.636 * [misc]backup-simplify: Simplify PI into PI 1539426661.636 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.636 * [misc]backup-simplify: Simplify -2 into -2 1539426661.636 * [misc]taylor: Taking taylor expansion of n in n 1539426661.636 * [misc]backup-simplify: Simplify 0 into 0 1539426661.636 * [misc]backup-simplify: Simplify 1 into 1 1539426661.636 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426661.636 * [misc]backup-simplify: Simplify (/ (* -2 PI) 1) into (* -2 PI) 1539426661.637 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.637 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426661.637 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539426661.637 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539426661.637 * [misc]taylor: Taking taylor expansion of -1 in n 1539426661.637 * [misc]backup-simplify: Simplify -1 into -1 1539426661.637 * [misc]taylor: Taking taylor expansion of k in n 1539426661.637 * [misc]backup-simplify: Simplify k into k 1539426661.637 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539426661.638 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539426661.638 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539426661.638 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539426661.638 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 1539426661.639 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.640 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426661.643 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426661.643 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539426661.643 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539426661.644 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.644 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539426661.646 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.647 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.648 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (sqrt (/ -1 k))) into (* +nan.0 (/ (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k)))) 1539426661.648 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.648 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.648 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of k in k 1539426661.648 * [misc]backup-simplify: Simplify 0 into 0 1539426661.648 * [misc]backup-simplify: Simplify 1 into 1 1539426661.648 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426661.648 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426661.648 * [misc]taylor: Taking taylor expansion of -2 in k 1539426661.649 * [misc]backup-simplify: Simplify -2 into -2 1539426661.649 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426661.649 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.649 * [misc]backup-simplify: Simplify PI into PI 1539426661.649 * [misc]taylor: Taking taylor expansion of n in k 1539426661.649 * [misc]backup-simplify: Simplify n into n 1539426661.649 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.649 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426661.649 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539426661.649 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426661.649 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539426661.649 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1539426661.649 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in k 1539426661.649 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in k 1539426661.649 * [misc]taylor: Taking taylor expansion of (* PI -2) in k 1539426661.649 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.649 * [misc]backup-simplify: Simplify PI into PI 1539426661.649 * [misc]taylor: Taking taylor expansion of -2 in k 1539426661.650 * [misc]backup-simplify: Simplify -2 into -2 1539426661.650 * [misc]taylor: Taking taylor expansion of n in k 1539426661.650 * [misc]backup-simplify: Simplify n into n 1539426661.650 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426661.650 * [misc]backup-simplify: Simplify (/ (* -2 PI) n) into (* -2 (/ PI n)) 1539426661.650 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539426661.651 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 1539426661.651 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (* -2 (/ PI n)) (/ 0 n)))) into 0 1539426661.651 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539426661.651 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426661.651 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426661.651 * [misc]taylor: Taking taylor expansion of -1 in k 1539426661.651 * [misc]backup-simplify: Simplify -1 into -1 1539426661.651 * [misc]taylor: Taking taylor expansion of k in k 1539426661.651 * [misc]backup-simplify: Simplify 0 into 0 1539426661.651 * [misc]backup-simplify: Simplify 1 into 1 1539426661.652 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426661.652 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.652 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426661.652 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) into (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1539426661.653 * [misc]backup-simplify: Simplify (/ (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) +nan.0) into (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) 1539426661.653 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) (sqrt (/ -1 k))) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) (sqrt (/ (* PI -2) n))) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (/ 1 k))) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n)))) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539426661.653 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.653 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of k in k 1539426661.653 * [misc]backup-simplify: Simplify 0 into 0 1539426661.653 * [misc]backup-simplify: Simplify 1 into 1 1539426661.653 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539426661.653 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of -2 in k 1539426661.653 * [misc]backup-simplify: Simplify -2 into -2 1539426661.653 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539426661.653 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.653 * [misc]backup-simplify: Simplify PI into PI 1539426661.653 * [misc]taylor: Taking taylor expansion of n in k 1539426661.653 * [misc]backup-simplify: Simplify n into n 1539426661.653 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539426661.654 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539426661.654 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539426661.654 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539426661.654 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539426661.654 * [misc]backup-simplify: Simplify (exp (* (* 1/2 (/ 1 k)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 1539426661.654 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI -2) n)) in k 1539426661.654 * [misc]taylor: Taking taylor expansion of (/ (* PI -2) n) in k 1539426661.654 * [misc]taylor: Taking taylor expansion of (* PI -2) in k 1539426661.654 * [misc]taylor: Taking taylor expansion of PI in k 1539426661.654 * [misc]backup-simplify: Simplify PI into PI 1539426661.654 * [misc]taylor: Taking taylor expansion of -2 in k 1539426661.654 * [misc]backup-simplify: Simplify -2 into -2 1539426661.654 * [misc]taylor: Taking taylor expansion of n in k 1539426661.654 * [misc]backup-simplify: Simplify n into n 1539426661.655 * [misc]backup-simplify: Simplify (* PI -2) into (* -2 PI) 1539426661.655 * [misc]backup-simplify: Simplify (/ (* -2 PI) n) into (* -2 (/ PI n)) 1539426661.655 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539426661.655 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 -2)) into 0 1539426661.656 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (* -2 (/ PI n)) (/ 0 n)))) into 0 1539426661.656 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539426661.656 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539426661.656 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539426661.656 * [misc]taylor: Taking taylor expansion of -1 in k 1539426661.656 * [misc]backup-simplify: Simplify -1 into -1 1539426661.656 * [misc]taylor: Taking taylor expansion of k in k 1539426661.656 * [misc]backup-simplify: Simplify 0 into 0 1539426661.656 * [misc]backup-simplify: Simplify 1 into 1 1539426661.656 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539426661.656 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.657 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539426661.657 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) into (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) 1539426661.657 * [misc]backup-simplify: Simplify (/ (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) +nan.0) into (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) 1539426661.657 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) in n 1539426661.657 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.657 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.657 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) in n 1539426661.657 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539426661.657 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.657 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.657 * [misc]backup-simplify: Simplify -2 into -2 1539426661.658 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.658 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.658 * [misc]backup-simplify: Simplify PI into PI 1539426661.658 * [misc]taylor: Taking taylor expansion of n in n 1539426661.658 * [misc]backup-simplify: Simplify 0 into 0 1539426661.658 * [misc]backup-simplify: Simplify 1 into 1 1539426661.658 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.658 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.658 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.659 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426661.659 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) in n 1539426661.659 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* -2 (/ PI n))) k)) in n 1539426661.659 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.659 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.659 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1539426661.659 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426661.659 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.659 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.659 * [misc]backup-simplify: Simplify -2 into -2 1539426661.659 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.659 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.659 * [misc]backup-simplify: Simplify PI into PI 1539426661.659 * [misc]taylor: Taking taylor expansion of n in n 1539426661.659 * [misc]backup-simplify: Simplify 0 into 0 1539426661.659 * [misc]backup-simplify: Simplify 1 into 1 1539426661.660 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.660 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.660 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426661.660 * [misc]taylor: Taking taylor expansion of k in n 1539426661.660 * [misc]backup-simplify: Simplify k into k 1539426661.661 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.662 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.662 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) 1539426661.663 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426661.663 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426661.664 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.665 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426661.668 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426661.668 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.669 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 1539426661.670 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.671 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.672 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1539426661.673 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* 0 0)) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.673 * [misc]backup-simplify: Simplify (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.674 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) 0) (* 0 (sqrt (* -2 (/ PI n))))) into 0 1539426661.674 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539426661.675 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539426661.676 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))))) 1539426661.676 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))))) in n 1539426661.676 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))))) in n 1539426661.676 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539426661.676 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539426661.676 * [misc]taylor: Taking taylor expansion of (* (sqrt (* -2 (/ PI n))) (exp (* 1/2 (/ (log (* -2 (/ PI n))) k)))) in n 1539426661.676 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539426661.676 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.676 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.676 * [misc]backup-simplify: Simplify -2 into -2 1539426661.676 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.676 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.676 * [misc]backup-simplify: Simplify PI into PI 1539426661.676 * [misc]taylor: Taking taylor expansion of n in n 1539426661.676 * [misc]backup-simplify: Simplify 0 into 0 1539426661.676 * [misc]backup-simplify: Simplify 1 into 1 1539426661.676 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.677 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.677 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539426661.677 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539426661.678 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* -2 (/ PI n))) k))) in n 1539426661.678 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* -2 (/ PI n))) k)) in n 1539426661.678 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539426661.678 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539426661.678 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1539426661.678 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539426661.678 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539426661.678 * [misc]taylor: Taking taylor expansion of -2 in n 1539426661.678 * [misc]backup-simplify: Simplify -2 into -2 1539426661.678 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539426661.678 * [misc]taylor: Taking taylor expansion of PI in n 1539426661.678 * [misc]backup-simplify: Simplify PI into PI 1539426661.678 * [misc]taylor: Taking taylor expansion of n in n 1539426661.678 * [misc]backup-simplify: Simplify 0 into 0 1539426661.678 * [misc]backup-simplify: Simplify 1 into 1 1539426661.678 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539426661.678 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539426661.679 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539426661.679 * [misc]taylor: Taking taylor expansion of k in n 1539426661.679 * [misc]backup-simplify: Simplify k into k 1539426661.680 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.680 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539426661.681 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) 1539426661.681 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539426661.682 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539426661.683 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.683 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426661.686 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539426661.687 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 1539426661.688 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 1539426661.689 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539426661.690 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.691 * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1539426661.691 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* 0 0)) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.692 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.693 * [misc]backup-simplify: Simplify (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.694 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539426661.695 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539426661.700 * [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 1539426661.701 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539426661.702 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 1539426661.704 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539426661.705 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539426661.706 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539426661.707 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539426661.709 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (* +nan.0 PI) 0) (* (* +nan.0 (pow PI 2)) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.711 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (+ (* 0 (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* 0 0))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.711 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539426661.714 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (pow PI 2) (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- n)) 1)) (+ (* (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* 1 (/ 1 (- k)))) (- (* +nan.0 (* PI (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))))) into (- (+ (* +nan.0 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI)) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow PI 2)) n))))))) 1539426661.714 * * * [misc]progress: simplifying candidates 1539426661.715 * * * * [misc]progress: [ 1 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 2 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 3 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 4 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 5 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 6 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 7 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 8 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 9 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 10 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 11 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 12 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 13 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 14 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 15 / 104 ] simplifiying candidate # 1539426661.715 * * * * [misc]progress: [ 16 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 17 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 18 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 19 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 20 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 21 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 22 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 23 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 24 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 25 / 104 ] simplifiying candidate # 1539426661.716 * * * * [misc]progress: [ 26 / 104 ] simplifiying candidate # 1539426661.716 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (- (/ k 2))))) 1539426661.717 * * [misc]simplify: iters left: 6 (16 enodes) 1539426661.722 * * [misc]simplify: iters left: 5 (37 enodes) 1539426661.736 * * [misc]simplify: iters left: 4 (89 enodes) 1539426661.774 * * [misc]simplify: iters left: 3 (257 enodes) 1539426661.909 * [exit]simplify: Simplified to (fma (+ -1/2 (/ k 2)) (log (* 2 (* PI n))) (log (sqrt k))) 1539426661.909 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ -1/2 (/ k 2)) (log (* 2 (* PI n))) (log (sqrt k)))))) 1539426661.909 * * * * [misc]progress: [ 27 / 104 ] simplifiying candidate # 1539426661.909 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (- (/ k 2))))) 1539426661.910 * * [misc]simplify: iters left: 6 (16 enodes) 1539426661.912 * * [misc]simplify: iters left: 5 (37 enodes) 1539426661.918 * * [misc]simplify: iters left: 4 (89 enodes) 1539426661.956 * * [misc]simplify: iters left: 3 (257 enodes) 1539426662.056 * [exit]simplify: Simplified to (fma (+ -1/2 (/ k 2)) (log (* 2 (* PI n))) (log (sqrt k))) 1539426662.056 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ -1/2 (/ k 2)) (log (* 2 (* PI n))) (log (sqrt k)))))) 1539426662.056 * * * * [misc]progress: [ 28 / 104 ] simplifiying candidate # 1539426662.057 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (* (log (* PI (* n 2))) 1/2) (log (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426662.057 * * [misc]simplify: iters left: 6 (17 enodes) 1539426662.062 * * [misc]simplify: iters left: 5 (34 enodes) 1539426662.073 * * [misc]simplify: iters left: 4 (76 enodes) 1539426662.090 * * [misc]simplify: iters left: 3 (228 enodes) 1539426662.206 * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (+ (/ k 2) -1/2) (log (sqrt k))) 1539426662.206 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (log (* (* PI n) 2)) (+ (/ k 2) -1/2) (log (sqrt k)))))) 1539426662.206 * * * * [misc]progress: [ 29 / 104 ] simplifiying candidate # 1539426662.207 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (- (/ k 2))))) 1539426662.207 * * [misc]simplify: iters left: 6 (16 enodes) 1539426662.209 * * [misc]simplify: iters left: 5 (37 enodes) 1539426662.216 * * [misc]simplify: iters left: 4 (89 enodes) 1539426662.239 * * [misc]simplify: iters left: 3 (257 enodes) 1539426662.370 * [exit]simplify: Simplified to (fma (+ -1/2 (/ k 2)) (log (* 2 (* PI n))) (log (sqrt k))) 1539426662.370 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ -1/2 (/ k 2)) (log (* 2 (* PI n))) (log (sqrt k)))))) 1539426662.371 * * * * [misc]progress: [ 30 / 104 ] simplifiying candidate # 1539426662.371 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (- (/ k 2))))) 1539426662.371 * * [misc]simplify: iters left: 6 (16 enodes) 1539426662.376 * * [misc]simplify: iters left: 5 (37 enodes) 1539426662.389 * * [misc]simplify: iters left: 4 (89 enodes) 1539426662.426 * * [misc]simplify: iters left: 3 (257 enodes) 1539426662.535 * [exit]simplify: Simplified to (fma (+ -1/2 (/ k 2)) (log (* 2 (* PI n))) (log (sqrt k))) 1539426662.535 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (+ -1/2 (/ k 2)) (log (* 2 (* PI n))) (log (sqrt k)))))) 1539426662.535 * * * * [misc]progress: [ 31 / 104 ] simplifiying candidate # 1539426662.536 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (* (log (* PI (* n 2))) 1/2) (log (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426662.536 * * [misc]simplify: iters left: 6 (17 enodes) 1539426662.538 * * [misc]simplify: iters left: 5 (34 enodes) 1539426662.544 * * [misc]simplify: iters left: 4 (76 enodes) 1539426662.581 * * [misc]simplify: iters left: 3 (228 enodes) 1539426662.698 * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (+ (/ k 2) -1/2) (log (sqrt k))) 1539426662.698 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (log (* (* PI n) 2)) (+ (/ k 2) -1/2) (log (sqrt k)))))) 1539426662.698 * * * * [misc]progress: [ 32 / 104 ] simplifiying candidate # 1539426662.698 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (log (pow (* PI (* n 2)) 1/2)) (* (log (* PI (* n 2))) (- (/ k 2))))) 1539426662.698 * * [misc]simplify: iters left: 6 (17 enodes) 1539426662.703 * * [misc]simplify: iters left: 5 (36 enodes) 1539426662.715 * * [misc]simplify: iters left: 4 (86 enodes) 1539426662.746 * * [misc]simplify: iters left: 3 (249 enodes) 1539426662.883 * [exit]simplify: Simplified to (fma (log (* n (* PI 2))) (+ (/ k 2) -1/2) (log (sqrt k))) 1539426662.883 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (log (* n (* PI 2))) (+ (/ k 2) -1/2) (log (sqrt k)))))) 1539426662.883 * * * * [misc]progress: [ 33 / 104 ] simplifiying candidate # 1539426662.883 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (log (pow (* PI (* n 2)) 1/2)) (* (log (* PI (* n 2))) (- (/ k 2))))) 1539426662.883 * * [misc]simplify: iters left: 6 (17 enodes) 1539426662.889 * * [misc]simplify: iters left: 5 (36 enodes) 1539426662.901 * * [misc]simplify: iters left: 4 (86 enodes) 1539426662.942 * * [misc]simplify: iters left: 3 (249 enodes) 1539426663.062 * [exit]simplify: Simplified to (fma (log (* n (* PI 2))) (+ (/ k 2) -1/2) (log (sqrt k))) 1539426663.062 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (log (* n (* PI 2))) (+ (/ k 2) -1/2) (log (sqrt k)))))) 1539426663.062 * * * * [misc]progress: [ 34 / 104 ] simplifiying candidate # 1539426663.062 * [enter]simplify: Simplifying (- (log (sqrt k)) (+ (log (pow (* PI (* n 2)) 1/2)) (log (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426663.062 * * [misc]simplify: iters left: 6 (17 enodes) 1539426663.068 * * [misc]simplify: iters left: 5 (32 enodes) 1539426663.078 * * [misc]simplify: iters left: 4 (65 enodes) 1539426663.102 * * [misc]simplify: iters left: 3 (172 enodes) 1539426663.220 * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (+ (/ k 2) -1/2) (log (sqrt k))) 1539426663.220 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (log (* (* PI 2) n)) (+ (/ k 2) -1/2) (log (sqrt k)))))) 1539426663.220 * * * * [misc]progress: [ 35 / 104 ] simplifiying candidate # 1539426663.220 * [enter]simplify: Simplifying (- (log (sqrt k)) (log (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426663.220 * * [misc]simplify: iters left: 6 (16 enodes) 1539426663.223 * * [misc]simplify: iters left: 5 (29 enodes) 1539426663.226 * * [misc]simplify: iters left: 4 (45 enodes) 1539426663.233 * * [misc]simplify: iters left: 3 (88 enodes) 1539426663.250 * * [misc]simplify: iters left: 2 (256 enodes) 1539426663.418 * [exit]simplify: Simplified to (fma (log (* n (* PI 2))) (+ -1/2 (/ k 2)) (log (sqrt k))) 1539426663.418 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (fma (log (* n (* PI 2))) (+ -1/2 (/ k 2)) (log (sqrt k)))))) 1539426663.418 * * * * [misc]progress: [ 36 / 104 ] simplifiying candidate # 1539426663.418 * * * * [misc]progress: [ 37 / 104 ] simplifiying candidate # 1539426663.419 * * * * [misc]progress: [ 38 / 104 ] simplifiying candidate # 1539426663.419 * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) 1/2)) (* (* (pow (* PI (* n 2)) (- (/ k 2))) (pow (* PI (* n 2)) (- (/ k 2)))) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426663.419 * * [misc]simplify: iters left: 6 (20 enodes) 1539426663.422 * * [misc]simplify: iters left: 5 (42 enodes) 1539426663.430 * * [misc]simplify: iters left: 4 (138 enodes) 1539426663.491 * [exit]simplify: Simplified to (/ (/ (* (/ k n) (/ (sqrt k) (* 2 PI))) (sqrt (* 2 (* PI n)))) (pow (pow (* 2 (* PI n)) (- (/ k 2))) 3)) 1539426663.491 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* (/ k n) (/ (sqrt k) (* 2 PI))) (sqrt (* 2 (* PI n)))) (pow (pow (* 2 (* PI n)) (- (/ k 2))) 3))))) 1539426663.491 * * * * [misc]progress: [ 39 / 104 ] simplifiying candidate # 1539426663.491 * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426663.491 * * [misc]simplify: iters left: 6 (18 enodes) 1539426663.495 * * [misc]simplify: iters left: 5 (41 enodes) 1539426663.502 * * [misc]simplify: iters left: 4 (121 enodes) 1539426663.563 * * [misc]simplify: iters left: 3 (448 enodes) 1539426664.114 * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (* (* n 2) PI))) (/ (/ (/ k (* (* n 2) PI)) (pow (* (* n 2) PI) (- (/ k 2)))) (* (pow (* (* n 2) PI) (- (/ k 2))) (pow (* (* n 2) PI) (- (/ k 2)))))) 1539426664.114 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (* (/ (sqrt k) (sqrt (* (* n 2) PI))) (/ (/ (/ k (* (* n 2) PI)) (pow (* (* n 2) PI) (- (/ k 2)))) (* (pow (* (* n 2) PI) (- (/ k 2))) (pow (* (* n 2) PI) (- (/ k 2))))))))) 1539426664.114 * * * * [misc]progress: [ 40 / 104 ] simplifiying candidate # 1539426664.114 * * * * [misc]progress: [ 41 / 104 ] simplifiying candidate # 1539426664.114 * * * * [misc]progress: [ 42 / 104 ] simplifiying candidate # 1539426664.114 * * * * [misc]progress: [ 43 / 104 ] simplifiying candidate # 1539426664.114 * * * * [misc]progress: [ 44 / 104 ] simplifiying candidate # 1539426664.115 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1539426664.115 * * [misc]simplify: iters left: 6 (12 enodes) 1539426664.122 * * [misc]simplify: iters left: 5 (19 enodes) 1539426664.128 * * [misc]simplify: iters left: 4 (27 enodes) 1539426664.133 * * [misc]simplify: iters left: 3 (29 enodes) 1539426664.136 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1539426664.136 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1539426664.137 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1539426664.137 * * [misc]simplify: iters left: 6 (12 enodes) 1539426664.138 * * [misc]simplify: iters left: 5 (18 enodes) 1539426664.141 * * [misc]simplify: iters left: 4 (24 enodes) 1539426664.144 * * [misc]simplify: iters left: 3 (25 enodes) 1539426664.147 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1539426664.147 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1539426664.147 * * * * [misc]progress: [ 45 / 104 ] simplifiying candidate # 1539426664.147 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1539426664.147 * * [misc]simplify: iters left: 6 (11 enodes) 1539426664.148 * * [misc]simplify: iters left: 5 (16 enodes) 1539426664.151 * * [misc]simplify: iters left: 4 (22 enodes) 1539426664.153 * * [misc]simplify: iters left: 3 (23 enodes) 1539426664.156 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1539426664.156 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1539426664.156 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1539426664.156 * * [misc]simplify: iters left: 6 (12 enodes) 1539426664.158 * * [misc]simplify: iters left: 5 (18 enodes) 1539426664.160 * * [misc]simplify: iters left: 4 (24 enodes) 1539426664.163 * * [misc]simplify: iters left: 3 (25 enodes) 1539426664.170 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1539426664.170 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1539426664.170 * * * * [misc]progress: [ 46 / 104 ] simplifiying candidate # 1539426664.170 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1539426664.170 * * [misc]simplify: iters left: 6 (9 enodes) 1539426664.173 * * [misc]simplify: iters left: 5 (16 enodes) 1539426664.177 * * [misc]simplify: iters left: 4 (22 enodes) 1539426664.183 * * [misc]simplify: iters left: 3 (23 enodes) 1539426664.188 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1539426664.189 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1539426664.189 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1539426664.189 * * [misc]simplify: iters left: 6 (11 enodes) 1539426664.192 * * [misc]simplify: iters left: 5 (17 enodes) 1539426664.197 * * [misc]simplify: iters left: 4 (23 enodes) 1539426664.203 * * [misc]simplify: iters left: 3 (24 enodes) 1539426664.209 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1539426664.209 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1539426664.209 * * * * [misc]progress: [ 47 / 104 ] simplifiying candidate # 1539426664.209 * * * * [misc]progress: [ 48 / 104 ] simplifiying candidate # 1539426664.209 * * * * [misc]progress: [ 49 / 104 ] simplifiying candidate # 1539426664.209 * * * * [misc]progress: [ 50 / 104 ] simplifiying candidate # 1539426664.209 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1539426664.209 * * [misc]simplify: iters left: 5 (9 enodes) 1539426664.212 * * [misc]simplify: iters left: 4 (15 enodes) 1539426664.216 * * [misc]simplify: iters left: 3 (21 enodes) 1539426664.222 * * [misc]simplify: iters left: 2 (22 enodes) 1539426664.227 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1539426664.227 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1539426664.227 * * * * [misc]progress: [ 51 / 104 ] simplifiying candidate # 1539426664.228 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1539426664.228 * * [misc]simplify: iters left: 4 (4 enodes) 1539426664.230 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1539426664.230 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (cbrt (sqrt k)))))) 1539426664.230 * * * * [misc]progress: [ 52 / 104 ] simplifiying candidate # 1539426664.230 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1539426664.230 * * [misc]simplify: iters left: 2 (3 enodes) 1539426664.231 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1539426664.231 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt (sqrt k)))))) 1539426664.231 * * * * [misc]progress: [ 53 / 104 ] simplifiying candidate # 1539426664.231 * * * * [misc]progress: [ 54 / 104 ] simplifiying candidate # 1539426664.231 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539426664.231 * * [misc]simplify: iters left: 5 (8 enodes) 1539426664.234 * * [misc]simplify: iters left: 4 (12 enodes) 1539426664.237 * * [misc]simplify: iters left: 3 (18 enodes) 1539426664.242 * * [misc]simplify: iters left: 2 (20 enodes) 1539426664.247 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539426664.247 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* 2 n) PI) (/ k 2))))) 1539426664.247 * * * * [misc]progress: [ 55 / 104 ] simplifiying candidate # 1539426664.247 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539426664.247 * * [misc]simplify: iters left: 5 (8 enodes) 1539426664.250 * * [misc]simplify: iters left: 4 (12 enodes) 1539426664.253 * * [misc]simplify: iters left: 3 (18 enodes) 1539426664.258 * * [misc]simplify: iters left: 2 (20 enodes) 1539426664.263 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539426664.263 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) 1)) (pow (* (* 2 n) PI) (/ k 2))))) 1539426664.264 * * * * [misc]progress: [ 56 / 104 ] simplifiying candidate # 1539426664.264 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539426664.264 * * [misc]simplify: iters left: 5 (8 enodes) 1539426664.266 * * [misc]simplify: iters left: 4 (12 enodes) 1539426664.270 * * [misc]simplify: iters left: 3 (18 enodes) 1539426664.275 * * [misc]simplify: iters left: 2 (20 enodes) 1539426664.280 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539426664.280 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) 0))) (pow (* (* 2 n) PI) (/ k 2))))) 1539426664.280 * * * * [misc]progress: [ 57 / 104 ] simplifiying candidate # 1539426664.280 * * * * [misc]progress: [ 58 / 104 ] simplifiying candidate # 1539426664.280 * * * * [misc]progress: [ 59 / 104 ] simplifiying candidate # 1539426664.280 * * * * [misc]progress: [ 60 / 104 ] simplifiying candidate # 1539426664.280 * [enter]simplify: Simplifying (- 1) 1539426664.280 * * [misc]simplify: iters left: 2 (2 enodes) 1539426664.281 * * [misc]simplify: iters left: 1 (5 enodes) 1539426664.281 * [exit]simplify: Simplified to -1 1539426664.281 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))) -1)) 1539426664.281 * * * * [misc]progress: [ 61 / 104 ] simplifiying candidate # 1539426664.281 * * * * [misc]progress: [ 62 / 104 ] simplifiying candidate # 1539426664.281 * * * * [misc]progress: [ 63 / 104 ] simplifiying candidate # 1539426664.281 * * * * [misc]progress: [ 64 / 104 ] simplifiying candidate # 1539426664.281 * * * * [misc]progress: [ 65 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 66 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 67 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 68 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 69 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 70 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 71 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 72 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 73 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 74 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 75 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 76 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 77 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 78 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 79 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 80 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 81 / 104 ] simplifiying candidate # 1539426664.282 * * * * [misc]progress: [ 82 / 104 ] simplifiying candidate # 1539426664.282 * [enter]simplify: Simplifying (cbrt (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426664.282 * * [misc]simplify: iters left: 6 (15 enodes) 1539426664.285 * * [misc]simplify: iters left: 5 (25 enodes) 1539426664.288 * * [misc]simplify: iters left: 4 (31 enodes) 1539426664.292 * * [misc]simplify: iters left: 3 (33 enodes) 1539426664.296 * [exit]simplify: Simplified to (cbrt (/ (sqrt k) (* (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (* n (* 2 PI)))))) 1539426664.296 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))))) (cbrt (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))))))) (cbrt (/ (sqrt k) (* (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (* n (* 2 PI)))))))) 1539426664.296 * * * * [misc]progress: [ 83 / 104 ] simplifiying candidate # 1539426664.296 * [enter]simplify: Simplifying (sqrt (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539426664.296 * * [misc]simplify: iters left: 6 (15 enodes) 1539426664.299 * * [misc]simplify: iters left: 5 (25 enodes) 1539426664.302 * * [misc]simplify: iters left: 4 (31 enodes) 1539426664.306 * * [misc]simplify: iters left: 3 (33 enodes) 1539426664.310 * [exit]simplify: Simplified to (sqrt (/ (sqrt k) (* (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (* n (* 2 PI)))))) 1539426664.310 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))))) (sqrt (/ (sqrt k) (* (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (* n (* 2 PI)))))))) 1539426664.310 * * * * [misc]progress: [ 84 / 104 ] simplifiying candidate # 1539426664.310 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1539426664.310 * * [misc]simplify: iters left: 6 (12 enodes) 1539426664.312 * * [misc]simplify: iters left: 5 (18 enodes) 1539426664.314 * * [misc]simplify: iters left: 4 (24 enodes) 1539426664.317 * * [misc]simplify: iters left: 3 (25 enodes) 1539426664.320 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1539426664.320 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1539426664.320 * * * * [misc]progress: [ 85 / 104 ] simplifiying candidate # 1539426664.321 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1539426664.321 * * [misc]simplify: iters left: 6 (12 enodes) 1539426664.322 * * [misc]simplify: iters left: 5 (18 enodes) 1539426664.325 * * [misc]simplify: iters left: 4 (24 enodes) 1539426664.329 * * [misc]simplify: iters left: 3 (25 enodes) 1539426664.332 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1539426664.332 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1539426664.332 * * * * [misc]progress: [ 86 / 104 ] simplifiying candidate # 1539426664.332 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1539426664.332 * * [misc]simplify: iters left: 6 (11 enodes) 1539426664.334 * * [misc]simplify: iters left: 5 (17 enodes) 1539426664.336 * * [misc]simplify: iters left: 4 (23 enodes) 1539426664.339 * * [misc]simplify: iters left: 3 (24 enodes) 1539426664.342 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1539426664.342 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1539426664.342 * * * * [misc]progress: [ 87 / 104 ] simplifiying candidate # 1539426664.342 * [enter]simplify: Simplifying (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))) 1539426664.342 * * [misc]simplify: iters left: 6 (14 enodes) 1539426664.344 * * [misc]simplify: iters left: 5 (24 enodes) 1539426664.347 * * [misc]simplify: iters left: 4 (30 enodes) 1539426664.351 * * [misc]simplify: iters left: 3 (32 enodes) 1539426664.355 * [exit]simplify: Simplified to (/ (sqrt k) (* (pow (* 2 (* PI n)) (- (/ k 2))) (sqrt (* 2 (* PI n))))) 1539426664.355 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 1) (/ (sqrt k) (* (pow (* 2 (* PI n)) (- (/ k 2))) (sqrt (* 2 (* PI n))))))) 1539426664.355 * * * * [misc]progress: [ 88 / 104 ] simplifiying candidate # 1539426664.355 * [enter]simplify: Simplifying (/ 1 (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))) 1539426664.355 * * [misc]simplify: iters left: 6 (14 enodes) 1539426664.358 * * [misc]simplify: iters left: 5 (26 enodes) 1539426664.361 * * [misc]simplify: iters left: 4 (32 enodes) 1539426664.365 * * [misc]simplify: iters left: 3 (33 enodes) 1539426664.369 * [exit]simplify: Simplified to (/ (/ 1 (sqrt (* 2 (* n PI)))) (pow (* 2 (* n PI)) (- (/ k 2)))) 1539426664.369 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt k)) (/ (/ 1 (sqrt (* 2 (* n PI)))) (pow (* 2 (* n PI)) (- (/ k 2)))))) 1539426664.369 * * * * [misc]progress: [ 89 / 104 ] simplifiying candidate # 1539426664.369 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539426664.369 * * [misc]simplify: iters left: 5 (8 enodes) 1539426664.370 * * [misc]simplify: iters left: 4 (12 enodes) 1539426664.372 * * [misc]simplify: iters left: 3 (18 enodes) 1539426664.375 * * [misc]simplify: iters left: 2 (20 enodes) 1539426664.377 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539426664.377 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) 1/2))) (pow (* (* 2 n) PI) (/ k 2)))) 1539426664.377 * * * * [misc]progress: [ 90 / 104 ] simplifiying candidate # 1539426664.377 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539426664.377 * * [misc]simplify: iters left: 5 (8 enodes) 1539426664.378 * * [misc]simplify: iters left: 4 (12 enodes) 1539426664.381 * * [misc]simplify: iters left: 3 (18 enodes) 1539426664.386 * * [misc]simplify: iters left: 2 (20 enodes) 1539426664.391 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539426664.391 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) 1))) (pow (* (* 2 n) PI) (/ k 2)))) 1539426664.391 * * * * [misc]progress: [ 91 / 104 ] simplifiying candidate # 1539426664.391 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539426664.391 * * [misc]simplify: iters left: 5 (8 enodes) 1539426664.394 * * [misc]simplify: iters left: 4 (12 enodes) 1539426664.397 * * [misc]simplify: iters left: 3 (18 enodes) 1539426664.402 * * [misc]simplify: iters left: 2 (20 enodes) 1539426664.407 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539426664.407 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) 0)))) (pow (* (* 2 n) PI) (/ k 2)))) 1539426664.407 * * * * [misc]progress: [ 92 / 104 ] simplifiying candidate # 1539426664.407 * [enter]simplify: Simplifying (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) 1539426664.407 * * [misc]simplify: iters left: 6 (12 enodes) 1539426664.411 * * [misc]simplify: iters left: 5 (20 enodes) 1539426664.417 * * [misc]simplify: iters left: 4 (26 enodes) 1539426664.424 * * [misc]simplify: iters left: 3 (28 enodes) 1539426664.431 * [exit]simplify: Simplified to (* (pow (* (* 2 n) PI) (/ (- k) 2)) (sqrt (* (* 2 n) PI))) 1539426664.431 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 n) PI) (/ (- k) 2)) (sqrt (* (* 2 n) PI))))) 1539426664.431 * * * * [misc]progress: [ 93 / 104 ] simplifiying candidate # 1539426664.432 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426664.432 * * [misc]simplify: iters left: 4 (5 enodes) 1539426664.433 * * [misc]simplify: iters left: 3 (9 enodes) 1539426664.436 * * [misc]simplify: iters left: 2 (15 enodes) 1539426664.440 * * [misc]simplify: iters left: 1 (17 enodes) 1539426664.444 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426664.444 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1539426664.444 * * * * [misc]progress: [ 94 / 104 ] simplifiying candidate # 1539426664.444 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426664.444 * * [misc]simplify: iters left: 4 (5 enodes) 1539426664.445 * * [misc]simplify: iters left: 3 (9 enodes) 1539426664.446 * * [misc]simplify: iters left: 2 (15 enodes) 1539426664.448 * * [misc]simplify: iters left: 1 (17 enodes) 1539426664.450 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426664.450 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1539426664.450 * * * * [misc]progress: [ 95 / 104 ] simplifiying candidate # 1539426664.450 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426664.450 * * [misc]simplify: iters left: 4 (5 enodes) 1539426664.451 * * [misc]simplify: iters left: 3 (9 enodes) 1539426664.452 * * [misc]simplify: iters left: 2 (15 enodes) 1539426664.454 * * [misc]simplify: iters left: 1 (17 enodes) 1539426664.456 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426664.456 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1539426664.456 * * * * [misc]progress: [ 96 / 104 ] simplifiying candidate # 1539426664.456 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426664.456 * * [misc]simplify: iters left: 4 (5 enodes) 1539426664.457 * * [misc]simplify: iters left: 3 (9 enodes) 1539426664.458 * * [misc]simplify: iters left: 2 (15 enodes) 1539426664.460 * * [misc]simplify: iters left: 1 (17 enodes) 1539426664.462 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426664.462 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))))) 1539426664.462 * * * * [misc]progress: [ 97 / 104 ] simplifiying candidate # 1539426664.462 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426664.462 * * [misc]simplify: iters left: 4 (5 enodes) 1539426664.463 * * [misc]simplify: iters left: 3 (9 enodes) 1539426664.466 * * [misc]simplify: iters left: 2 (15 enodes) 1539426664.470 * * [misc]simplify: iters left: 1 (17 enodes) 1539426664.474 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426664.474 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))))) 1539426664.474 * * * * [misc]progress: [ 98 / 104 ] simplifiying candidate # 1539426664.474 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539426664.474 * * [misc]simplify: iters left: 4 (5 enodes) 1539426664.476 * * [misc]simplify: iters left: 3 (9 enodes) 1539426664.478 * * [misc]simplify: iters left: 2 (15 enodes) 1539426664.482 * * [misc]simplify: iters left: 1 (17 enodes) 1539426664.486 * [exit]simplify: Simplified to (* (* PI n) 2) 1539426664.486 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (- (/ k 2))))))) 1539426664.486 * * * * [misc]progress: [ 99 / 104 ] simplifiying candidate # 1539426664.486 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ k (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (* (pow (log n) 2) (pow k 3)) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (* (pow k 3) (pow (log (* 2 PI)) 2)) (* (sqrt 2) (* n PI)))) (- (* +nan.0 (/ (* (pow k 3) (* (log n) (log (* 2 PI)))) (* (sqrt 2) (* n PI))))))))))))))) 1539426664.487 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539426664.487 * * * * [misc]progress: [ 100 / 104 ] simplifiying candidate # 1539426664.487 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 3) (* (pow PI 3) (pow k 2))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI))))) (- (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 2) (* (pow PI 2) k))))))))))) 1539426664.487 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539426664.487 * * * * [misc]progress: [ 101 / 104 ] simplifiying candidate # 1539426664.487 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) n))) (- (+ (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI))) (- (* +nan.0 (/ 1 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (* PI k))))))))) 1539426664.487 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539426664.487 * * * * [misc]progress: [ 102 / 104 ] simplifiying candidate # 1539426664.488 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (pow (log n) 2) (pow k 2)))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (* n (* PI (pow k 2)))))) (- (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI (* (log n) (pow k 2)))))))))))))))))) 1539426664.488 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426664.488 * * * * [misc]progress: [ 103 / 104 ] simplifiying candidate # 1539426664.488 * [enter]simplify: Simplifying (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI))) k)) 1539426664.488 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426664.488 * * * * [misc]progress: [ 104 / 104 ] simplifiying candidate # 1539426664.488 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI)) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) PI) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow PI 2)) n))))))) 1539426664.488 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539426664.488 * * * [misc]progress: adding candidates to table 1539426665.833 * [misc]progress: [Phase 3 of 3] Extracting. 1539426665.833 * * [misc]regime: Finding splitpoints for: (# # # # # # # # #) 1539426665.838 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1539426665.838 * * * * [misc]regimes: Trying to branch on n from (# # # # # # # # #) 1539426665.936 * * * * [misc]regimes: Trying to branch on k from (# # # # # # # # #) 1539426665.997 * * * [misc]regime: Found split indices: #