1539342801.380 * [misc]progress: [Phase 1 of 3] Setting up. 1539342801.380 * * * [misc]progress: [1/2] Preparing points 1539342801.380 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1539342801.381 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision 1539342801.384 * * * * [misc]points: Setting MPFR precision to 64 1539342801.385 * * * * [misc]points: Setting MPFR precision to 320 1539342801.385 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision 1539342801.388 * * * * [misc]points: Setting MPFR precision to 64 1539342801.389 * * * * [misc]points: Setting MPFR precision to 320 1539342801.391 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision 1539342801.394 * * * * [misc]points: Setting MPFR precision to 64 1539342801.395 * * * * [misc]points: Setting MPFR precision to 320 1539342801.397 * * * * [misc]points: Setting MPFR precision to 576 1539342801.399 * * * * [misc]points: Setting MPFR precision to 832 1539342801.402 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.406 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision 1539342801.422 * * * * [misc]points: Setting MPFR precision to 832 1539342801.428 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.431 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.435 * * * * [misc]points: Computing exacts for 256 points 1539342801.455 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.465 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.475 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342801.475 * * * * [misc]points: Sampling 208 additional inputs, on iter 1 have 48 / 256 1539342801.476 * * * * [misc]points: Computing exacts on every 13 of 208 points to ramp up precision 1539342801.490 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.491 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.492 * * * * [misc]points: Computing exacts on every 6 of 208 points to ramp up precision 1539342801.528 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.530 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.533 * * * * [misc]points: Computing exacts on every 3 of 208 points to ramp up precision 1539342801.556 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.560 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.565 * * * * [misc]points: Computing exacts for 208 points 1539342801.593 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.610 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.628 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342801.629 * * * * [misc]points: Sampling 165 additional inputs, on iter 2 have 91 / 256 1539342801.630 * * * * [misc]points: Computing exacts on every 10 of 165 points to ramp up precision 1539342801.641 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.642 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.642 * * * * [misc]points: Computing exacts on every 5 of 165 points to ramp up precision 1539342801.659 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.661 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.663 * * * * [misc]points: Computing exacts on every 2 of 165 points to ramp up precision 1539342801.674 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.676 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.679 * * * * [misc]points: Computing exacts for 165 points 1539342801.689 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.707 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.720 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342801.720 * * * * [misc]points: Sampling 136 additional inputs, on iter 3 have 120 / 256 1539342801.721 * * * * [misc]points: Computing exacts on every 8 of 136 points to ramp up precision 1539342801.735 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.736 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.737 * * * * [misc]points: Computing exacts on every 4 of 136 points to ramp up precision 1539342801.747 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.748 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.749 * * * * [misc]points: Computing exacts on every 2 of 136 points to ramp up precision 1539342801.773 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.775 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.777 * * * * [misc]points: Computing exacts for 136 points 1539342801.788 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.794 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.801 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342801.801 * * * * [misc]points: Sampling 111 additional inputs, on iter 4 have 145 / 256 1539342801.802 * * * * [misc]points: Computing exacts on every 6 of 111 points to ramp up precision 1539342801.835 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.836 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.837 * * * * [misc]points: Computing exacts on every 3 of 111 points to ramp up precision 1539342801.848 * * * * [misc]points: Setting MPFR precision to 1088 1539342801.850 * * * * [misc]points: Setting MPFR precision to 1344 1539342801.851 * * * * [misc]points: Computing exacts for 111 points 1539342802.197 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.207 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.217 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.217 * * * * [misc]points: Sampling 92 additional inputs, on iter 5 have 164 / 256 1539342802.218 * * * * [misc]points: Computing exacts on every 5 of 92 points to ramp up precision 1539342802.241 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.242 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.243 * * * * [misc]points: Computing exacts on every 2 of 92 points to ramp up precision 1539342802.272 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.274 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.275 * * * * [misc]points: Computing exacts for 92 points 1539342802.286 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.291 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.295 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.295 * * * * [misc]points: Sampling 75 additional inputs, on iter 6 have 181 / 256 1539342802.296 * * * * [misc]points: Computing exacts on every 4 of 75 points to ramp up precision 1539342802.321 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.322 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.324 * * * * [misc]points: Computing exacts on every 2 of 75 points to ramp up precision 1539342802.347 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.349 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.352 * * * * [misc]points: Computing exacts for 75 points 1539342802.375 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.379 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.382 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.382 * * * * [misc]points: Sampling 60 additional inputs, on iter 7 have 196 / 256 1539342802.383 * * * * [misc]points: Computing exacts on every 3 of 60 points to ramp up precision 1539342802.405 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.406 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.407 * * * * [misc]points: Computing exacts for 60 points 1539342802.420 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.423 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.426 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.426 * * * * [misc]points: Sampling 42 additional inputs, on iter 8 have 214 / 256 1539342802.427 * * * * [misc]points: Computing exacts on every 2 of 42 points to ramp up precision 1539342802.444 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.445 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.447 * * * * [misc]points: Computing exacts for 42 points 1539342802.473 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.477 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.481 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.481 * * * * [misc]points: Sampling 35 additional inputs, on iter 9 have 221 / 256 1539342802.481 * * * * [misc]points: Computing exacts on every 2 of 35 points to ramp up precision 1539342802.510 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.511 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.512 * * * * [misc]points: Computing exacts for 35 points 1539342802.535 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.537 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.540 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.540 * * * * [misc]points: Sampling 28 additional inputs, on iter 10 have 228 / 256 1539342802.540 * * * * [misc]points: Computing exacts for 28 points 1539342802.568 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.570 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.573 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.573 * * * * [misc]points: Sampling 21 additional inputs, on iter 11 have 235 / 256 1539342802.573 * * * * [misc]points: Computing exacts for 21 points 1539342802.595 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.597 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.600 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.600 * * * * [misc]points: Sampling 13 additional inputs, on iter 12 have 243 / 256 1539342802.600 * * * * [misc]points: Computing exacts for 13 points 1539342802.627 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.628 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.629 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.629 * * * * [misc]points: Sampling 8 additional inputs, on iter 13 have 248 / 256 1539342802.630 * * * * [misc]points: Computing exacts for 8 points 1539342802.652 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.653 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.654 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.654 * * * * [misc]points: Sampling 8 additional inputs, on iter 14 have 248 / 256 1539342802.654 * * * * [misc]points: Computing exacts for 8 points 1539342802.677 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.678 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.678 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.679 * * * * [misc]points: Sampling 5 additional inputs, on iter 15 have 251 / 256 1539342802.679 * * * * [misc]points: Computing exacts for 5 points 1539342802.705 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.705 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.705 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.705 * * * * [misc]points: Sampling 5 additional inputs, on iter 16 have 251 / 256 1539342802.705 * * * * [misc]points: Computing exacts for 5 points 1539342802.716 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.716 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.717 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.717 * * * * [misc]points: Sampling 4 additional inputs, on iter 17 have 253 / 256 1539342802.717 * * * * [misc]points: Computing exacts for 4 points 1539342802.729 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.730 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.730 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.730 * * * * [misc]points: Sampling 4 additional inputs, on iter 18 have 255 / 256 1539342802.730 * * * * [misc]points: Computing exacts for 4 points 1539342802.747 * * * * [misc]points: Setting MPFR precision to 1088 1539342802.747 * * * * [misc]points: Setting MPFR precision to 1344 1539342802.747 * * * * [misc]points: Filtering points with unrepresentable outputs 1539342802.748 * * * * [exit]points: Sampled 256 points with exact outputs 1539342802.748 * * * [misc]progress: [2/2] Setting up program. 1539342802.753 * [misc]progress: [Phase 2 of 3] Improving. 1539342802.754 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1539342802.754 * * [misc]simplify: iters left: 6 (13 enodes) 1539342802.759 * * [misc]simplify: iters left: 5 (28 enodes) 1539342802.767 * * [misc]simplify: iters left: 4 (44 enodes) 1539342802.779 * * [misc]simplify: iters left: 3 (54 enodes) 1539342802.791 * * [misc]simplify: iters left: 2 (57 enodes) 1539342802.805 * * [misc]simplify: iters left: 1 (65 enodes) 1539342802.820 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1539342802.828 * * [misc]progress: iteration 1 / 4 1539342802.828 * * * [misc]progress: picking best candidate 1539342802.833 * * * * [misc]pick: Picked # 1539342802.833 * * * [misc]progress: localizing error 1539342802.866 * * * [misc]progress: generating rewritten candidates 1539342802.867 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1 1) 1539342802.871 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1) 1539342802.878 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1539342802.893 * * * [misc]progress: generating series expansions 1539342802.893 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1 1) 1539342802.893 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539342802.893 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539342802.893 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342802.893 * [misc]taylor: Taking taylor expansion of 2 in n 1539342802.893 * [misc]backup-simplify: Simplify 2 into 2 1539342802.893 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342802.893 * [misc]taylor: Taking taylor expansion of n in n 1539342802.893 * [misc]backup-simplify: Simplify 0 into 0 1539342802.893 * [misc]backup-simplify: Simplify 1 into 1 1539342802.893 * [misc]taylor: Taking taylor expansion of PI in n 1539342802.893 * [misc]backup-simplify: Simplify PI into PI 1539342802.893 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342802.893 * [misc]taylor: Taking taylor expansion of 2 in n 1539342802.893 * [misc]backup-simplify: Simplify 2 into 2 1539342802.893 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342802.893 * [misc]taylor: Taking taylor expansion of n in n 1539342802.893 * [misc]backup-simplify: Simplify 0 into 0 1539342802.893 * [misc]backup-simplify: Simplify 1 into 1 1539342802.893 * [misc]taylor: Taking taylor expansion of PI in n 1539342802.893 * [misc]backup-simplify: Simplify PI into PI 1539342802.894 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342802.894 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342802.894 * [misc]backup-simplify: Simplify 0 into 0 1539342802.895 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342802.896 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342802.896 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342802.897 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342802.898 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342802.898 * [misc]backup-simplify: Simplify 0 into 0 1539342802.900 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342802.902 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342802.902 * [misc]backup-simplify: Simplify 0 into 0 1539342802.904 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342802.906 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342802.906 * [misc]backup-simplify: Simplify 0 into 0 1539342802.908 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342802.911 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539342802.911 * [misc]backup-simplify: Simplify 0 into 0 1539342802.914 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342802.918 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539342802.918 * [misc]backup-simplify: Simplify 0 into 0 1539342802.928 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539342802.931 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539342802.932 * [misc]backup-simplify: Simplify 0 into 0 1539342802.932 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539342802.932 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539342802.932 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539342802.932 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342802.932 * [misc]taylor: Taking taylor expansion of 2 in n 1539342802.932 * [misc]backup-simplify: Simplify 2 into 2 1539342802.932 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342802.932 * [misc]taylor: Taking taylor expansion of PI in n 1539342802.932 * [misc]backup-simplify: Simplify PI into PI 1539342802.932 * [misc]taylor: Taking taylor expansion of n in n 1539342802.932 * [misc]backup-simplify: Simplify 0 into 0 1539342802.932 * [misc]backup-simplify: Simplify 1 into 1 1539342802.932 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342802.932 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342802.932 * [misc]taylor: Taking taylor expansion of 2 in n 1539342802.932 * [misc]backup-simplify: Simplify 2 into 2 1539342802.932 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342802.932 * [misc]taylor: Taking taylor expansion of PI in n 1539342802.932 * [misc]backup-simplify: Simplify PI into PI 1539342802.933 * [misc]taylor: Taking taylor expansion of n in n 1539342802.933 * [misc]backup-simplify: Simplify 0 into 0 1539342802.933 * [misc]backup-simplify: Simplify 1 into 1 1539342802.933 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342802.933 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342802.933 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342802.934 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342802.934 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342802.934 * [misc]backup-simplify: Simplify 0 into 0 1539342802.935 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342802.936 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342802.936 * [misc]backup-simplify: Simplify 0 into 0 1539342802.937 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342802.937 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342802.937 * [misc]backup-simplify: Simplify 0 into 0 1539342802.938 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342802.940 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342802.940 * [misc]backup-simplify: Simplify 0 into 0 1539342802.941 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342802.943 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342802.943 * [misc]backup-simplify: Simplify 0 into 0 1539342802.944 * [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 1539342802.946 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342802.946 * [misc]backup-simplify: Simplify 0 into 0 1539342802.946 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539342802.947 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539342802.947 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539342802.947 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342802.947 * [misc]taylor: Taking taylor expansion of -2 in n 1539342802.947 * [misc]backup-simplify: Simplify -2 into -2 1539342802.947 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342802.947 * [misc]taylor: Taking taylor expansion of PI in n 1539342802.947 * [misc]backup-simplify: Simplify PI into PI 1539342802.947 * [misc]taylor: Taking taylor expansion of n in n 1539342802.947 * [misc]backup-simplify: Simplify 0 into 0 1539342802.947 * [misc]backup-simplify: Simplify 1 into 1 1539342802.947 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342802.947 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342802.947 * [misc]taylor: Taking taylor expansion of -2 in n 1539342802.947 * [misc]backup-simplify: Simplify -2 into -2 1539342802.947 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342802.947 * [misc]taylor: Taking taylor expansion of PI in n 1539342802.947 * [misc]backup-simplify: Simplify PI into PI 1539342802.947 * [misc]taylor: Taking taylor expansion of n in n 1539342802.947 * [misc]backup-simplify: Simplify 0 into 0 1539342802.947 * [misc]backup-simplify: Simplify 1 into 1 1539342802.947 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342802.947 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342802.948 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342802.948 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342802.949 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342802.949 * [misc]backup-simplify: Simplify 0 into 0 1539342802.949 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342802.950 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342802.950 * [misc]backup-simplify: Simplify 0 into 0 1539342802.951 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342802.952 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342802.952 * [misc]backup-simplify: Simplify 0 into 0 1539342802.953 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342802.954 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342802.954 * [misc]backup-simplify: Simplify 0 into 0 1539342802.955 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342802.957 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342802.957 * [misc]backup-simplify: Simplify 0 into 0 1539342802.958 * [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 1539342802.960 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342802.960 * [misc]backup-simplify: Simplify 0 into 0 1539342802.961 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539342802.961 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1) 1539342802.961 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1539342802.961 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1539342802.961 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1539342802.961 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539342802.961 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539342802.961 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1539342802.961 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342802.961 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342802.961 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342802.961 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342802.961 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342802.961 * [misc]taylor: Taking taylor expansion of k in k 1539342802.961 * [misc]backup-simplify: Simplify 0 into 0 1539342802.961 * [misc]backup-simplify: Simplify 1 into 1 1539342802.961 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539342802.961 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539342802.961 * [misc]taylor: Taking taylor expansion of 2 in k 1539342802.961 * [misc]backup-simplify: Simplify 2 into 2 1539342802.961 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342802.961 * [misc]taylor: Taking taylor expansion of n in k 1539342802.961 * [misc]backup-simplify: Simplify n into n 1539342802.961 * [misc]taylor: Taking taylor expansion of PI in k 1539342802.961 * [misc]backup-simplify: Simplify PI into PI 1539342802.961 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342802.961 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539342802.961 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539342802.961 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342802.961 * [misc]backup-simplify: Simplify (- 0) into 0 1539342802.962 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539342802.962 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1539342802.962 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1539342802.962 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1539342802.962 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539342802.962 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539342802.962 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1539342802.962 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342802.962 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342802.962 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342802.962 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342802.962 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342802.962 * [misc]taylor: Taking taylor expansion of k in n 1539342802.962 * [misc]backup-simplify: Simplify k into k 1539342802.962 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342802.962 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342802.962 * [misc]taylor: Taking taylor expansion of 2 in n 1539342802.962 * [misc]backup-simplify: Simplify 2 into 2 1539342802.962 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342802.962 * [misc]taylor: Taking taylor expansion of n in n 1539342802.962 * [misc]backup-simplify: Simplify 0 into 0 1539342802.962 * [misc]backup-simplify: Simplify 1 into 1 1539342802.962 * [misc]taylor: Taking taylor expansion of PI in n 1539342802.962 * [misc]backup-simplify: Simplify PI into PI 1539342802.962 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342802.963 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342802.963 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342802.963 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342802.964 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342802.964 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342802.964 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539342802.964 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1539342802.965 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342802.966 * [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)))) 1539342802.966 * [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))))) 1539342802.966 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1539342802.966 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539342802.966 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539342802.966 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1539342802.966 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342802.966 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342802.966 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342802.966 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342802.966 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342802.966 * [misc]taylor: Taking taylor expansion of k in n 1539342802.966 * [misc]backup-simplify: Simplify k into k 1539342802.967 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342802.967 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342802.967 * [misc]taylor: Taking taylor expansion of 2 in n 1539342802.967 * [misc]backup-simplify: Simplify 2 into 2 1539342802.967 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342802.967 * [misc]taylor: Taking taylor expansion of n in n 1539342802.967 * [misc]backup-simplify: Simplify 0 into 0 1539342802.967 * [misc]backup-simplify: Simplify 1 into 1 1539342802.967 * [misc]taylor: Taking taylor expansion of PI in n 1539342802.967 * [misc]backup-simplify: Simplify PI into PI 1539342802.967 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342802.967 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342802.968 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342802.968 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342802.969 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342802.969 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342802.969 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539342802.969 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1539342802.970 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342802.970 * [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)))) 1539342802.971 * [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))))) 1539342802.971 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1539342802.971 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1539342802.971 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1539342802.971 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342802.971 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342802.971 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342802.971 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342802.971 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342802.971 * [misc]taylor: Taking taylor expansion of k in k 1539342802.971 * [misc]backup-simplify: Simplify 0 into 0 1539342802.971 * [misc]backup-simplify: Simplify 1 into 1 1539342802.971 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539342802.971 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342802.972 * [misc]taylor: Taking taylor expansion of n in k 1539342802.972 * [misc]backup-simplify: Simplify n into n 1539342802.972 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342802.972 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342802.972 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342802.972 * [misc]taylor: Taking taylor expansion of 2 in k 1539342802.972 * [misc]backup-simplify: Simplify 2 into 2 1539342802.972 * [misc]taylor: Taking taylor expansion of PI in k 1539342802.972 * [misc]backup-simplify: Simplify PI into PI 1539342802.972 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342802.973 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342802.973 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342802.973 * [misc]backup-simplify: Simplify (- 0) into 0 1539342802.973 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539342802.974 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342802.974 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1539342802.975 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539342802.975 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539342802.977 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342802.978 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342802.980 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342802.981 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1539342802.981 * [misc]backup-simplify: Simplify (- 0) into 0 1539342802.981 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342802.982 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342802.982 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539342802.984 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342802.984 * [misc]taylor: Taking taylor expansion of 0 in k 1539342802.984 * [misc]backup-simplify: Simplify 0 into 0 1539342802.984 * [misc]backup-simplify: Simplify 0 into 0 1539342802.985 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539342802.985 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342802.988 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342802.988 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342802.988 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539342802.988 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539342802.988 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539342802.989 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1539342802.989 * [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))))))) 1539342802.990 * [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))))))) 1539342802.992 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342802.993 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342802.996 * [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 1539342802.996 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1539342802.996 * [misc]backup-simplify: Simplify (- 0) into 0 1539342802.996 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342802.997 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342802.997 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539342802.999 * [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 1539342802.999 * [misc]taylor: Taking taylor expansion of 0 in k 1539342802.999 * [misc]backup-simplify: Simplify 0 into 0 1539342802.999 * [misc]backup-simplify: Simplify 0 into 0 1539342802.999 * [misc]backup-simplify: Simplify 0 into 0 1539342803.000 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1539342803.000 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342803.003 * [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 1539342803.003 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.003 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1539342803.004 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.004 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.004 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539342803.005 * [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))))) 1539342803.007 * [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))))) 1539342803.010 * [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))))) 1539342803.010 * [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)))) 1539342803.010 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1539342803.010 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.011 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.011 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.011 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.011 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of k in k 1539342803.011 * [misc]backup-simplify: Simplify 0 into 0 1539342803.011 * [misc]backup-simplify: Simplify 1 into 1 1539342803.011 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.011 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of 2 in k 1539342803.011 * [misc]backup-simplify: Simplify 2 into 2 1539342803.011 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342803.011 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.011 * [misc]backup-simplify: Simplify PI into PI 1539342803.011 * [misc]taylor: Taking taylor expansion of n in k 1539342803.011 * [misc]backup-simplify: Simplify n into n 1539342803.011 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342803.011 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539342803.011 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539342803.011 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539342803.011 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539342803.011 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539342803.011 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539342803.012 * [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)))) 1539342803.012 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.012 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.012 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.012 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.012 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of k in n 1539342803.012 * [misc]backup-simplify: Simplify k into k 1539342803.012 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.012 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of 2 in n 1539342803.012 * [misc]backup-simplify: Simplify 2 into 2 1539342803.012 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342803.012 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.012 * [misc]backup-simplify: Simplify PI into PI 1539342803.012 * [misc]taylor: Taking taylor expansion of n in n 1539342803.012 * [misc]backup-simplify: Simplify 0 into 0 1539342803.012 * [misc]backup-simplify: Simplify 1 into 1 1539342803.012 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342803.012 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342803.013 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.013 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539342803.013 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539342803.013 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1539342803.013 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.014 * [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))) 1539342803.014 * [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)))) 1539342803.014 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.014 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.014 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.014 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.014 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of k in n 1539342803.014 * [misc]backup-simplify: Simplify k into k 1539342803.014 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.014 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of 2 in n 1539342803.014 * [misc]backup-simplify: Simplify 2 into 2 1539342803.014 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342803.014 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.014 * [misc]backup-simplify: Simplify PI into PI 1539342803.014 * [misc]taylor: Taking taylor expansion of n in n 1539342803.014 * [misc]backup-simplify: Simplify 0 into 0 1539342803.014 * [misc]backup-simplify: Simplify 1 into 1 1539342803.015 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342803.015 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342803.015 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.015 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539342803.015 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539342803.015 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1539342803.016 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.016 * [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))) 1539342803.016 * [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)))) 1539342803.017 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.017 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.017 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.017 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.017 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of k in k 1539342803.017 * [misc]backup-simplify: Simplify 0 into 0 1539342803.017 * [misc]backup-simplify: Simplify 1 into 1 1539342803.017 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.017 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of 2 in k 1539342803.017 * [misc]backup-simplify: Simplify 2 into 2 1539342803.017 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.017 * [misc]backup-simplify: Simplify PI into PI 1539342803.017 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342803.017 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.017 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342803.017 * [misc]taylor: Taking taylor expansion of n in k 1539342803.017 * [misc]backup-simplify: Simplify n into n 1539342803.017 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342803.018 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539342803.018 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539342803.018 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539342803.018 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342803.018 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342803.018 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539342803.019 * [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)))) 1539342803.019 * [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)))) 1539342803.020 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342803.020 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342803.022 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342803.022 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539342803.022 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539342803.022 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.022 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.023 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.023 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539342803.025 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342803.025 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.025 * [misc]backup-simplify: Simplify 0 into 0 1539342803.025 * [misc]backup-simplify: Simplify 0 into 0 1539342803.025 * [misc]backup-simplify: Simplify 0 into 0 1539342803.025 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.026 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342803.029 * [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 1539342803.029 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.029 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539342803.029 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.030 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.030 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.030 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539342803.032 * [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 1539342803.032 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.032 * [misc]backup-simplify: Simplify 0 into 0 1539342803.032 * [misc]backup-simplify: Simplify 0 into 0 1539342803.032 * [misc]backup-simplify: Simplify 0 into 0 1539342803.032 * [misc]backup-simplify: Simplify 0 into 0 1539342803.033 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.034 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342803.041 * [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 1539342803.041 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.041 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1539342803.041 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.041 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.042 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.042 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539342803.046 * [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 1539342803.046 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.046 * [misc]backup-simplify: Simplify 0 into 0 1539342803.047 * [misc]backup-simplify: Simplify 0 into 0 1539342803.047 * [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))))) 1539342803.048 * [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)) 1539342803.048 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1539342803.048 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.048 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.048 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of k in k 1539342803.048 * [misc]backup-simplify: Simplify 0 into 0 1539342803.048 * [misc]backup-simplify: Simplify 1 into 1 1539342803.048 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.048 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.048 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.048 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of -2 in k 1539342803.048 * [misc]backup-simplify: Simplify -2 into -2 1539342803.048 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342803.048 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.048 * [misc]backup-simplify: Simplify PI into PI 1539342803.049 * [misc]taylor: Taking taylor expansion of n in k 1539342803.049 * [misc]backup-simplify: Simplify n into n 1539342803.049 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342803.049 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342803.049 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539342803.049 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539342803.049 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539342803.049 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539342803.049 * [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))) 1539342803.049 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.050 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.050 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of k in n 1539342803.050 * [misc]backup-simplify: Simplify k into k 1539342803.050 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.050 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.050 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.050 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of -2 in n 1539342803.050 * [misc]backup-simplify: Simplify -2 into -2 1539342803.050 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342803.050 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.050 * [misc]backup-simplify: Simplify PI into PI 1539342803.050 * [misc]taylor: Taking taylor expansion of n in n 1539342803.050 * [misc]backup-simplify: Simplify 0 into 0 1539342803.050 * [misc]backup-simplify: Simplify 1 into 1 1539342803.051 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342803.051 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342803.051 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342803.051 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539342803.051 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1539342803.052 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.053 * [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))) 1539342803.053 * [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)))) 1539342803.053 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1539342803.053 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1539342803.053 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1539342803.053 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1539342803.053 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539342803.053 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.053 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.054 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.054 * [misc]taylor: Taking taylor expansion of k in n 1539342803.054 * [misc]backup-simplify: Simplify k into k 1539342803.054 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.054 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.054 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.054 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342803.054 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342803.054 * [misc]taylor: Taking taylor expansion of -2 in n 1539342803.054 * [misc]backup-simplify: Simplify -2 into -2 1539342803.054 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342803.054 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.054 * [misc]backup-simplify: Simplify PI into PI 1539342803.054 * [misc]taylor: Taking taylor expansion of n in n 1539342803.054 * [misc]backup-simplify: Simplify 0 into 0 1539342803.054 * [misc]backup-simplify: Simplify 1 into 1 1539342803.054 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342803.054 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342803.055 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342803.055 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539342803.055 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1539342803.056 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.056 * [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))) 1539342803.057 * [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)))) 1539342803.057 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1539342803.057 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1539342803.057 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1539342803.057 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539342803.057 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.057 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.057 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.057 * [misc]taylor: Taking taylor expansion of k in k 1539342803.057 * [misc]backup-simplify: Simplify 0 into 0 1539342803.057 * [misc]backup-simplify: Simplify 1 into 1 1539342803.058 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.058 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.058 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.058 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539342803.058 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539342803.058 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539342803.058 * [misc]taylor: Taking taylor expansion of -2 in k 1539342803.058 * [misc]backup-simplify: Simplify -2 into -2 1539342803.058 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.058 * [misc]backup-simplify: Simplify PI into PI 1539342803.058 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342803.059 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342803.059 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342803.059 * [misc]taylor: Taking taylor expansion of n in k 1539342803.059 * [misc]backup-simplify: Simplify n into n 1539342803.059 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342803.059 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539342803.059 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539342803.059 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342803.060 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539342803.060 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539342803.061 * [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)))) 1539342803.061 * [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)))) 1539342803.062 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342803.063 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342803.066 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539342803.066 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539342803.066 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539342803.066 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.067 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.068 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539342803.069 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342803.069 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.069 * [misc]backup-simplify: Simplify 0 into 0 1539342803.069 * [misc]backup-simplify: Simplify 0 into 0 1539342803.070 * [misc]backup-simplify: Simplify 0 into 0 1539342803.071 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.072 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342803.077 * [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 1539342803.077 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.078 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539342803.078 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.078 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.079 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1539342803.082 * [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 1539342803.082 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.082 * [misc]backup-simplify: Simplify 0 into 0 1539342803.082 * [misc]backup-simplify: Simplify 0 into 0 1539342803.082 * [misc]backup-simplify: Simplify 0 into 0 1539342803.082 * [misc]backup-simplify: Simplify 0 into 0 1539342803.084 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.085 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342803.093 * [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 1539342803.093 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.094 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1539342803.094 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.095 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.096 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1539342803.099 * [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 1539342803.099 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.100 * [misc]backup-simplify: Simplify 0 into 0 1539342803.100 * [misc]backup-simplify: Simplify 0 into 0 1539342803.100 * [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))))) 1539342803.100 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1539342803.101 * [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)))) 1539342803.101 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1539342803.101 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1539342803.101 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1539342803.101 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.101 * [misc]taylor: Taking taylor expansion of k in k 1539342803.101 * [misc]backup-simplify: Simplify 0 into 0 1539342803.101 * [misc]backup-simplify: Simplify 1 into 1 1539342803.101 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.102 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342803.102 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1539342803.102 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1539342803.102 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1539342803.102 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1539342803.102 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1539342803.103 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.103 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.103 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342803.103 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.103 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.103 * [misc]taylor: Taking taylor expansion of k in k 1539342803.103 * [misc]backup-simplify: Simplify 0 into 0 1539342803.103 * [misc]backup-simplify: Simplify 1 into 1 1539342803.103 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539342803.103 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539342803.103 * [misc]taylor: Taking taylor expansion of 2 in k 1539342803.103 * [misc]backup-simplify: Simplify 2 into 2 1539342803.103 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342803.103 * [misc]taylor: Taking taylor expansion of n in k 1539342803.103 * [misc]backup-simplify: Simplify n into n 1539342803.103 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.103 * [misc]backup-simplify: Simplify PI into PI 1539342803.103 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342803.103 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539342803.103 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539342803.103 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342803.104 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.104 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539342803.104 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1539342803.104 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1539342803.104 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1539342803.104 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1539342803.104 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.104 * [misc]taylor: Taking taylor expansion of k in n 1539342803.104 * [misc]backup-simplify: Simplify k into k 1539342803.104 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.104 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1539342803.104 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539342803.104 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1539342803.104 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1539342803.104 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539342803.105 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539342803.105 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1539342803.105 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.105 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.105 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342803.105 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.105 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.105 * [misc]taylor: Taking taylor expansion of k in n 1539342803.105 * [misc]backup-simplify: Simplify k into k 1539342803.105 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342803.105 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342803.105 * [misc]taylor: Taking taylor expansion of 2 in n 1539342803.105 * [misc]backup-simplify: Simplify 2 into 2 1539342803.105 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342803.105 * [misc]taylor: Taking taylor expansion of n in n 1539342803.105 * [misc]backup-simplify: Simplify 0 into 0 1539342803.105 * [misc]backup-simplify: Simplify 1 into 1 1539342803.105 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.105 * [misc]backup-simplify: Simplify PI into PI 1539342803.105 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342803.105 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342803.106 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342803.107 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342803.107 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.107 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342803.107 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539342803.107 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1539342803.108 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342803.109 * [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)))) 1539342803.109 * [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))))) 1539342803.109 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1539342803.109 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1539342803.109 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.109 * [misc]taylor: Taking taylor expansion of k in n 1539342803.109 * [misc]backup-simplify: Simplify k into k 1539342803.109 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.110 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1539342803.110 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539342803.110 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1539342803.110 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1539342803.110 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1539342803.110 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1539342803.110 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1539342803.110 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.110 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.110 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342803.110 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.110 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.110 * [misc]taylor: Taking taylor expansion of k in n 1539342803.110 * [misc]backup-simplify: Simplify k into k 1539342803.110 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342803.110 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342803.110 * [misc]taylor: Taking taylor expansion of 2 in n 1539342803.110 * [misc]backup-simplify: Simplify 2 into 2 1539342803.110 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342803.110 * [misc]taylor: Taking taylor expansion of n in n 1539342803.110 * [misc]backup-simplify: Simplify 0 into 0 1539342803.110 * [misc]backup-simplify: Simplify 1 into 1 1539342803.110 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.110 * [misc]backup-simplify: Simplify PI into PI 1539342803.111 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342803.111 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342803.111 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342803.112 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342803.112 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.113 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342803.113 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1539342803.113 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1539342803.113 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342803.114 * [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)))) 1539342803.115 * [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))))) 1539342803.115 * [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))) 1539342803.115 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.116 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.116 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.116 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.116 * [misc]taylor: Taking taylor expansion of k in k 1539342803.116 * [misc]backup-simplify: Simplify 0 into 0 1539342803.116 * [misc]backup-simplify: Simplify 1 into 1 1539342803.116 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of n in k 1539342803.116 * [misc]backup-simplify: Simplify n into n 1539342803.116 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342803.116 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342803.116 * [misc]taylor: Taking taylor expansion of 2 in k 1539342803.116 * [misc]backup-simplify: Simplify 2 into 2 1539342803.116 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.116 * [misc]backup-simplify: Simplify PI into PI 1539342803.116 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342803.117 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.117 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342803.117 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.117 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539342803.118 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342803.118 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1539342803.119 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1539342803.119 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1539342803.119 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.119 * [misc]taylor: Taking taylor expansion of k in k 1539342803.119 * [misc]backup-simplify: Simplify 0 into 0 1539342803.119 * [misc]backup-simplify: Simplify 1 into 1 1539342803.119 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.119 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342803.120 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1539342803.120 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1539342803.120 * [misc]backup-simplify: Simplify 0 into 0 1539342803.121 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342803.122 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342803.125 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342803.125 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1539342803.126 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.126 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.126 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342803.127 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539342803.129 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342803.129 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1539342803.129 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.130 * [misc]backup-simplify: Simplify 0 into 0 1539342803.130 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539342803.131 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342803.134 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342803.134 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.134 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539342803.134 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539342803.134 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539342803.135 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1539342803.137 * [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))))))) 1539342803.139 * [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))))))) 1539342803.139 * [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))))))) 1539342803.141 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342803.142 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342803.148 * [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 1539342803.148 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1539342803.148 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.148 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.149 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342803.150 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539342803.152 * [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 1539342803.153 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.154 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1539342803.154 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1539342803.154 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.154 * [misc]backup-simplify: Simplify 0 into 0 1539342803.154 * [misc]backup-simplify: Simplify 0 into 0 1539342803.155 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1539342803.156 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539342803.157 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1539342803.159 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342803.164 * [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 1539342803.164 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.164 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1539342803.164 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.164 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.165 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539342803.168 * [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))))) 1539342803.172 * [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)))))))) 1539342803.175 * [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)))))))) 1539342803.177 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342803.179 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342803.185 * [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 1539342803.186 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1539342803.186 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.186 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.186 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342803.187 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1539342803.189 * [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 1539342803.189 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.189 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1539342803.190 * [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 1539342803.190 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.190 * [misc]backup-simplify: Simplify 0 into 0 1539342803.190 * [misc]backup-simplify: Simplify 0 into 0 1539342803.190 * [misc]backup-simplify: Simplify 0 into 0 1539342803.190 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.191 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1539342803.194 * [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 1539342803.195 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342803.200 * [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 1539342803.200 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.200 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539342803.200 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.200 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.201 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1539342803.203 * [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))))))) 1539342803.208 * [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)))))))))))))) 1539342803.213 * [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)))))))))))))) 1539342803.224 * [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)))))))))))))))))))))) 1539342803.225 * [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))))) 1539342803.225 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1539342803.225 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1539342803.225 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1539342803.225 * [misc]taylor: Taking taylor expansion of k in k 1539342803.225 * [misc]backup-simplify: Simplify 0 into 0 1539342803.225 * [misc]backup-simplify: Simplify 1 into 1 1539342803.225 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342803.226 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1539342803.226 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1539342803.226 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1539342803.226 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1539342803.226 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1539342803.226 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.226 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.226 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539342803.226 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.226 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.226 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.226 * [misc]taylor: Taking taylor expansion of k in k 1539342803.226 * [misc]backup-simplify: Simplify 0 into 0 1539342803.226 * [misc]backup-simplify: Simplify 1 into 1 1539342803.226 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.226 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539342803.226 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539342803.226 * [misc]taylor: Taking taylor expansion of 2 in k 1539342803.226 * [misc]backup-simplify: Simplify 2 into 2 1539342803.226 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342803.227 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.227 * [misc]backup-simplify: Simplify PI into PI 1539342803.227 * [misc]taylor: Taking taylor expansion of n in k 1539342803.227 * [misc]backup-simplify: Simplify n into n 1539342803.227 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342803.227 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539342803.227 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539342803.227 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539342803.227 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539342803.227 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539342803.227 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1539342803.228 * [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)))) 1539342803.228 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1539342803.228 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1539342803.228 * [misc]taylor: Taking taylor expansion of k in n 1539342803.228 * [misc]backup-simplify: Simplify k into k 1539342803.228 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1539342803.228 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1539342803.228 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1539342803.228 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539342803.228 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539342803.228 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1539342803.228 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.228 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.228 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539342803.228 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.228 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.228 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.229 * [misc]taylor: Taking taylor expansion of k in n 1539342803.229 * [misc]backup-simplify: Simplify k into k 1539342803.229 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.229 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342803.229 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342803.229 * [misc]taylor: Taking taylor expansion of 2 in n 1539342803.229 * [misc]backup-simplify: Simplify 2 into 2 1539342803.229 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342803.229 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.229 * [misc]backup-simplify: Simplify PI into PI 1539342803.229 * [misc]taylor: Taking taylor expansion of n in n 1539342803.229 * [misc]backup-simplify: Simplify 0 into 0 1539342803.229 * [misc]backup-simplify: Simplify 1 into 1 1539342803.230 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342803.230 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342803.231 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.231 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539342803.231 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539342803.231 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1539342803.232 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.232 * [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))) 1539342803.233 * [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)))) 1539342803.233 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1539342803.233 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1539342803.233 * [misc]taylor: Taking taylor expansion of k in n 1539342803.233 * [misc]backup-simplify: Simplify k into k 1539342803.233 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1539342803.233 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1539342803.233 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1539342803.233 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1539342803.233 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1539342803.233 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1539342803.233 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.233 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.233 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539342803.233 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.233 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.233 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.233 * [misc]taylor: Taking taylor expansion of k in n 1539342803.233 * [misc]backup-simplify: Simplify k into k 1539342803.234 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.234 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342803.234 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342803.234 * [misc]taylor: Taking taylor expansion of 2 in n 1539342803.234 * [misc]backup-simplify: Simplify 2 into 2 1539342803.234 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342803.234 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.234 * [misc]backup-simplify: Simplify PI into PI 1539342803.234 * [misc]taylor: Taking taylor expansion of n in n 1539342803.234 * [misc]backup-simplify: Simplify 0 into 0 1539342803.234 * [misc]backup-simplify: Simplify 1 into 1 1539342803.234 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342803.234 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342803.235 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.235 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539342803.235 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1539342803.235 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1539342803.236 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.236 * [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))) 1539342803.237 * [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)))) 1539342803.238 * [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)) 1539342803.238 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1539342803.238 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1539342803.238 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1539342803.238 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1539342803.238 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.238 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.238 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539342803.238 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.238 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.238 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.238 * [misc]taylor: Taking taylor expansion of k in k 1539342803.238 * [misc]backup-simplify: Simplify 0 into 0 1539342803.238 * [misc]backup-simplify: Simplify 1 into 1 1539342803.238 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.238 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342803.238 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342803.239 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342803.239 * [misc]taylor: Taking taylor expansion of 2 in k 1539342803.239 * [misc]backup-simplify: Simplify 2 into 2 1539342803.239 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.239 * [misc]backup-simplify: Simplify PI into PI 1539342803.239 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342803.239 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342803.239 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342803.239 * [misc]taylor: Taking taylor expansion of n in k 1539342803.239 * [misc]backup-simplify: Simplify n into n 1539342803.240 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342803.240 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539342803.240 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1539342803.240 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1539342803.240 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342803.241 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342803.241 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1539342803.242 * [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)))) 1539342803.242 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1539342803.242 * [misc]taylor: Taking taylor expansion of k in k 1539342803.242 * [misc]backup-simplify: Simplify 0 into 0 1539342803.242 * [misc]backup-simplify: Simplify 1 into 1 1539342803.242 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342803.242 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1539342803.243 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1539342803.243 * [misc]backup-simplify: Simplify 0 into 0 1539342803.245 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342803.245 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342803.248 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342803.248 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539342803.249 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539342803.249 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.249 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.249 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.250 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539342803.252 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342803.252 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1539342803.252 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.252 * [misc]backup-simplify: Simplify 0 into 0 1539342803.252 * [misc]backup-simplify: Simplify 0 into 0 1539342803.253 * [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)))))) 1539342803.254 * [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)))))) 1539342803.256 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.257 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342803.262 * [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 1539342803.262 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.262 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539342803.263 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.263 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.263 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.264 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539342803.267 * [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 1539342803.267 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1539342803.268 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1539342803.268 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.268 * [misc]backup-simplify: Simplify 0 into 0 1539342803.268 * [misc]backup-simplify: Simplify 0 into 0 1539342803.268 * [misc]backup-simplify: Simplify 0 into 0 1539342803.269 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539342803.270 * [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)))))) 1539342803.271 * [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)))))) 1539342803.273 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.274 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342803.283 * [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 1539342803.283 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.283 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1539342803.283 * [misc]backup-simplify: Simplify (- 0) into 0 1539342803.284 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.284 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342803.285 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539342803.289 * [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 1539342803.289 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1539342803.290 * [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 1539342803.290 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.291 * [misc]backup-simplify: Simplify 0 into 0 1539342803.291 * [misc]backup-simplify: Simplify 0 into 0 1539342803.291 * [misc]backup-simplify: Simplify 0 into 0 1539342803.291 * [misc]backup-simplify: Simplify 0 into 0 1539342803.292 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1539342803.293 * [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)))))) 1539342803.293 * [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)))))) 1539342803.296 * [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)))))))) 1539342803.296 * [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))) 1539342803.297 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1539342803.297 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.297 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.297 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of k in k 1539342803.297 * [misc]backup-simplify: Simplify 0 into 0 1539342803.297 * [misc]backup-simplify: Simplify 1 into 1 1539342803.297 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.297 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.297 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.297 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of -2 in k 1539342803.297 * [misc]backup-simplify: Simplify -2 into -2 1539342803.297 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342803.297 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.297 * [misc]backup-simplify: Simplify PI into PI 1539342803.297 * [misc]taylor: Taking taylor expansion of n in k 1539342803.297 * [misc]backup-simplify: Simplify n into n 1539342803.298 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342803.298 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342803.298 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539342803.298 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539342803.298 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539342803.298 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1539342803.298 * [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))) 1539342803.298 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342803.298 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342803.298 * [misc]taylor: Taking taylor expansion of -1 in k 1539342803.298 * [misc]backup-simplify: Simplify -1 into -1 1539342803.299 * [misc]taylor: Taking taylor expansion of k in k 1539342803.299 * [misc]backup-simplify: Simplify 0 into 0 1539342803.299 * [misc]backup-simplify: Simplify 1 into 1 1539342803.299 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342803.299 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342803.299 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342803.300 * [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)))) 1539342803.300 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.300 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.300 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of k in n 1539342803.300 * [misc]backup-simplify: Simplify k into k 1539342803.300 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.300 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.300 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.300 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of -2 in n 1539342803.300 * [misc]backup-simplify: Simplify -2 into -2 1539342803.300 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342803.300 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.300 * [misc]backup-simplify: Simplify PI into PI 1539342803.300 * [misc]taylor: Taking taylor expansion of n in n 1539342803.300 * [misc]backup-simplify: Simplify 0 into 0 1539342803.300 * [misc]backup-simplify: Simplify 1 into 1 1539342803.301 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342803.301 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342803.301 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342803.302 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539342803.302 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1539342803.302 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.303 * [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))) 1539342803.303 * [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)))) 1539342803.304 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539342803.304 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539342803.304 * [misc]taylor: Taking taylor expansion of -1 in n 1539342803.304 * [misc]backup-simplify: Simplify -1 into -1 1539342803.304 * [misc]taylor: Taking taylor expansion of k in n 1539342803.304 * [misc]backup-simplify: Simplify k into k 1539342803.304 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539342803.304 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539342803.304 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539342803.304 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539342803.305 * [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))) 1539342803.305 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1539342803.305 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1539342803.305 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1539342803.305 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1539342803.305 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1539342803.305 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1539342803.305 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.305 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1539342803.305 * [misc]taylor: Taking taylor expansion of k in n 1539342803.305 * [misc]backup-simplify: Simplify k into k 1539342803.305 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1539342803.305 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342803.305 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.305 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342803.306 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342803.306 * [misc]taylor: Taking taylor expansion of -2 in n 1539342803.306 * [misc]backup-simplify: Simplify -2 into -2 1539342803.306 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342803.306 * [misc]taylor: Taking taylor expansion of PI in n 1539342803.306 * [misc]backup-simplify: Simplify PI into PI 1539342803.306 * [misc]taylor: Taking taylor expansion of n in n 1539342803.306 * [misc]backup-simplify: Simplify 0 into 0 1539342803.306 * [misc]backup-simplify: Simplify 1 into 1 1539342803.306 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342803.306 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342803.307 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342803.307 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1539342803.307 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1539342803.308 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.308 * [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))) 1539342803.309 * [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)))) 1539342803.309 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539342803.309 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539342803.309 * [misc]taylor: Taking taylor expansion of -1 in n 1539342803.309 * [misc]backup-simplify: Simplify -1 into -1 1539342803.309 * [misc]taylor: Taking taylor expansion of k in n 1539342803.309 * [misc]backup-simplify: Simplify k into k 1539342803.309 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539342803.309 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539342803.309 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539342803.309 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539342803.310 * [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))) 1539342803.310 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1539342803.310 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1539342803.310 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1539342803.310 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1539342803.310 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1539342803.310 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.310 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.310 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1539342803.310 * [misc]taylor: Taking taylor expansion of k in k 1539342803.310 * [misc]backup-simplify: Simplify 0 into 0 1539342803.311 * [misc]backup-simplify: Simplify 1 into 1 1539342803.311 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1539342803.311 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342803.311 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342803.311 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539342803.311 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539342803.311 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539342803.311 * [misc]taylor: Taking taylor expansion of -2 in k 1539342803.311 * [misc]backup-simplify: Simplify -2 into -2 1539342803.311 * [misc]taylor: Taking taylor expansion of PI in k 1539342803.311 * [misc]backup-simplify: Simplify PI into PI 1539342803.311 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342803.312 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342803.312 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342803.312 * [misc]taylor: Taking taylor expansion of n in k 1539342803.312 * [misc]backup-simplify: Simplify n into n 1539342803.312 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342803.312 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1539342803.312 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1539342803.312 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342803.313 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539342803.313 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1539342803.314 * [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)))) 1539342803.314 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342803.314 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342803.314 * [misc]taylor: Taking taylor expansion of -1 in k 1539342803.314 * [misc]backup-simplify: Simplify -1 into -1 1539342803.314 * [misc]taylor: Taking taylor expansion of k in k 1539342803.314 * [misc]backup-simplify: Simplify 0 into 0 1539342803.314 * [misc]backup-simplify: Simplify 1 into 1 1539342803.314 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342803.315 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342803.315 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342803.316 * [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))))) 1539342803.316 * [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))))) 1539342803.317 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342803.318 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342803.321 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539342803.321 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1539342803.321 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1539342803.321 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.322 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.323 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539342803.324 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342803.325 * [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 1539342803.325 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.325 * [misc]backup-simplify: Simplify 0 into 0 1539342803.325 * [misc]backup-simplify: Simplify 0 into 0 1539342803.325 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539342803.327 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539342803.328 * [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)))))) 1539342803.328 * [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)))))) 1539342803.330 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.331 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342803.336 * [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 1539342803.336 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.336 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1539342803.336 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342803.337 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342803.338 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1539342803.340 * [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 1539342803.340 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342803.341 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1539342803.342 * [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 1539342803.342 * [misc]taylor: Taking taylor expansion of 0 in k 1539342803.342 * [misc]backup-simplify: Simplify 0 into 0 1539342803.342 * [misc]backup-simplify: Simplify 0 into 0 1539342803.342 * [misc]backup-simplify: Simplify 0 into 0 1539342803.342 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342803.345 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1539342803.347 * [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)))))) 1539342803.347 * [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)))))) 1539342803.350 * [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))))))))))) 1539342803.350 * * * [misc]progress: simplifying candidates 1539342803.350 * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # 1539342803.350 * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # 1539342803.350 * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # 1539342803.350 * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # 1539342803.350 * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # 1539342803.350 * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # 1539342803.350 * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # 1539342803.350 * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # 1539342803.351 * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # 1539342803.351 * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # 1539342803.351 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1539342803.351 * * [misc]simplify: iters left: 6 (11 enodes) 1539342803.354 * * [misc]simplify: iters left: 5 (21 enodes) 1539342803.362 * * [misc]simplify: iters left: 4 (47 enodes) 1539342803.377 * * [misc]simplify: iters left: 3 (109 enodes) 1539342803.428 * * [misc]simplify: iters left: 2 (300 enodes) 1539342803.617 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1539342803.617 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1539342803.617 * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # 1539342803.617 * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # 1539342803.617 * [enter]simplify: Simplifying (* PI (* n 2)) 1539342803.617 * * [misc]simplify: iters left: 4 (5 enodes) 1539342803.619 * * [misc]simplify: iters left: 3 (9 enodes) 1539342803.621 * * [misc]simplify: iters left: 2 (15 enodes) 1539342803.627 * * [misc]simplify: iters left: 1 (17 enodes) 1539342803.628 * [exit]simplify: Simplified to (* (* 2 n) PI) 1539342803.628 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1539342803.628 * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # 1539342803.629 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539342803.629 * * [misc]simplify: iters left: 5 (8 enodes) 1539342803.630 * * [misc]simplify: iters left: 4 (12 enodes) 1539342803.631 * * [misc]simplify: iters left: 3 (18 enodes) 1539342803.634 * * [misc]simplify: iters left: 2 (20 enodes) 1539342803.636 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539342803.636 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1539342803.636 * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # 1539342803.636 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1539342803.636 * * [misc]simplify: iters left: 5 (6 enodes) 1539342803.637 * * [misc]simplify: iters left: 4 (8 enodes) 1539342803.638 * * [misc]simplify: iters left: 3 (11 enodes) 1539342803.639 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1539342803.639 * [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))) 1539342803.639 * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # 1539342803.640 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1539342803.640 * * [misc]simplify: iters left: 5 (6 enodes) 1539342803.640 * * [misc]simplify: iters left: 4 (8 enodes) 1539342803.641 * * [misc]simplify: iters left: 3 (11 enodes) 1539342803.643 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1539342803.643 * [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))) 1539342803.643 * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # 1539342803.643 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1539342803.643 * * [misc]simplify: iters left: 4 (5 enodes) 1539342803.644 * * [misc]simplify: iters left: 3 (7 enodes) 1539342803.645 * * [misc]simplify: iters left: 2 (10 enodes) 1539342803.646 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1539342803.646 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1539342803.646 * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # 1539342803.646 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1539342803.646 * * [misc]simplify: iters left: 5 (9 enodes) 1539342803.647 * * [misc]simplify: iters left: 4 (15 enodes) 1539342803.649 * * [misc]simplify: iters left: 3 (21 enodes) 1539342803.652 * * [misc]simplify: iters left: 2 (22 enodes) 1539342803.657 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1539342803.657 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1539342803.658 * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # 1539342803.658 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1539342803.658 * * [misc]simplify: iters left: 5 (9 enodes) 1539342803.661 * * [misc]simplify: iters left: 4 (15 enodes) 1539342803.665 * * [misc]simplify: iters left: 3 (21 enodes) 1539342803.670 * * [misc]simplify: iters left: 2 (22 enodes) 1539342803.675 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1539342803.675 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1539342803.676 * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # 1539342803.676 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1539342803.676 * * [misc]simplify: iters left: 5 (7 enodes) 1539342803.678 * * [misc]simplify: iters left: 4 (9 enodes) 1539342803.681 * * [misc]simplify: iters left: 3 (12 enodes) 1539342803.684 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1539342803.684 * [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))) 1539342803.684 * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # 1539342803.684 * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # 1539342803.684 * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # 1539342803.684 * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # 1539342803.684 * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # 1539342803.684 * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # 1539342803.684 * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # 1539342803.685 * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # 1539342803.685 * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # 1539342803.685 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1539342803.685 * * [misc]simplify: iters left: 6 (14 enodes) 1539342803.689 * * [misc]simplify: iters left: 5 (26 enodes) 1539342803.698 * * [misc]simplify: iters left: 4 (53 enodes) 1539342803.717 * * [misc]simplify: iters left: 3 (137 enodes) 1539342803.782 * * [misc]simplify: iters left: 2 (487 enodes) 1539342804.329 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1539342804.329 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1539342804.329 * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # 1539342804.329 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1539342804.329 * * [misc]simplify: iters left: 6 (14 enodes) 1539342804.334 * * [misc]simplify: iters left: 5 (26 enodes) 1539342804.342 * * [misc]simplify: iters left: 4 (53 enodes) 1539342804.363 * * [misc]simplify: iters left: 3 (137 enodes) 1539342804.414 * * [misc]simplify: iters left: 2 (487 enodes) 1539342804.955 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1539342804.955 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1539342804.955 * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # 1539342804.955 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1539342804.955 * * [misc]simplify: iters left: 6 (14 enodes) 1539342804.957 * * [misc]simplify: iters left: 5 (24 enodes) 1539342804.961 * * [misc]simplify: iters left: 4 (42 enodes) 1539342804.967 * * [misc]simplify: iters left: 3 (71 enodes) 1539342804.982 * * [misc]simplify: iters left: 2 (208 enodes) 1539342805.183 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1539342805.183 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1539342805.183 * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # 1539342805.183 * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # 1539342805.183 * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # 1539342805.183 * [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))) 1539342805.183 * * [misc]simplify: iters left: 6 (16 enodes) 1539342805.189 * * [misc]simplify: iters left: 5 (31 enodes) 1539342805.203 * * [misc]simplify: iters left: 4 (67 enodes) 1539342805.224 * * [misc]simplify: iters left: 3 (124 enodes) 1539342805.256 * * [misc]simplify: iters left: 2 (195 enodes) 1539342805.331 * * [misc]simplify: iters left: 1 (309 enodes) 1539342805.448 * [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)))) 1539342805.448 * [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)))))) 1539342805.448 * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # 1539342805.448 * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # 1539342805.448 * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # 1539342805.448 * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # 1539342805.448 * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # 1539342805.448 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.449 * * [misc]simplify: iters left: 6 (12 enodes) 1539342805.452 * * [misc]simplify: iters left: 5 (19 enodes) 1539342805.459 * * [misc]simplify: iters left: 4 (25 enodes) 1539342805.466 * * [misc]simplify: iters left: 3 (26 enodes) 1539342805.472 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.472 * [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))))) 1539342805.473 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1539342805.473 * * [misc]simplify: iters left: 6 (12 enodes) 1539342805.476 * * [misc]simplify: iters left: 5 (18 enodes) 1539342805.481 * * [misc]simplify: iters left: 4 (24 enodes) 1539342805.487 * * [misc]simplify: iters left: 3 (25 enodes) 1539342805.492 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1539342805.492 * [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))))) 1539342805.492 * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # 1539342805.493 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1539342805.493 * * [misc]simplify: iters left: 6 (11 enodes) 1539342805.494 * * [misc]simplify: iters left: 5 (16 enodes) 1539342805.496 * * [misc]simplify: iters left: 4 (22 enodes) 1539342805.500 * * [misc]simplify: iters left: 3 (24 enodes) 1539342805.503 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1539342805.503 * [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))))) 1539342805.503 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1539342805.503 * * [misc]simplify: iters left: 6 (12 enodes) 1539342805.505 * * [misc]simplify: iters left: 5 (18 enodes) 1539342805.507 * * [misc]simplify: iters left: 4 (24 enodes) 1539342805.513 * * [misc]simplify: iters left: 3 (25 enodes) 1539342805.519 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1539342805.519 * [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))))) 1539342805.519 * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # 1539342805.520 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1539342805.520 * * [misc]simplify: iters left: 6 (9 enodes) 1539342805.522 * * [misc]simplify: iters left: 5 (16 enodes) 1539342805.527 * * [misc]simplify: iters left: 4 (24 enodes) 1539342805.532 * * [misc]simplify: iters left: 3 (26 enodes) 1539342805.537 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1539342805.537 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539342805.538 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1539342805.538 * * [misc]simplify: iters left: 6 (11 enodes) 1539342805.541 * * [misc]simplify: iters left: 5 (17 enodes) 1539342805.545 * * [misc]simplify: iters left: 4 (23 enodes) 1539342805.551 * * [misc]simplify: iters left: 3 (24 enodes) 1539342805.557 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1539342805.557 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1539342805.557 * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # 1539342805.557 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.557 * * [misc]simplify: iters left: 6 (12 enodes) 1539342805.561 * * [misc]simplify: iters left: 5 (19 enodes) 1539342805.566 * * [misc]simplify: iters left: 4 (25 enodes) 1539342805.569 * * [misc]simplify: iters left: 3 (26 enodes) 1539342805.572 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.572 * [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))))) 1539342805.572 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1539342805.572 * * [misc]simplify: iters left: 6 (12 enodes) 1539342805.574 * * [misc]simplify: iters left: 5 (18 enodes) 1539342805.576 * * [misc]simplify: iters left: 4 (24 enodes) 1539342805.580 * * [misc]simplify: iters left: 3 (25 enodes) 1539342805.583 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1539342805.583 * [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))))) 1539342805.583 * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # 1539342805.583 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1539342805.583 * * [misc]simplify: iters left: 6 (11 enodes) 1539342805.585 * * [misc]simplify: iters left: 5 (16 enodes) 1539342805.587 * * [misc]simplify: iters left: 4 (22 enodes) 1539342805.589 * * [misc]simplify: iters left: 3 (24 enodes) 1539342805.593 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1539342805.593 * [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))))) 1539342805.593 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1539342805.593 * * [misc]simplify: iters left: 6 (12 enodes) 1539342805.597 * * [misc]simplify: iters left: 5 (18 enodes) 1539342805.602 * * [misc]simplify: iters left: 4 (24 enodes) 1539342805.608 * * [misc]simplify: iters left: 3 (25 enodes) 1539342805.614 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1539342805.614 * [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))))) 1539342805.614 * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # 1539342805.614 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1539342805.614 * * [misc]simplify: iters left: 6 (9 enodes) 1539342805.617 * * [misc]simplify: iters left: 5 (16 enodes) 1539342805.622 * * [misc]simplify: iters left: 4 (24 enodes) 1539342805.627 * * [misc]simplify: iters left: 3 (26 enodes) 1539342805.633 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1539342805.633 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1539342805.633 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1539342805.633 * * [misc]simplify: iters left: 6 (11 enodes) 1539342805.636 * * [misc]simplify: iters left: 5 (17 enodes) 1539342805.641 * * [misc]simplify: iters left: 4 (23 enodes) 1539342805.647 * * [misc]simplify: iters left: 3 (24 enodes) 1539342805.653 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1539342805.653 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1539342805.653 * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # 1539342805.653 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.653 * * [misc]simplify: iters left: 6 (11 enodes) 1539342805.657 * * [misc]simplify: iters left: 5 (15 enodes) 1539342805.661 * * [misc]simplify: iters left: 4 (18 enodes) 1539342805.666 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.666 * [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))))) 1539342805.666 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1539342805.667 * * [misc]simplify: iters left: 6 (11 enodes) 1539342805.670 * * [misc]simplify: iters left: 5 (14 enodes) 1539342805.674 * * [misc]simplify: iters left: 4 (17 enodes) 1539342805.678 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1539342805.678 * [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))))) 1539342805.678 * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # 1539342805.678 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539342805.679 * * [misc]simplify: iters left: 6 (10 enodes) 1539342805.681 * * [misc]simplify: iters left: 5 (12 enodes) 1539342805.685 * * [misc]simplify: iters left: 4 (15 enodes) 1539342805.689 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539342805.689 * [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))))) 1539342805.689 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539342805.689 * * [misc]simplify: iters left: 6 (11 enodes) 1539342805.692 * * [misc]simplify: iters left: 5 (14 enodes) 1539342805.696 * * [misc]simplify: iters left: 4 (17 enodes) 1539342805.701 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539342805.701 * [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))))) 1539342805.701 * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # 1539342805.701 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1539342805.701 * * [misc]simplify: iters left: 6 (9 enodes) 1539342805.704 * * [misc]simplify: iters left: 5 (13 enodes) 1539342805.708 * * [misc]simplify: iters left: 4 (18 enodes) 1539342805.713 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1539342805.713 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1539342805.713 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1539342805.713 * * [misc]simplify: iters left: 6 (10 enodes) 1539342805.716 * * [misc]simplify: iters left: 5 (13 enodes) 1539342805.717 * * [misc]simplify: iters left: 4 (16 enodes) 1539342805.719 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1539342805.719 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1539342805.719 * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # 1539342805.720 * [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)))) 1539342805.720 * * [misc]simplify: iters left: 6 (16 enodes) 1539342805.722 * * [misc]simplify: iters left: 5 (28 enodes) 1539342805.726 * * [misc]simplify: iters left: 4 (46 enodes) 1539342805.732 * * [misc]simplify: iters left: 3 (50 enodes) 1539342805.737 * * [misc]simplify: iters left: 2 (53 enodes) 1539342805.744 * [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)))) 1539342805.744 * [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))))) 1539342805.744 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1539342805.744 * * [misc]simplify: iters left: 6 (14 enodes) 1539342805.748 * * [misc]simplify: iters left: 5 (20 enodes) 1539342805.754 * * [misc]simplify: iters left: 4 (29 enodes) 1539342805.762 * * [misc]simplify: iters left: 3 (30 enodes) 1539342805.769 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1539342805.769 * [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))))) 1539342805.770 * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # 1539342805.770 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1539342805.770 * * [misc]simplify: iters left: 6 (15 enodes) 1539342805.774 * * [misc]simplify: iters left: 5 (23 enodes) 1539342805.781 * * [misc]simplify: iters left: 4 (34 enodes) 1539342805.789 * * [misc]simplify: iters left: 3 (37 enodes) 1539342805.799 * [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)))))) 1539342805.799 * [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))))) 1539342805.799 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539342805.799 * * [misc]simplify: iters left: 6 (14 enodes) 1539342805.803 * * [misc]simplify: iters left: 5 (20 enodes) 1539342805.809 * * [misc]simplify: iters left: 4 (29 enodes) 1539342805.817 * * [misc]simplify: iters left: 3 (30 enodes) 1539342805.825 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539342805.825 * [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))))) 1539342805.825 * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # 1539342805.825 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1539342805.825 * * [misc]simplify: iters left: 6 (14 enodes) 1539342805.828 * * [misc]simplify: iters left: 5 (24 enodes) 1539342805.832 * * [misc]simplify: iters left: 4 (39 enodes) 1539342805.837 * * [misc]simplify: iters left: 3 (54 enodes) 1539342805.843 * * [misc]simplify: iters left: 2 (80 enodes) 1539342805.852 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1539342805.852 * [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)))) 1539342805.853 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1539342805.853 * * [misc]simplify: iters left: 6 (13 enodes) 1539342805.854 * * [misc]simplify: iters left: 5 (19 enodes) 1539342805.859 * * [misc]simplify: iters left: 4 (28 enodes) 1539342805.866 * * [misc]simplify: iters left: 3 (30 enodes) 1539342805.873 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1539342805.874 * [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)))) 1539342805.874 * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # 1539342805.874 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.874 * * [misc]simplify: iters left: 6 (15 enodes) 1539342805.878 * * [misc]simplify: iters left: 5 (23 enodes) 1539342805.884 * * [misc]simplify: iters left: 4 (32 enodes) 1539342805.888 * * [misc]simplify: iters left: 3 (34 enodes) 1539342805.892 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.892 * [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))))) 1539342805.892 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1539342805.892 * * [misc]simplify: iters left: 6 (14 enodes) 1539342805.894 * * [misc]simplify: iters left: 5 (20 enodes) 1539342805.896 * * [misc]simplify: iters left: 4 (29 enodes) 1539342805.900 * * [misc]simplify: iters left: 3 (30 enodes) 1539342805.903 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1539342805.903 * [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))))) 1539342805.903 * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # 1539342805.904 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539342805.904 * * [misc]simplify: iters left: 6 (14 enodes) 1539342805.905 * * [misc]simplify: iters left: 5 (20 enodes) 1539342805.908 * * [misc]simplify: iters left: 4 (29 enodes) 1539342805.913 * * [misc]simplify: iters left: 3 (30 enodes) 1539342805.921 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539342805.921 * [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))))) 1539342805.921 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539342805.921 * * [misc]simplify: iters left: 6 (14 enodes) 1539342805.925 * * [misc]simplify: iters left: 5 (20 enodes) 1539342805.931 * * [misc]simplify: iters left: 4 (29 enodes) 1539342805.938 * * [misc]simplify: iters left: 3 (30 enodes) 1539342805.945 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1539342805.945 * [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))))) 1539342805.945 * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # 1539342805.946 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1539342805.946 * * [misc]simplify: iters left: 6 (13 enodes) 1539342805.948 * * [misc]simplify: iters left: 5 (21 enodes) 1539342805.951 * * [misc]simplify: iters left: 4 (32 enodes) 1539342805.955 * * [misc]simplify: iters left: 3 (33 enodes) 1539342805.958 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1539342805.959 * [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)))) 1539342805.959 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1539342805.959 * * [misc]simplify: iters left: 6 (13 enodes) 1539342805.961 * * [misc]simplify: iters left: 5 (19 enodes) 1539342805.963 * * [misc]simplify: iters left: 4 (28 enodes) 1539342805.967 * * [misc]simplify: iters left: 3 (30 enodes) 1539342805.970 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1539342805.970 * [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)))) 1539342805.970 * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # 1539342805.970 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1539342805.970 * * [misc]simplify: iters left: 6 (6 enodes) 1539342805.971 * * [misc]simplify: iters left: 5 (10 enodes) 1539342805.973 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1539342805.973 * [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))))) 1539342805.973 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1539342805.973 * * [misc]simplify: iters left: 6 (13 enodes) 1539342805.975 * * [misc]simplify: iters left: 5 (19 enodes) 1539342805.979 * * [misc]simplify: iters left: 4 (28 enodes) 1539342805.987 * * [misc]simplify: iters left: 3 (30 enodes) 1539342805.994 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1539342805.994 * [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))))) 1539342805.994 * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # 1539342805.994 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1539342805.994 * * [misc]simplify: iters left: 4 (5 enodes) 1539342805.996 * * [misc]simplify: iters left: 3 (7 enodes) 1539342805.997 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1539342805.997 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1539342805.998 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539342805.998 * * [misc]simplify: iters left: 6 (13 enodes) 1539342806.002 * * [misc]simplify: iters left: 5 (19 enodes) 1539342806.007 * * [misc]simplify: iters left: 4 (28 enodes) 1539342806.014 * * [misc]simplify: iters left: 3 (30 enodes) 1539342806.021 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1539342806.021 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1539342806.021 * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # 1539342806.022 * [enter]simplify: Simplifying (/ 1 1) 1539342806.022 * * [misc]simplify: iters left: 2 (2 enodes) 1539342806.023 * * [misc]simplify: iters left: 1 (4 enodes) 1539342806.023 * [exit]simplify: Simplified to 1 1539342806.023 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1539342806.023 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1539342806.025 * * [misc]simplify: iters left: 6 (12 enodes) 1539342806.028 * * [misc]simplify: iters left: 5 (18 enodes) 1539342806.033 * * [misc]simplify: iters left: 4 (27 enodes) 1539342806.040 * * [misc]simplify: iters left: 3 (29 enodes) 1539342806.047 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1539342806.047 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1539342806.047 * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # 1539342806.047 * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # 1539342806.048 * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # 1539342806.048 * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # 1539342806.048 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1539342806.048 * * [misc]simplify: iters left: 2 (3 enodes) 1539342806.049 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1539342806.049 * [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)))) 1539342806.049 * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # 1539342806.049 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1539342806.049 * * [misc]simplify: iters left: 2 (3 enodes) 1539342806.050 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1539342806.050 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1539342806.050 * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # 1539342806.050 * [enter]simplify: Simplifying (sqrt k) 1539342806.050 * * [misc]simplify: iters left: 1 (2 enodes) 1539342806.051 * [exit]simplify: Simplified to (sqrt k) 1539342806.051 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1539342806.051 * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # 1539342806.051 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1539342806.051 * * [misc]simplify: iters left: 5 (7 enodes) 1539342806.054 * * [misc]simplify: iters left: 4 (12 enodes) 1539342806.057 * * [misc]simplify: iters left: 3 (18 enodes) 1539342806.062 * * [misc]simplify: iters left: 2 (20 enodes) 1539342806.066 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539342806.066 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539342806.067 * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # 1539342806.067 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1539342806.067 * * [misc]simplify: iters left: 5 (7 enodes) 1539342806.069 * * [misc]simplify: iters left: 4 (12 enodes) 1539342806.072 * * [misc]simplify: iters left: 3 (18 enodes) 1539342806.077 * * [misc]simplify: iters left: 2 (20 enodes) 1539342806.082 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539342806.082 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1539342806.082 * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # 1539342806.082 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1539342806.082 * * [misc]simplify: iters left: 5 (7 enodes) 1539342806.084 * * [misc]simplify: iters left: 4 (9 enodes) 1539342806.086 * * [misc]simplify: iters left: 3 (12 enodes) 1539342806.090 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1539342806.090 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1539342806.090 * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # 1539342806.090 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1539342806.090 * * [misc]simplify: iters left: 6 (12 enodes) 1539342806.094 * * [misc]simplify: iters left: 5 (18 enodes) 1539342806.099 * * [misc]simplify: iters left: 4 (27 enodes) 1539342806.105 * * [misc]simplify: iters left: 3 (29 enodes) 1539342806.108 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1539342806.108 * [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))))))) 1539342806.108 * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # 1539342806.108 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1539342806.108 * * [misc]simplify: iters left: 6 (11 enodes) 1539342806.110 * * [misc]simplify: iters left: 5 (17 enodes) 1539342806.112 * * [misc]simplify: iters left: 4 (26 enodes) 1539342806.115 * * [misc]simplify: iters left: 3 (27 enodes) 1539342806.118 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1539342806.118 * [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))))))) 1539342806.118 * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # 1539342806.118 * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # 1539342806.119 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1539342806.119 * * [misc]simplify: iters left: 5 (7 enodes) 1539342806.120 * * [misc]simplify: iters left: 4 (12 enodes) 1539342806.121 * * [misc]simplify: iters left: 3 (18 enodes) 1539342806.123 * * [misc]simplify: iters left: 2 (20 enodes) 1539342806.126 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539342806.126 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342806.126 * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # 1539342806.126 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342806.126 * * [misc]simplify: iters left: 4 (5 enodes) 1539342806.127 * * [misc]simplify: iters left: 3 (9 enodes) 1539342806.128 * * [misc]simplify: iters left: 2 (15 enodes) 1539342806.130 * * [misc]simplify: iters left: 1 (17 enodes) 1539342806.132 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342806.132 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1539342806.132 * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # 1539342806.132 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342806.132 * * [misc]simplify: iters left: 4 (5 enodes) 1539342806.134 * * [misc]simplify: iters left: 3 (9 enodes) 1539342806.136 * * [misc]simplify: iters left: 2 (15 enodes) 1539342806.140 * * [misc]simplify: iters left: 1 (17 enodes) 1539342806.145 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342806.145 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1539342806.145 * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # 1539342806.145 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342806.145 * * [misc]simplify: iters left: 4 (5 enodes) 1539342806.147 * * [misc]simplify: iters left: 3 (9 enodes) 1539342806.150 * * [misc]simplify: iters left: 2 (15 enodes) 1539342806.154 * * [misc]simplify: iters left: 1 (17 enodes) 1539342806.157 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342806.158 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1539342806.158 * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # 1539342806.158 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1539342806.158 * * [misc]simplify: iters left: 6 (37 enodes) 1539342806.171 * * [misc]simplify: iters left: 5 (105 enodes) 1539342806.191 * * [misc]simplify: iters left: 4 (339 enodes) 1539342806.390 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1539342806.390 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) 1539342806.390 * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # 1539342806.390 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1539342806.390 * * [misc]simplify: iters left: 6 (15 enodes) 1539342806.393 * * [misc]simplify: iters left: 5 (33 enodes) 1539342806.399 * * [misc]simplify: iters left: 4 (64 enodes) 1539342806.410 * * [misc]simplify: iters left: 3 (171 enodes) 1539342806.505 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1539342806.505 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) 1539342806.505 * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # 1539342806.505 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1539342806.505 * * [misc]simplify: iters left: 6 (15 enodes) 1539342806.511 * * [misc]simplify: iters left: 5 (30 enodes) 1539342806.522 * * [misc]simplify: iters left: 4 (65 enodes) 1539342806.548 * * [misc]simplify: iters left: 3 (200 enodes) 1539342806.680 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1539342806.680 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1539342806.680 * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # 1539342806.681 * [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)))))))))))))))))))))) 1539342806.681 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539342806.681 * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # 1539342806.681 * [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)))))))) 1539342806.681 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539342806.681 * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # 1539342806.681 * [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))))))))))) 1539342806.681 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539342806.681 * * * [misc]progress: adding candidates to table 1539342807.499 * * [misc]progress: iteration 2 / 4 1539342807.499 * * * [misc]progress: picking best candidate 1539342807.534 * * * * [misc]pick: Picked # 1539342807.534 * * * [misc]progress: localizing error 1539342807.568 * * * [misc]progress: generating rewritten candidates 1539342807.569 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 1) 1539342807.571 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1) 1539342807.573 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) 1539342807.591 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1) 1539342807.592 * * * [misc]progress: generating series expansions 1539342807.592 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 1) 1539342807.592 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539342807.592 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539342807.592 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342807.592 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.592 * [misc]backup-simplify: Simplify 2 into 2 1539342807.592 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342807.592 * [misc]taylor: Taking taylor expansion of n in n 1539342807.592 * [misc]backup-simplify: Simplify 0 into 0 1539342807.592 * [misc]backup-simplify: Simplify 1 into 1 1539342807.592 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.592 * [misc]backup-simplify: Simplify PI into PI 1539342807.592 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342807.592 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.592 * [misc]backup-simplify: Simplify 2 into 2 1539342807.592 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342807.592 * [misc]taylor: Taking taylor expansion of n in n 1539342807.592 * [misc]backup-simplify: Simplify 0 into 0 1539342807.592 * [misc]backup-simplify: Simplify 1 into 1 1539342807.592 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.592 * [misc]backup-simplify: Simplify PI into PI 1539342807.593 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342807.593 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342807.593 * [misc]backup-simplify: Simplify 0 into 0 1539342807.594 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342807.594 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342807.594 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.595 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342807.596 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342807.596 * [misc]backup-simplify: Simplify 0 into 0 1539342807.597 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342807.599 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342807.599 * [misc]backup-simplify: Simplify 0 into 0 1539342807.601 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342807.602 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342807.603 * [misc]backup-simplify: Simplify 0 into 0 1539342807.605 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342807.607 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539342807.607 * [misc]backup-simplify: Simplify 0 into 0 1539342807.610 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342807.613 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539342807.613 * [misc]backup-simplify: Simplify 0 into 0 1539342807.617 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539342807.621 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539342807.621 * [misc]backup-simplify: Simplify 0 into 0 1539342807.621 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539342807.621 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539342807.621 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539342807.621 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342807.621 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.621 * [misc]backup-simplify: Simplify 2 into 2 1539342807.621 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.621 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.621 * [misc]backup-simplify: Simplify PI into PI 1539342807.621 * [misc]taylor: Taking taylor expansion of n in n 1539342807.621 * [misc]backup-simplify: Simplify 0 into 0 1539342807.621 * [misc]backup-simplify: Simplify 1 into 1 1539342807.622 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.622 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342807.622 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.622 * [misc]backup-simplify: Simplify 2 into 2 1539342807.622 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.622 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.622 * [misc]backup-simplify: Simplify PI into PI 1539342807.622 * [misc]taylor: Taking taylor expansion of n in n 1539342807.622 * [misc]backup-simplify: Simplify 0 into 0 1539342807.622 * [misc]backup-simplify: Simplify 1 into 1 1539342807.622 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.623 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.623 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.624 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342807.624 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342807.624 * [misc]backup-simplify: Simplify 0 into 0 1539342807.626 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.626 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342807.627 * [misc]backup-simplify: Simplify 0 into 0 1539342807.628 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.629 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342807.629 * [misc]backup-simplify: Simplify 0 into 0 1539342807.631 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.632 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342807.632 * [misc]backup-simplify: Simplify 0 into 0 1539342807.634 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.635 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342807.635 * [misc]backup-simplify: Simplify 0 into 0 1539342807.636 * [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 1539342807.638 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342807.638 * [misc]backup-simplify: Simplify 0 into 0 1539342807.639 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539342807.639 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539342807.639 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539342807.639 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342807.639 * [misc]taylor: Taking taylor expansion of -2 in n 1539342807.639 * [misc]backup-simplify: Simplify -2 into -2 1539342807.639 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.639 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.639 * [misc]backup-simplify: Simplify PI into PI 1539342807.639 * [misc]taylor: Taking taylor expansion of n in n 1539342807.639 * [misc]backup-simplify: Simplify 0 into 0 1539342807.639 * [misc]backup-simplify: Simplify 1 into 1 1539342807.639 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.639 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342807.639 * [misc]taylor: Taking taylor expansion of -2 in n 1539342807.639 * [misc]backup-simplify: Simplify -2 into -2 1539342807.639 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.639 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.639 * [misc]backup-simplify: Simplify PI into PI 1539342807.639 * [misc]taylor: Taking taylor expansion of n in n 1539342807.639 * [misc]backup-simplify: Simplify 0 into 0 1539342807.639 * [misc]backup-simplify: Simplify 1 into 1 1539342807.640 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.640 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342807.640 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342807.641 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342807.641 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342807.641 * [misc]backup-simplify: Simplify 0 into 0 1539342807.642 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.642 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342807.642 * [misc]backup-simplify: Simplify 0 into 0 1539342807.643 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.644 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342807.644 * [misc]backup-simplify: Simplify 0 into 0 1539342807.648 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.649 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342807.649 * [misc]backup-simplify: Simplify 0 into 0 1539342807.650 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.652 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342807.652 * [misc]backup-simplify: Simplify 0 into 0 1539342807.653 * [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 1539342807.655 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342807.655 * [misc]backup-simplify: Simplify 0 into 0 1539342807.655 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539342807.655 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1) 1539342807.655 * [misc]backup-simplify: Simplify (* (* 2 n) PI) into (* 2 (* n PI)) 1539342807.655 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539342807.655 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342807.655 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.656 * [misc]backup-simplify: Simplify 2 into 2 1539342807.656 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342807.656 * [misc]taylor: Taking taylor expansion of n in n 1539342807.656 * [misc]backup-simplify: Simplify 0 into 0 1539342807.656 * [misc]backup-simplify: Simplify 1 into 1 1539342807.656 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.656 * [misc]backup-simplify: Simplify PI into PI 1539342807.656 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342807.656 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.656 * [misc]backup-simplify: Simplify 2 into 2 1539342807.656 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342807.656 * [misc]taylor: Taking taylor expansion of n in n 1539342807.656 * [misc]backup-simplify: Simplify 0 into 0 1539342807.656 * [misc]backup-simplify: Simplify 1 into 1 1539342807.656 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.656 * [misc]backup-simplify: Simplify PI into PI 1539342807.656 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342807.656 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342807.656 * [misc]backup-simplify: Simplify 0 into 0 1539342807.657 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342807.657 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342807.657 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.658 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342807.658 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342807.658 * [misc]backup-simplify: Simplify 0 into 0 1539342807.659 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342807.660 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342807.660 * [misc]backup-simplify: Simplify 0 into 0 1539342807.661 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342807.663 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342807.663 * [misc]backup-simplify: Simplify 0 into 0 1539342807.664 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342807.666 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539342807.666 * [misc]backup-simplify: Simplify 0 into 0 1539342807.668 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342807.669 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539342807.669 * [misc]backup-simplify: Simplify 0 into 0 1539342807.672 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539342807.674 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539342807.674 * [misc]backup-simplify: Simplify 0 into 0 1539342807.674 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539342807.674 * [misc]backup-simplify: Simplify (* (* 2 (/ 1 n)) PI) into (* 2 (/ PI n)) 1539342807.675 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539342807.675 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342807.675 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.675 * [misc]backup-simplify: Simplify 2 into 2 1539342807.675 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.675 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.675 * [misc]backup-simplify: Simplify PI into PI 1539342807.675 * [misc]taylor: Taking taylor expansion of n in n 1539342807.675 * [misc]backup-simplify: Simplify 0 into 0 1539342807.675 * [misc]backup-simplify: Simplify 1 into 1 1539342807.675 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.675 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342807.675 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.675 * [misc]backup-simplify: Simplify 2 into 2 1539342807.675 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.675 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.675 * [misc]backup-simplify: Simplify PI into PI 1539342807.675 * [misc]taylor: Taking taylor expansion of n in n 1539342807.675 * [misc]backup-simplify: Simplify 0 into 0 1539342807.675 * [misc]backup-simplify: Simplify 1 into 1 1539342807.675 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.676 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.676 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.676 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342807.677 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342807.677 * [misc]backup-simplify: Simplify 0 into 0 1539342807.678 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.678 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342807.678 * [misc]backup-simplify: Simplify 0 into 0 1539342807.679 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.680 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342807.680 * [misc]backup-simplify: Simplify 0 into 0 1539342807.681 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.683 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342807.683 * [misc]backup-simplify: Simplify 0 into 0 1539342807.684 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.685 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342807.685 * [misc]backup-simplify: Simplify 0 into 0 1539342807.687 * [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 1539342807.689 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342807.689 * [misc]backup-simplify: Simplify 0 into 0 1539342807.689 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539342807.689 * [misc]backup-simplify: Simplify (* (* 2 (/ 1 (- n))) PI) into (* -2 (/ PI n)) 1539342807.689 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539342807.689 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342807.689 * [misc]taylor: Taking taylor expansion of -2 in n 1539342807.689 * [misc]backup-simplify: Simplify -2 into -2 1539342807.689 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.689 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.689 * [misc]backup-simplify: Simplify PI into PI 1539342807.689 * [misc]taylor: Taking taylor expansion of n in n 1539342807.689 * [misc]backup-simplify: Simplify 0 into 0 1539342807.689 * [misc]backup-simplify: Simplify 1 into 1 1539342807.689 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.689 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342807.689 * [misc]taylor: Taking taylor expansion of -2 in n 1539342807.689 * [misc]backup-simplify: Simplify -2 into -2 1539342807.689 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.690 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.690 * [misc]backup-simplify: Simplify PI into PI 1539342807.690 * [misc]taylor: Taking taylor expansion of n in n 1539342807.690 * [misc]backup-simplify: Simplify 0 into 0 1539342807.690 * [misc]backup-simplify: Simplify 1 into 1 1539342807.690 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.690 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342807.690 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342807.691 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342807.691 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342807.691 * [misc]backup-simplify: Simplify 0 into 0 1539342807.693 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.694 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342807.694 * [misc]backup-simplify: Simplify 0 into 0 1539342807.695 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.697 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342807.697 * [misc]backup-simplify: Simplify 0 into 0 1539342807.699 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.701 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342807.701 * [misc]backup-simplify: Simplify 0 into 0 1539342807.703 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.706 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342807.706 * [misc]backup-simplify: Simplify 0 into 0 1539342807.708 * [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 1539342807.712 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342807.712 * [misc]backup-simplify: Simplify 0 into 0 1539342807.712 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539342807.712 * * * * [misc]progress: [ 3 / 4 ] generating series at (2) 1539342807.713 * [misc]backup-simplify: Simplify (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))) into (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) 1539342807.713 * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in (n k) around 0 1539342807.713 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in k 1539342807.713 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in k 1539342807.713 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342807.713 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.713 * [misc]backup-simplify: Simplify 2 into 2 1539342807.713 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.713 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.713 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1539342807.713 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1539342807.713 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1539342807.713 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342807.713 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342807.713 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.713 * [misc]taylor: Taking taylor expansion of k in k 1539342807.713 * [misc]backup-simplify: Simplify 0 into 0 1539342807.713 * [misc]backup-simplify: Simplify 1 into 1 1539342807.713 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539342807.713 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539342807.714 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.714 * [misc]backup-simplify: Simplify 2 into 2 1539342807.714 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342807.714 * [misc]taylor: Taking taylor expansion of n in k 1539342807.714 * [misc]backup-simplify: Simplify n into n 1539342807.714 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.714 * [misc]backup-simplify: Simplify PI into PI 1539342807.714 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342807.714 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539342807.714 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539342807.714 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342807.714 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539342807.715 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342807.715 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539342807.716 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539342807.716 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539342807.716 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1/2 (log (* 2 (* n PI))))) into (* 1/2 (log (* 2 (* n PI)))) 1539342807.716 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342807.717 * [misc]backup-simplify: Simplify (/ (sqrt 2) 1) into (sqrt 2) 1539342807.717 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1539342807.717 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in k 1539342807.717 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342807.717 * [misc]taylor: Taking taylor expansion of n in k 1539342807.717 * [misc]backup-simplify: Simplify n into n 1539342807.717 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.717 * [misc]backup-simplify: Simplify PI into PI 1539342807.717 * [misc]taylor: Taking taylor expansion of k in k 1539342807.717 * [misc]backup-simplify: Simplify 0 into 0 1539342807.717 * [misc]backup-simplify: Simplify 1 into 1 1539342807.717 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342807.717 * [misc]backup-simplify: Simplify (/ (* n PI) 1) into (* n PI) 1539342807.717 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342807.717 * [misc]backup-simplify: Simplify (/ (* n PI) (* 2 (sqrt 0))) into (* +nan.0 (* n PI)) 1539342807.717 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in n 1539342807.717 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.718 * [misc]backup-simplify: Simplify 2 into 2 1539342807.718 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.718 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.718 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342807.718 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.718 * [misc]taylor: Taking taylor expansion of k in n 1539342807.718 * [misc]backup-simplify: Simplify k into k 1539342807.718 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.718 * [misc]backup-simplify: Simplify 2 into 2 1539342807.718 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342807.718 * [misc]taylor: Taking taylor expansion of n in n 1539342807.718 * [misc]backup-simplify: Simplify 0 into 0 1539342807.718 * [misc]backup-simplify: Simplify 1 into 1 1539342807.718 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.718 * [misc]backup-simplify: Simplify PI into PI 1539342807.719 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342807.719 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342807.720 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342807.720 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342807.721 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.721 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342807.721 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342807.722 * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539342807.723 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539342807.723 * [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)))) 1539342807.723 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1539342807.723 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1539342807.723 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342807.723 * [misc]taylor: Taking taylor expansion of n in n 1539342807.723 * [misc]backup-simplify: Simplify 0 into 0 1539342807.723 * [misc]backup-simplify: Simplify 1 into 1 1539342807.724 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.724 * [misc]backup-simplify: Simplify PI into PI 1539342807.724 * [misc]taylor: Taking taylor expansion of k in n 1539342807.724 * [misc]backup-simplify: Simplify k into k 1539342807.724 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342807.724 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342807.725 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1539342807.725 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342807.725 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1539342807.725 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in n 1539342807.725 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 1539342807.725 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342807.725 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.725 * [misc]backup-simplify: Simplify 2 into 2 1539342807.725 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.725 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.725 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1539342807.726 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1539342807.726 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1539342807.726 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342807.726 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342807.726 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.726 * [misc]taylor: Taking taylor expansion of k in n 1539342807.726 * [misc]backup-simplify: Simplify k into k 1539342807.726 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342807.726 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342807.726 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.726 * [misc]backup-simplify: Simplify 2 into 2 1539342807.726 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342807.726 * [misc]taylor: Taking taylor expansion of n in n 1539342807.726 * [misc]backup-simplify: Simplify 0 into 0 1539342807.726 * [misc]backup-simplify: Simplify 1 into 1 1539342807.726 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.726 * [misc]backup-simplify: Simplify PI into PI 1539342807.726 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342807.726 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342807.727 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342807.728 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342807.728 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.728 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342807.729 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342807.729 * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539342807.730 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539342807.731 * [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)))) 1539342807.731 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1539342807.731 * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) in n 1539342807.731 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342807.731 * [misc]taylor: Taking taylor expansion of n in n 1539342807.731 * [misc]backup-simplify: Simplify 0 into 0 1539342807.731 * [misc]backup-simplify: Simplify 1 into 1 1539342807.731 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.731 * [misc]backup-simplify: Simplify PI into PI 1539342807.731 * [misc]taylor: Taking taylor expansion of k in n 1539342807.731 * [misc]backup-simplify: Simplify k into k 1539342807.731 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342807.732 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342807.732 * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) 1539342807.732 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342807.732 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) 1539342807.733 * [misc]backup-simplify: Simplify (* (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 0) into 0 1539342807.733 * [misc]taylor: Taking taylor expansion of 0 in k 1539342807.733 * [misc]backup-simplify: Simplify 0 into 0 1539342807.734 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342807.735 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342807.738 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342807.738 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1539342807.739 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342807.740 * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539342807.741 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342807.744 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0 1539342807.745 * [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)))) 1539342807.745 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k)))) in k 1539342807.745 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k))) in k 1539342807.745 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342807.745 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342807.745 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k)) in k 1539342807.745 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) PI) in k 1539342807.745 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342807.745 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.745 * [misc]backup-simplify: Simplify 2 into 2 1539342807.745 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.745 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.745 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.745 * [misc]backup-simplify: Simplify PI into PI 1539342807.745 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k) in k 1539342807.745 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1539342807.745 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1539342807.746 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342807.746 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.746 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1539342807.746 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539342807.746 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342807.746 * [misc]taylor: Taking taylor expansion of n in k 1539342807.746 * [misc]backup-simplify: Simplify n into n 1539342807.746 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342807.746 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342807.746 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342807.746 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.746 * [misc]backup-simplify: Simplify 2 into 2 1539342807.746 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.746 * [misc]backup-simplify: Simplify PI into PI 1539342807.746 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.747 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.747 * [misc]taylor: Taking taylor expansion of k in k 1539342807.747 * [misc]backup-simplify: Simplify 0 into 0 1539342807.747 * [misc]backup-simplify: Simplify 1 into 1 1539342807.747 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342807.748 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539342807.748 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342807.749 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539342807.749 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342807.752 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342807.752 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342807.753 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1539342807.753 * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1539342807.754 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342807.754 * [misc]taylor: Taking taylor expansion of k in k 1539342807.754 * [misc]backup-simplify: Simplify 0 into 0 1539342807.754 * [misc]backup-simplify: Simplify 1 into 1 1539342807.754 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1539342807.754 * [misc]backup-simplify: Simplify (* 1 0) into 0 1539342807.755 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1539342807.756 * [misc]backup-simplify: Simplify (+ (* 1 1) (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 0)) into 1 1539342807.757 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) PI) 1) into (* (sqrt 2) PI) 1539342807.758 * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) PI)) into (* +nan.0 (* (sqrt 2) PI)) 1539342807.759 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342807.760 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342807.760 * [misc]backup-simplify: Simplify 0 into 0 1539342807.761 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342807.761 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ PI k) (/ 0 k)))) into 0 1539342807.761 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow PI 2) (pow k 2))) 1539342807.763 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342807.764 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342807.766 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342807.771 * [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 1539342807.771 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1539342807.773 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342807.774 * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539342807.776 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539342807.779 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0 1539342807.780 * [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))))) 1539342807.780 * [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 1539342807.780 * [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 1539342807.781 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342807.781 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342807.781 * [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 1539342807.781 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.781 * [misc]backup-simplify: Simplify 2 into 2 1539342807.781 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.781 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.781 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.781 * [misc]backup-simplify: Simplify PI into PI 1539342807.781 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (pow k 2)) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342807.781 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.781 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342807.781 * [misc]taylor: Taking taylor expansion of n in k 1539342807.781 * [misc]backup-simplify: Simplify n into n 1539342807.782 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342807.782 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342807.782 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342807.782 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.782 * [misc]backup-simplify: Simplify 2 into 2 1539342807.782 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.782 * [misc]backup-simplify: Simplify PI into PI 1539342807.782 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.782 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.783 * [misc]taylor: Taking taylor expansion of k in k 1539342807.783 * [misc]backup-simplify: Simplify 0 into 0 1539342807.783 * [misc]backup-simplify: Simplify 1 into 1 1539342807.783 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342807.784 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539342807.784 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342807.785 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539342807.785 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342807.788 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342807.788 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342807.789 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1539342807.789 * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1539342807.790 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342807.790 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1539342807.790 * [misc]taylor: Taking taylor expansion of k in k 1539342807.790 * [misc]backup-simplify: Simplify 0 into 0 1539342807.790 * [misc]backup-simplify: Simplify 1 into 1 1539342807.790 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342807.791 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342807.792 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342807.792 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342807.793 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 2)) 1) into (* (sqrt 2) (pow PI 2)) 1539342807.794 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342807.795 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539342807.795 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342807.796 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1539342807.796 * [misc]backup-simplify: Simplify (+ (* 1 0) (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1539342807.798 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) (pow PI 2)) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* (pow PI 2) (log (* 2 PI))))) (* 1/2 (* (sqrt 2) (* (pow PI 2) (log n)))))) 1539342807.800 * [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))))))) 1539342807.802 * [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))))))) 1539342807.804 * [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))))))) 1539342807.804 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 PI)) into 0 1539342807.805 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1539342807.806 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342807.808 * [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 1539342807.808 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342807.809 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0 1539342807.809 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0 1539342807.810 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1539342807.812 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 0))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1539342807.813 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* (sqrt 2) PI) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (sqrt 2) (* PI (log n)))) (* 1/2 (* (sqrt 2) (* PI (log (* 2 PI))))))) 1539342807.815 * [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)))))))) 1539342807.816 * [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)))))))) 1539342807.817 * [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)))))))) 1539342807.822 * [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)))))))))))))) 1539342807.822 * [misc]backup-simplify: Simplify (/ (sqrt (* (* 2 (/ 1 n)) PI)) (* (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) into (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) 1539342807.822 * [misc]approximate: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) in (n k) around 0 1539342807.822 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) in k 1539342807.822 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in k 1539342807.822 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342807.822 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.822 * [misc]backup-simplify: Simplify 2 into 2 1539342807.822 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.822 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.822 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1539342807.822 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1539342807.822 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1539342807.822 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in k 1539342807.822 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342807.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.822 * [misc]taylor: Taking taylor expansion of k in k 1539342807.822 * [misc]backup-simplify: Simplify 0 into 0 1539342807.822 * [misc]backup-simplify: Simplify 1 into 1 1539342807.822 * [misc]backup-simplify: Simplify (/ 1/2 1) into 1/2 1539342807.823 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539342807.823 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539342807.823 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.823 * [misc]backup-simplify: Simplify 2 into 2 1539342807.823 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342807.823 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.823 * [misc]backup-simplify: Simplify PI into PI 1539342807.823 * [misc]taylor: Taking taylor expansion of n in k 1539342807.823 * [misc]backup-simplify: Simplify n into n 1539342807.823 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342807.823 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539342807.823 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539342807.823 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) 1539342807.823 * [misc]backup-simplify: Simplify (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1539342807.823 * [misc]backup-simplify: Simplify (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1539342807.823 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in k 1539342807.823 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in k 1539342807.823 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539342807.823 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.823 * [misc]backup-simplify: Simplify PI into PI 1539342807.823 * [misc]taylor: Taking taylor expansion of k in k 1539342807.823 * [misc]backup-simplify: Simplify 0 into 0 1539342807.823 * [misc]backup-simplify: Simplify 1 into 1 1539342807.823 * [misc]taylor: Taking taylor expansion of n in k 1539342807.823 * [misc]backup-simplify: Simplify n into n 1539342807.824 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539342807.824 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539342807.824 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342807.825 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342807.825 * [misc]backup-simplify: Simplify (/ (/ PI n) (* 2 (sqrt 0))) into (* +nan.0 (/ PI n)) 1539342807.825 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) in n 1539342807.825 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 1539342807.825 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342807.825 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.825 * [misc]backup-simplify: Simplify 2 into 2 1539342807.825 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.825 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.825 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1539342807.825 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1539342807.826 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1539342807.826 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in n 1539342807.826 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342807.826 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.826 * [misc]taylor: Taking taylor expansion of k in n 1539342807.826 * [misc]backup-simplify: Simplify k into k 1539342807.826 * [misc]backup-simplify: Simplify (/ 1/2 k) into (/ 1/2 k) 1539342807.826 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342807.826 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342807.826 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.826 * [misc]backup-simplify: Simplify 2 into 2 1539342807.826 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.826 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.826 * [misc]backup-simplify: Simplify PI into PI 1539342807.826 * [misc]taylor: Taking taylor expansion of n in n 1539342807.826 * [misc]backup-simplify: Simplify 0 into 0 1539342807.826 * [misc]backup-simplify: Simplify 1 into 1 1539342807.826 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.827 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.827 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.828 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342807.828 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342807.829 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342807.830 * [misc]backup-simplify: Simplify (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1539342807.830 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1539342807.830 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1539342807.830 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539342807.830 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.830 * [misc]backup-simplify: Simplify PI into PI 1539342807.830 * [misc]taylor: Taking taylor expansion of k in n 1539342807.830 * [misc]backup-simplify: Simplify k into k 1539342807.830 * [misc]taylor: Taking taylor expansion of n in n 1539342807.830 * [misc]backup-simplify: Simplify 0 into 0 1539342807.830 * [misc]backup-simplify: Simplify 1 into 1 1539342807.830 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539342807.830 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1539342807.830 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342807.831 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1539342807.831 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) (sqrt (/ (* PI k) n))) in n 1539342807.831 * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 1539342807.831 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342807.831 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.831 * [misc]backup-simplify: Simplify 2 into 2 1539342807.831 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.831 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.831 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1539342807.831 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1539342807.831 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1539342807.831 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in n 1539342807.831 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342807.831 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.831 * [misc]taylor: Taking taylor expansion of k in n 1539342807.832 * [misc]backup-simplify: Simplify k into k 1539342807.832 * [misc]backup-simplify: Simplify (/ 1/2 k) into (/ 1/2 k) 1539342807.832 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342807.832 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342807.832 * [misc]taylor: Taking taylor expansion of 2 in n 1539342807.832 * [misc]backup-simplify: Simplify 2 into 2 1539342807.832 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342807.832 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.832 * [misc]backup-simplify: Simplify PI into PI 1539342807.832 * [misc]taylor: Taking taylor expansion of n in n 1539342807.832 * [misc]backup-simplify: Simplify 0 into 0 1539342807.832 * [misc]backup-simplify: Simplify 1 into 1 1539342807.832 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342807.832 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.833 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.834 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342807.834 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342807.835 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342807.836 * [misc]backup-simplify: Simplify (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1539342807.836 * [misc]taylor: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 1539342807.836 * [misc]taylor: Taking taylor expansion of (/ (* PI k) n) in n 1539342807.836 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539342807.836 * [misc]taylor: Taking taylor expansion of PI in n 1539342807.836 * [misc]backup-simplify: Simplify PI into PI 1539342807.836 * [misc]taylor: Taking taylor expansion of k in n 1539342807.836 * [misc]backup-simplify: Simplify k into k 1539342807.836 * [misc]taylor: Taking taylor expansion of n in n 1539342807.836 * [misc]backup-simplify: Simplify 0 into 0 1539342807.836 * [misc]backup-simplify: Simplify 1 into 1 1539342807.836 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539342807.836 * [misc]backup-simplify: Simplify (/ (* PI k) 1) into (* PI k) 1539342807.836 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342807.836 * [misc]backup-simplify: Simplify (/ (* PI k) (* 2 (sqrt 0))) into (* +nan.0 (* PI k)) 1539342807.837 * [misc]backup-simplify: Simplify (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0 1539342807.837 * [misc]taylor: Taking taylor expansion of 0 in k 1539342807.837 * [misc]backup-simplify: Simplify 0 into 0 1539342807.837 * [misc]backup-simplify: Simplify 0 into 0 1539342807.839 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342807.839 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342807.842 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342807.842 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)))) into 0 1539342807.843 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342807.844 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539342807.845 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342807.847 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342807.848 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +nan.0 (* PI k))) (* 0 0)) into (- (* +nan.0 (/ (* (sqrt 2) (* PI k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342807.848 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* PI k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* PI k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342807.849 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342807.849 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* PI k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* PI k)) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.849 * [misc]backup-simplify: Simplify 2 into 2 1539342807.849 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.849 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.849 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.849 * [misc]backup-simplify: Simplify PI into PI 1539342807.849 * [misc]taylor: Taking taylor expansion of k in k 1539342807.849 * [misc]backup-simplify: Simplify 0 into 0 1539342807.849 * [misc]backup-simplify: Simplify 1 into 1 1539342807.849 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342807.849 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.849 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342807.849 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.849 * [misc]backup-simplify: Simplify 2 into 2 1539342807.849 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.849 * [misc]backup-simplify: Simplify PI into PI 1539342807.850 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.850 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.850 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342807.850 * [misc]taylor: Taking taylor expansion of n in k 1539342807.850 * [misc]backup-simplify: Simplify n into n 1539342807.850 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342807.850 * [misc]taylor: Taking taylor expansion of k in k 1539342807.850 * [misc]backup-simplify: Simplify 0 into 0 1539342807.850 * [misc]backup-simplify: Simplify 1 into 1 1539342807.850 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342807.851 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342807.852 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342807.852 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342807.853 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342807.853 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539342807.853 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342807.854 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539342807.854 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539342807.855 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1539342807.855 * [misc]backup-simplify: Simplify 0 into 0 1539342807.856 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 k)) into 0 1539342807.856 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)))) into 0 1539342807.856 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (* PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (* (pow PI 2) (pow k 2))) 1539342807.857 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342807.858 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.858 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342807.862 * [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 1539342807.862 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342807.863 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342807.864 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539342807.866 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539342807.868 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342807.870 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +nan.0 (* (pow PI 2) (pow k 2)))) (+ (* 0 (* +nan.0 (* PI k))) (* 0 0))) into (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (pow k 2))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342807.870 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (pow k 2))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1539342807.870 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 2) (pow k 2))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1539342807.870 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342807.870 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342807.870 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 2) (pow k 2))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1539342807.870 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 2) (pow k 2))) in k 1539342807.870 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342807.870 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.870 * [misc]backup-simplify: Simplify 2 into 2 1539342807.870 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.870 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.870 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (pow k 2)) in k 1539342807.870 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539342807.870 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.870 * [misc]backup-simplify: Simplify PI into PI 1539342807.870 * [misc]taylor: Taking taylor expansion of (pow k 2) in k 1539342807.870 * [misc]taylor: Taking taylor expansion of k in k 1539342807.871 * [misc]backup-simplify: Simplify 0 into 0 1539342807.871 * [misc]backup-simplify: Simplify 1 into 1 1539342807.871 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342807.871 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342807.871 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342807.871 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.871 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342807.871 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342807.871 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342807.871 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342807.871 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.871 * [misc]backup-simplify: Simplify 2 into 2 1539342807.871 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.871 * [misc]backup-simplify: Simplify PI into PI 1539342807.871 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.872 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.872 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342807.872 * [misc]taylor: Taking taylor expansion of n in k 1539342807.872 * [misc]backup-simplify: Simplify n into n 1539342807.872 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342807.872 * [misc]taylor: Taking taylor expansion of k in k 1539342807.872 * [misc]backup-simplify: Simplify 0 into 0 1539342807.872 * [misc]backup-simplify: Simplify 1 into 1 1539342807.872 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342807.872 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342807.873 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342807.873 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342807.874 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342807.874 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342807.874 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342807.875 * [misc]backup-simplify: Simplify (* (pow PI 2) 1) into (pow PI 2) 1539342807.876 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342807.877 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1539342807.878 * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1539342807.879 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342807.880 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342807.880 * [misc]backup-simplify: Simplify 0 into 0 1539342807.881 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 k))) into 0 1539342807.881 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.882 * [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))) 1539342807.882 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342807.884 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.885 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342807.893 * [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 1539342807.893 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342807.894 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342807.895 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539342807.899 * [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 1539342807.902 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342807.904 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +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 (/ (* (sqrt 2) (* (pow PI 3) (pow k 3))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342807.904 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 3) (pow k 3))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1539342807.904 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 3) (pow k 3))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1539342807.904 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342807.904 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342807.905 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 3) (pow k 3))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 3) (pow k 3))) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.905 * [misc]backup-simplify: Simplify 2 into 2 1539342807.905 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.905 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.905 * [misc]taylor: Taking taylor expansion of (* (pow PI 3) (pow k 3)) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of (pow PI 3) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.905 * [misc]backup-simplify: Simplify PI into PI 1539342807.905 * [misc]taylor: Taking taylor expansion of (pow k 3) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of k in k 1539342807.905 * [misc]backup-simplify: Simplify 0 into 0 1539342807.905 * [misc]backup-simplify: Simplify 1 into 1 1539342807.905 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342807.905 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.905 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342807.905 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342807.906 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342807.906 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.906 * [misc]backup-simplify: Simplify 2 into 2 1539342807.906 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.906 * [misc]backup-simplify: Simplify PI into PI 1539342807.906 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.907 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.907 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342807.907 * [misc]taylor: Taking taylor expansion of n in k 1539342807.907 * [misc]backup-simplify: Simplify n into n 1539342807.907 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342807.907 * [misc]taylor: Taking taylor expansion of k in k 1539342807.907 * [misc]backup-simplify: Simplify 0 into 0 1539342807.907 * [misc]backup-simplify: Simplify 1 into 1 1539342807.907 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342807.908 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342807.908 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342807.909 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342807.909 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342807.909 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342807.910 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342807.910 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342807.910 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342807.911 * [misc]backup-simplify: Simplify (* (pow PI 3) 1) into (pow PI 3) 1539342807.912 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539342807.913 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1539342807.914 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1539342807.916 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342807.917 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1539342807.919 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342807.921 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1539342807.921 * [misc]backup-simplify: Simplify (- 0) into 0 1539342807.921 * [misc]backup-simplify: Simplify 0 into 0 1539342807.921 * [misc]backup-simplify: Simplify 0 into 0 1539342807.921 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1539342807.922 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.923 * [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))) 1539342807.925 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342807.927 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.929 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342807.942 * [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 1539342807.943 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342807.943 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342807.945 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 1539342807.951 * [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 1539342807.955 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342807.957 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +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 (/ (* (sqrt 2) (* (pow PI 4) (pow k 4))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342807.957 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 4) (pow k 4))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1539342807.957 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 4) (pow k 4))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342807.958 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342807.958 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 4) (pow k 4))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 4) (pow k 4))) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.958 * [misc]backup-simplify: Simplify 2 into 2 1539342807.958 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342807.958 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342807.958 * [misc]taylor: Taking taylor expansion of (* (pow PI 4) (pow k 4)) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of (pow PI 4) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.958 * [misc]backup-simplify: Simplify PI into PI 1539342807.958 * [misc]taylor: Taking taylor expansion of (pow k 4) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of k in k 1539342807.958 * [misc]backup-simplify: Simplify 0 into 0 1539342807.958 * [misc]backup-simplify: Simplify 1 into 1 1539342807.958 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342807.958 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342807.958 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342807.959 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342807.959 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342807.959 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342807.959 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342807.959 * [misc]taylor: Taking taylor expansion of 2 in k 1539342807.959 * [misc]backup-simplify: Simplify 2 into 2 1539342807.959 * [misc]taylor: Taking taylor expansion of PI in k 1539342807.959 * [misc]backup-simplify: Simplify PI into PI 1539342807.959 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342807.960 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342807.960 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342807.960 * [misc]taylor: Taking taylor expansion of n in k 1539342807.960 * [misc]backup-simplify: Simplify n into n 1539342807.960 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342807.960 * [misc]taylor: Taking taylor expansion of k in k 1539342807.960 * [misc]backup-simplify: Simplify 0 into 0 1539342807.960 * [misc]backup-simplify: Simplify 1 into 1 1539342807.960 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342807.961 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342807.961 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342807.962 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342807.962 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342807.963 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342807.963 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1539342807.964 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342807.964 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342807.964 * [misc]backup-simplify: Simplify (* (pow PI 4) 1) into (pow PI 4) 1539342807.965 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 4)) into (* (sqrt 2) (pow PI 4)) 1539342807.966 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 4)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 4)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1539342807.967 * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1539342807.969 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342807.970 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342807.971 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539342807.972 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342807.973 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342807.977 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342807.978 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342807.978 * [misc]backup-simplify: Simplify (- 0) into 0 1539342807.978 * [misc]backup-simplify: Simplify 0 into 0 1539342807.978 * [misc]backup-simplify: Simplify 0 into 0 1539342807.979 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k))))) into 0 1539342807.980 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.982 * [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))) 1539342807.982 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342807.985 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342807.988 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342808.007 * [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 1539342808.008 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342808.008 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342808.009 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 1539342808.019 * [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 1539342808.023 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342808.026 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +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 (/ (* (sqrt 2) (* (pow PI 5) (pow k 5))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342808.026 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 5) (pow k 5))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1539342808.026 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 5) (pow k 5))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1539342808.026 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342808.026 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342808.026 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 5) (pow k 5))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1539342808.026 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 5) (pow k 5))) in k 1539342808.026 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342808.026 * [misc]taylor: Taking taylor expansion of 2 in k 1539342808.026 * [misc]backup-simplify: Simplify 2 into 2 1539342808.026 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342808.027 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342808.027 * [misc]taylor: Taking taylor expansion of (* (pow PI 5) (pow k 5)) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of (pow PI 5) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.027 * [misc]backup-simplify: Simplify PI into PI 1539342808.027 * [misc]taylor: Taking taylor expansion of (pow k 5) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of k in k 1539342808.027 * [misc]backup-simplify: Simplify 0 into 0 1539342808.027 * [misc]backup-simplify: Simplify 1 into 1 1539342808.027 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342808.027 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342808.027 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342808.027 * [misc]taylor: Taking taylor expansion of 2 in k 1539342808.027 * [misc]backup-simplify: Simplify 2 into 2 1539342808.027 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.027 * [misc]backup-simplify: Simplify PI into PI 1539342808.027 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342808.028 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342808.028 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342808.028 * [misc]taylor: Taking taylor expansion of n in k 1539342808.028 * [misc]backup-simplify: Simplify n into n 1539342808.028 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342808.028 * [misc]taylor: Taking taylor expansion of k in k 1539342808.028 * [misc]backup-simplify: Simplify 0 into 0 1539342808.028 * [misc]backup-simplify: Simplify 1 into 1 1539342808.028 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342808.029 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342808.029 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342808.030 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342808.030 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342808.031 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342808.031 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1539342808.032 * [misc]backup-simplify: Simplify (* PI (pow PI 4)) into (pow PI 5) 1539342808.032 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342808.032 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342808.032 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342808.033 * [misc]backup-simplify: Simplify (* (pow PI 5) 1) into (pow PI 5) 1539342808.034 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 5)) into (* (sqrt 2) (pow PI 5)) 1539342808.035 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 5)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 5)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1539342808.035 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342808.036 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342808.037 * [misc]backup-simplify: Simplify (+ (* (pow PI 2) 0) (* 0 1)) into 0 1539342808.038 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539342808.040 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342808.042 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1539342808.042 * [misc]backup-simplify: Simplify (- 0) into 0 1539342808.042 * [misc]backup-simplify: Simplify 0 into 0 1539342808.043 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539342808.044 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342808.046 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342808.050 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342808.051 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 1539342808.051 * [misc]backup-simplify: Simplify (- 0) into 0 1539342808.051 * [misc]backup-simplify: Simplify 0 into 0 1539342808.051 * [misc]backup-simplify: Simplify 0 into 0 1539342808.052 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))))) into 0 1539342808.053 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (* PI k) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342808.055 * [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))) 1539342808.057 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342808.060 * [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 1539342808.063 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342808.094 * [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 1539342808.095 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342808.095 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342808.096 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 1539342808.108 * [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 1539342808.113 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 1539342808.116 * [misc]backup-simplify: Simplify (+ (* (/ (sqrt 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* +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 (/ (* (sqrt 2) (* (pow PI 6) (pow k 6))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342808.116 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt 2) (* (pow PI 6) (pow k 6))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) in k 1539342808.116 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt 2) (* (pow PI 6) (pow k 6))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 1539342808.116 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342808.117 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342808.117 * [misc]taylor: Taking taylor expansion of (/ (* (sqrt 2) (* (pow PI 6) (pow k 6))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow PI 6) (pow k 6))) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of 2 in k 1539342808.117 * [misc]backup-simplify: Simplify 2 into 2 1539342808.117 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342808.117 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342808.117 * [misc]taylor: Taking taylor expansion of (* (pow PI 6) (pow k 6)) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of (pow PI 6) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.117 * [misc]backup-simplify: Simplify PI into PI 1539342808.117 * [misc]taylor: Taking taylor expansion of (pow k 6) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of k in k 1539342808.117 * [misc]backup-simplify: Simplify 0 into 0 1539342808.117 * [misc]backup-simplify: Simplify 1 into 1 1539342808.117 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342808.117 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342808.117 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342808.117 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342808.118 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342808.118 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342808.118 * [misc]taylor: Taking taylor expansion of 2 in k 1539342808.118 * [misc]backup-simplify: Simplify 2 into 2 1539342808.118 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.118 * [misc]backup-simplify: Simplify PI into PI 1539342808.118 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342808.119 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342808.119 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342808.119 * [misc]taylor: Taking taylor expansion of n in k 1539342808.119 * [misc]backup-simplify: Simplify n into n 1539342808.119 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342808.119 * [misc]taylor: Taking taylor expansion of k in k 1539342808.119 * [misc]backup-simplify: Simplify 0 into 0 1539342808.119 * [misc]backup-simplify: Simplify 1 into 1 1539342808.119 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342808.119 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342808.120 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342808.120 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342808.121 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342808.121 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342808.122 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342808.123 * [misc]backup-simplify: Simplify (* (pow PI 3) (pow PI 3)) into (pow PI 6) 1539342808.123 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342808.123 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342808.123 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342808.124 * [misc]backup-simplify: Simplify (* (pow PI 6) 1) into (pow PI 6) 1539342808.124 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 6)) into (* (sqrt 2) (pow PI 6)) 1539342808.126 * [misc]backup-simplify: Simplify (/ (* (sqrt 2) (pow PI 6)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (* (sqrt 2) (pow PI 6)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1539342808.127 * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1539342808.128 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342808.130 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 1539342808.135 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (pow (/ 1 k) 3) (pow (/ 1 n) 2))) (+ (* (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (pow (/ 1 k) 2) (/ 1 n))) (* (- (* +nan.0 (/ (* (sqrt 2) PI) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (pow n 2) (pow k 3))))) (- (+ (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* n (pow k 2)))))))))) 1539342808.136 * [misc]backup-simplify: Simplify (/ (sqrt (* (* 2 (/ 1 (- n))) PI)) (* (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) into (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) 1539342808.136 * [misc]approximate: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) in (n k) around 0 1539342808.136 * [misc]taylor: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) in k 1539342808.136 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1539342808.136 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342808.136 * [misc]taylor: Taking taylor expansion of -2 in k 1539342808.136 * [misc]backup-simplify: Simplify -2 into -2 1539342808.136 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342808.136 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.136 * [misc]backup-simplify: Simplify PI into PI 1539342808.136 * [misc]taylor: Taking taylor expansion of n in k 1539342808.136 * [misc]backup-simplify: Simplify n into n 1539342808.136 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342808.136 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342808.136 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539342808.136 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1539342808.137 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1539342808.137 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539342808.137 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in k 1539342808.137 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1539342808.137 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1539342808.137 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1539342808.137 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in k 1539342808.137 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342808.137 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342808.137 * [misc]taylor: Taking taylor expansion of k in k 1539342808.137 * [misc]backup-simplify: Simplify 0 into 0 1539342808.137 * [misc]backup-simplify: Simplify 1 into 1 1539342808.137 * [misc]backup-simplify: Simplify (/ -1/2 1) into -1/2 1539342808.137 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539342808.137 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342808.137 * [misc]taylor: Taking taylor expansion of -2 in k 1539342808.137 * [misc]backup-simplify: Simplify -2 into -2 1539342808.137 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342808.137 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.137 * [misc]backup-simplify: Simplify PI into PI 1539342808.138 * [misc]taylor: Taking taylor expansion of n in k 1539342808.138 * [misc]backup-simplify: Simplify n into n 1539342808.138 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342808.138 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342808.138 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539342808.138 * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) 1539342808.138 * [misc]backup-simplify: Simplify (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1539342808.138 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342808.138 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342808.138 * [misc]taylor: Taking taylor expansion of -1 in k 1539342808.138 * [misc]backup-simplify: Simplify -1 into -1 1539342808.138 * [misc]taylor: Taking taylor expansion of k in k 1539342808.138 * [misc]backup-simplify: Simplify 0 into 0 1539342808.138 * [misc]backup-simplify: Simplify 1 into 1 1539342808.138 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342808.139 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.139 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342808.140 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 0) into 0 1539342808.140 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1539342808.140 * [misc]backup-simplify: Simplify (/ (sqrt (* -2 (/ PI n))) (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1539342808.140 * [misc]taylor: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) in n 1539342808.140 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342808.140 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342808.140 * [misc]taylor: Taking taylor expansion of -2 in n 1539342808.140 * [misc]backup-simplify: Simplify -2 into -2 1539342808.140 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342808.140 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.140 * [misc]backup-simplify: Simplify PI into PI 1539342808.140 * [misc]taylor: Taking taylor expansion of n in n 1539342808.140 * [misc]backup-simplify: Simplify 0 into 0 1539342808.141 * [misc]backup-simplify: Simplify 1 into 1 1539342808.141 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342808.141 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342808.141 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.142 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342808.142 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in n 1539342808.142 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1539342808.142 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1539342808.142 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1539342808.142 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in n 1539342808.142 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342808.142 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342808.142 * [misc]taylor: Taking taylor expansion of k in n 1539342808.142 * [misc]backup-simplify: Simplify k into k 1539342808.142 * [misc]backup-simplify: Simplify (/ -1/2 k) into (/ -1/2 k) 1539342808.142 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342808.142 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342808.142 * [misc]taylor: Taking taylor expansion of -2 in n 1539342808.142 * [misc]backup-simplify: Simplify -2 into -2 1539342808.142 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342808.142 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.142 * [misc]backup-simplify: Simplify PI into PI 1539342808.142 * [misc]taylor: Taking taylor expansion of n in n 1539342808.143 * [misc]backup-simplify: Simplify 0 into 0 1539342808.143 * [misc]backup-simplify: Simplify 1 into 1 1539342808.143 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342808.143 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342808.144 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342808.144 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342808.145 * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342808.145 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342808.145 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539342808.145 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539342808.145 * [misc]taylor: Taking taylor expansion of -1 in n 1539342808.145 * [misc]backup-simplify: Simplify -1 into -1 1539342808.145 * [misc]taylor: Taking taylor expansion of k in n 1539342808.146 * [misc]backup-simplify: Simplify k into k 1539342808.146 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539342808.146 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539342808.146 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539342808.146 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539342808.147 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539342808.147 * [misc]backup-simplify: Simplify (/ (* +nan.0 PI) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) 1539342808.147 * [misc]taylor: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k)))) in n 1539342808.148 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342808.148 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342808.148 * [misc]taylor: Taking taylor expansion of -2 in n 1539342808.148 * [misc]backup-simplify: Simplify -2 into -2 1539342808.148 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342808.148 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.148 * [misc]backup-simplify: Simplify PI into PI 1539342808.148 * [misc]taylor: Taking taylor expansion of n in n 1539342808.148 * [misc]backup-simplify: Simplify 0 into 0 1539342808.148 * [misc]backup-simplify: Simplify 1 into 1 1539342808.148 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342808.148 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342808.148 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.149 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342808.149 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in n 1539342808.149 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1539342808.149 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1539342808.149 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1539342808.149 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in n 1539342808.149 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342808.149 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342808.149 * [misc]taylor: Taking taylor expansion of k in n 1539342808.149 * [misc]backup-simplify: Simplify k into k 1539342808.149 * [misc]backup-simplify: Simplify (/ -1/2 k) into (/ -1/2 k) 1539342808.149 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342808.149 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342808.149 * [misc]taylor: Taking taylor expansion of -2 in n 1539342808.150 * [misc]backup-simplify: Simplify -2 into -2 1539342808.150 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342808.150 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.150 * [misc]backup-simplify: Simplify PI into PI 1539342808.150 * [misc]taylor: Taking taylor expansion of n in n 1539342808.150 * [misc]backup-simplify: Simplify 0 into 0 1539342808.150 * [misc]backup-simplify: Simplify 1 into 1 1539342808.150 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342808.150 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342808.151 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342808.151 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342808.152 * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342808.152 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342808.152 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539342808.152 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539342808.153 * [misc]taylor: Taking taylor expansion of -1 in n 1539342808.153 * [misc]backup-simplify: Simplify -1 into -1 1539342808.153 * [misc]taylor: Taking taylor expansion of k in n 1539342808.153 * [misc]backup-simplify: Simplify k into k 1539342808.153 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539342808.153 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539342808.153 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539342808.153 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539342808.154 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539342808.154 * [misc]backup-simplify: Simplify (/ (* +nan.0 PI) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) 1539342808.155 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342808.155 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342808.155 * [misc]taylor: Taking taylor expansion of (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.155 * [misc]backup-simplify: Simplify PI into PI 1539342808.155 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342808.155 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342808.155 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539342808.155 * [misc]taylor: Taking taylor expansion of -2 in k 1539342808.155 * [misc]backup-simplify: Simplify -2 into -2 1539342808.155 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.155 * [misc]backup-simplify: Simplify PI into PI 1539342808.155 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342808.156 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342808.156 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342808.156 * [misc]taylor: Taking taylor expansion of n in k 1539342808.156 * [misc]backup-simplify: Simplify n into n 1539342808.156 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342808.156 * [misc]taylor: Taking taylor expansion of k in k 1539342808.156 * [misc]backup-simplify: Simplify 0 into 0 1539342808.156 * [misc]backup-simplify: Simplify 1 into 1 1539342808.156 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342808.157 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539342808.157 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539342808.158 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) 1539342808.158 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342808.158 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342808.158 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342808.158 * [misc]taylor: Taking taylor expansion of -1 in k 1539342808.158 * [misc]backup-simplify: Simplify -1 into -1 1539342808.158 * [misc]taylor: Taking taylor expansion of k in k 1539342808.158 * [misc]backup-simplify: Simplify 0 into 0 1539342808.158 * [misc]backup-simplify: Simplify 1 into 1 1539342808.159 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342808.159 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.159 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342808.160 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 1539342808.161 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342808.161 * [misc]backup-simplify: Simplify (/ PI (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342808.162 * [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))))) 1539342808.163 * [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))))) 1539342808.164 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342808.164 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342808.166 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342808.167 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342808.168 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342808.170 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539342808.170 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1/2 k) (/ 0 k)))) into 0 1539342808.171 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342808.172 * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539342808.173 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342808.174 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) (* 0 (sqrt (/ -1 k)))) into 0 1539342808.176 * [misc]backup-simplify: Simplify (- (/ (* +nan.0 (pow PI 2)) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (+ (* (* +nan.0 (/ PI (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) (/ 0 (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))))) into (- (* +nan.0 (/ (pow PI 2) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))))) 1539342808.176 * [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 1539342808.176 * [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 1539342808.176 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342808.176 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342808.176 * [misc]taylor: Taking taylor expansion of (/ (pow PI 2) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.176 * [misc]backup-simplify: Simplify PI into PI 1539342808.176 * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342808.176 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342808.176 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539342808.176 * [misc]taylor: Taking taylor expansion of -2 in k 1539342808.176 * [misc]backup-simplify: Simplify -2 into -2 1539342808.176 * [misc]taylor: Taking taylor expansion of PI in k 1539342808.176 * [misc]backup-simplify: Simplify PI into PI 1539342808.176 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342808.177 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342808.177 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342808.177 * [misc]taylor: Taking taylor expansion of n in k 1539342808.177 * [misc]backup-simplify: Simplify n into n 1539342808.177 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342808.177 * [misc]taylor: Taking taylor expansion of k in k 1539342808.177 * [misc]backup-simplify: Simplify 0 into 0 1539342808.177 * [misc]backup-simplify: Simplify 1 into 1 1539342808.177 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342808.177 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539342808.178 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539342808.178 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) 1539342808.178 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342808.178 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342808.178 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342808.178 * [misc]taylor: Taking taylor expansion of -1 in k 1539342808.178 * [misc]backup-simplify: Simplify -1 into -1 1539342808.178 * [misc]taylor: Taking taylor expansion of k in k 1539342808.178 * [misc]backup-simplify: Simplify 0 into 0 1539342808.178 * [misc]backup-simplify: Simplify 1 into 1 1539342808.179 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342808.179 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.179 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342808.179 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342808.179 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 1539342808.180 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342808.180 * [misc]backup-simplify: Simplify (/ (pow PI 2) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (pow PI 2) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342808.181 * [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))))) 1539342808.182 * [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)))))) 1539342808.182 * [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)))))) 1539342808.182 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539342808.183 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539342808.184 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342808.185 * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539342808.186 * [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)))))) 1539342808.186 * [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)))))) 1539342808.188 * [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 (/ (pow PI 2) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) n))) (- (+ (* +nan.0 (/ PI (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ PI (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))))))) 1539342808.188 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1) 1539342808.189 * [misc]backup-simplify: Simplify (sqrt (* (* 2 n) PI)) into (* (sqrt 2) (sqrt (* n PI))) 1539342808.189 * [misc]approximate: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in (n) around 0 1539342808.189 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1539342808.189 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342808.189 * [misc]taylor: Taking taylor expansion of 2 in n 1539342808.189 * [misc]backup-simplify: Simplify 2 into 2 1539342808.189 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342808.189 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342808.189 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1539342808.189 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342808.189 * [misc]taylor: Taking taylor expansion of n in n 1539342808.189 * [misc]backup-simplify: Simplify 0 into 0 1539342808.189 * [misc]backup-simplify: Simplify 1 into 1 1539342808.189 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.189 * [misc]backup-simplify: Simplify PI into PI 1539342808.189 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342808.190 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342808.190 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.190 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342808.190 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1539342808.190 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342808.190 * [misc]taylor: Taking taylor expansion of 2 in n 1539342808.190 * [misc]backup-simplify: Simplify 2 into 2 1539342808.190 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342808.190 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342808.190 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1539342808.190 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342808.190 * [misc]taylor: Taking taylor expansion of n in n 1539342808.190 * [misc]backup-simplify: Simplify 0 into 0 1539342808.190 * [misc]backup-simplify: Simplify 1 into 1 1539342808.190 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.190 * [misc]backup-simplify: Simplify PI into PI 1539342808.191 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342808.191 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342808.191 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.191 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342808.192 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342808.192 * [misc]backup-simplify: Simplify 0 into 0 1539342808.192 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342808.193 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342808.193 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342808.194 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342808.195 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342808.196 * [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)))) 1539342808.197 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1539342808.198 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342808.200 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539342808.200 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342808.204 * [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)))) 1539342808.205 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1539342808.209 * [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))))))))) 1539342808.210 * [misc]backup-simplify: Simplify (sqrt (* (* 2 (/ 1 n)) PI)) into (* (sqrt 2) (sqrt (/ PI n))) 1539342808.210 * [misc]approximate: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in (n) around 0 1539342808.210 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 1539342808.210 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342808.210 * [misc]taylor: Taking taylor expansion of 2 in n 1539342808.210 * [misc]backup-simplify: Simplify 2 into 2 1539342808.210 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342808.210 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342808.210 * [misc]taylor: Taking taylor expansion of (sqrt (/ PI n)) in n 1539342808.210 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342808.210 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.210 * [misc]backup-simplify: Simplify PI into PI 1539342808.210 * [misc]taylor: Taking taylor expansion of n in n 1539342808.210 * [misc]backup-simplify: Simplify 0 into 0 1539342808.210 * [misc]backup-simplify: Simplify 1 into 1 1539342808.211 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342808.211 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.211 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342808.211 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 1539342808.211 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342808.211 * [misc]taylor: Taking taylor expansion of 2 in n 1539342808.212 * [misc]backup-simplify: Simplify 2 into 2 1539342808.212 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342808.212 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342808.212 * [misc]taylor: Taking taylor expansion of (sqrt (/ PI n)) in n 1539342808.212 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342808.212 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.212 * [misc]backup-simplify: Simplify PI into PI 1539342808.212 * [misc]taylor: Taking taylor expansion of n in n 1539342808.212 * [misc]backup-simplify: Simplify 0 into 0 1539342808.212 * [misc]backup-simplify: Simplify 1 into 1 1539342808.212 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342808.213 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.213 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342808.213 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342808.213 * [misc]backup-simplify: Simplify 0 into 0 1539342808.215 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342808.215 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342808.216 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342808.217 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342808.218 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342808.220 * [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)))) 1539342808.221 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1539342808.221 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342808.223 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539342808.223 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342808.225 * [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)))) 1539342808.226 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1539342808.228 * [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))))))) 1539342808.229 * [misc]backup-simplify: Simplify (sqrt (* (* 2 (/ 1 (- n))) PI)) into (sqrt (* -2 (/ PI n))) 1539342808.229 * [misc]approximate: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in (n) around 0 1539342808.229 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342808.229 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342808.229 * [misc]taylor: Taking taylor expansion of -2 in n 1539342808.229 * [misc]backup-simplify: Simplify -2 into -2 1539342808.229 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342808.229 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.229 * [misc]backup-simplify: Simplify PI into PI 1539342808.229 * [misc]taylor: Taking taylor expansion of n in n 1539342808.229 * [misc]backup-simplify: Simplify 0 into 0 1539342808.229 * [misc]backup-simplify: Simplify 1 into 1 1539342808.229 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342808.229 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342808.229 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.230 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342808.230 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342808.230 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342808.230 * [misc]taylor: Taking taylor expansion of -2 in n 1539342808.230 * [misc]backup-simplify: Simplify -2 into -2 1539342808.230 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342808.230 * [misc]taylor: Taking taylor expansion of PI in n 1539342808.230 * [misc]backup-simplify: Simplify PI into PI 1539342808.230 * [misc]taylor: Taking taylor expansion of n in n 1539342808.230 * [misc]backup-simplify: Simplify 0 into 0 1539342808.230 * [misc]backup-simplify: Simplify 1 into 1 1539342808.230 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342808.230 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342808.230 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342808.231 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342808.231 * [misc]backup-simplify: Simplify 0 into 0 1539342808.231 * [misc]backup-simplify: Simplify (* +nan.0 PI) into (* +nan.0 PI) 1539342808.232 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342808.232 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342808.233 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342808.233 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 2)) into (* +nan.0 (pow PI 2)) 1539342808.234 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342808.235 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342808.236 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539342808.236 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 3)) into (* +nan.0 (pow PI 3)) 1539342808.237 * [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))))))) 1539342808.237 * * * [misc]progress: simplifying candidates 1539342808.237 * * * * [misc]progress: [ 1 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 2 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 3 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 4 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 5 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 6 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 7 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 8 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 9 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 10 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 11 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 12 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 13 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 14 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 15 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 16 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 17 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 18 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 19 / 64 ] simplifiying candidate # 1539342808.238 * * * * [misc]progress: [ 20 / 64 ] simplifiying candidate # 1539342808.238 * [enter]simplify: Simplifying (- (log (sqrt (* (* 2 n) PI))) (+ (log (sqrt k)) (* (log (* PI (* n 2))) (/ k 2)))) 1539342808.238 * * [misc]simplify: iters left: 6 (17 enodes) 1539342808.241 * * [misc]simplify: iters left: 5 (33 enodes) 1539342808.246 * * [misc]simplify: iters left: 4 (60 enodes) 1539342808.260 * * [misc]simplify: iters left: 3 (142 enodes) 1539342808.287 * * [misc]simplify: iters left: 2 (355 enodes) 1539342808.402 * [exit]simplify: Simplified to (- (log (sqrt (* (* 2 n) PI))) (+ (+ (log (sqrt k)) (* (log 2) (/ k 2))) (* (/ k 2) (log (* PI n))))) 1539342808.402 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* 2 n) PI))) (+ (+ (log (sqrt k)) (* (log 2) (/ k 2))) (* (/ k 2) (log (* PI n))))))) 1539342808.402 * * * * [misc]progress: [ 21 / 64 ] simplifiying candidate # 1539342808.402 * [enter]simplify: Simplifying (- (log (sqrt (* (* 2 n) PI))) (+ (log (sqrt k)) (* (log (* PI (* n 2))) (/ k 2)))) 1539342808.402 * * [misc]simplify: iters left: 6 (17 enodes) 1539342808.405 * * [misc]simplify: iters left: 5 (33 enodes) 1539342808.410 * * [misc]simplify: iters left: 4 (60 enodes) 1539342808.429 * * [misc]simplify: iters left: 3 (142 enodes) 1539342808.461 * * [misc]simplify: iters left: 2 (355 enodes) 1539342808.604 * [exit]simplify: Simplified to (- (log (sqrt (* (* 2 n) PI))) (+ (+ (log (sqrt k)) (* (log 2) (/ k 2))) (* (/ k 2) (log (* PI n))))) 1539342808.604 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* 2 n) PI))) (+ (+ (log (sqrt k)) (* (log 2) (/ k 2))) (* (/ k 2) (log (* PI n))))))) 1539342808.604 * * * * [misc]progress: [ 22 / 64 ] simplifiying candidate # 1539342808.604 * [enter]simplify: Simplifying (- (log (sqrt (* (* 2 n) PI))) (+ (log (sqrt k)) (log (pow (* PI (* n 2)) (/ k 2))))) 1539342808.604 * * [misc]simplify: iters left: 6 (17 enodes) 1539342808.609 * * [misc]simplify: iters left: 5 (29 enodes) 1539342808.618 * * [misc]simplify: iters left: 4 (54 enodes) 1539342808.634 * * [misc]simplify: iters left: 3 (120 enodes) 1539342808.659 * * [misc]simplify: iters left: 2 (312 enodes) 1539342808.768 * [exit]simplify: Simplified to (- (log (sqrt (* (* 2 n) PI))) (+ (+ (* (log 2) (/ k 2)) (log (sqrt k))) (/ (log (* PI n)) (/ 2 k)))) 1539342808.768 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* 2 n) PI))) (+ (+ (* (log 2) (/ k 2)) (log (sqrt k))) (/ (log (* PI n)) (/ 2 k)))))) 1539342808.768 * * * * [misc]progress: [ 23 / 64 ] simplifiying candidate # 1539342808.768 * [enter]simplify: Simplifying (- (log (sqrt (* (* 2 n) PI))) (log (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342808.769 * * [misc]simplify: iters left: 6 (16 enodes) 1539342808.771 * * [misc]simplify: iters left: 5 (27 enodes) 1539342808.774 * * [misc]simplify: iters left: 4 (40 enodes) 1539342808.788 * * [misc]simplify: iters left: 3 (70 enodes) 1539342808.810 * * [misc]simplify: iters left: 2 (193 enodes) 1539342808.958 * [exit]simplify: Simplified to (- (log (sqrt (* (* 2 n) PI))) (+ (* (log (* 2 n)) (/ k 2)) (+ (* (/ k 2) (log PI)) (log (sqrt k))))) 1539342808.958 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (log (sqrt (* (* 2 n) PI))) (+ (* (log (* 2 n)) (/ k 2)) (+ (* (/ k 2) (log PI)) (log (sqrt k))))))) 1539342808.958 * * * * [misc]progress: [ 24 / 64 ] simplifiying candidate # 1539342808.958 * * * * [misc]progress: [ 25 / 64 ] simplifiying candidate # 1539342808.959 * * * * [misc]progress: [ 26 / 64 ] simplifiying candidate # 1539342808.959 * [enter]simplify: Simplifying (/ (* (* (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI))) (sqrt (* (* 2 n) PI))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* PI (* n 2)) (/ k 2)) (pow (* PI (* n 2)) (/ k 2))) (pow (* PI (* n 2)) (/ k 2))))) 1539342808.959 * * [misc]simplify: iters left: 6 (20 enodes) 1539342808.966 * * [misc]simplify: iters left: 5 (39 enodes) 1539342808.981 * * [misc]simplify: iters left: 4 (167 enodes) 1539342809.135 * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (* (/ (sqrt k) (* 2 n)) (/ k PI))) (pow (pow (* (* 2 n) PI) (/ k 2)) 3)) 1539342809.135 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (/ (/ (sqrt (* (* 2 n) PI)) (* (/ (sqrt k) (* 2 n)) (/ k PI))) (pow (pow (* (* 2 n) PI) (/ k 2)) 3)))) 1539342809.135 * * * * [misc]progress: [ 27 / 64 ] simplifiying candidate # 1539342809.136 * [enter]simplify: Simplifying (/ (* (* (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI))) (sqrt (* (* 2 n) PI))) (* (* (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.136 * * [misc]simplify: iters left: 6 (18 enodes) 1539342809.142 * * [misc]simplify: iters left: 5 (38 enodes) 1539342809.160 * * [misc]simplify: iters left: 4 (167 enodes) 1539342809.329 * [exit]simplify: Simplified to (* (/ (sqrt (* (* 2 n) PI)) (* (pow (* (* 2 n) PI) (/ k 2)) k)) (/ (/ (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ k 2))) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2))))) 1539342809.329 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (sqrt (* (* 2 n) PI)) (* (pow (* (* 2 n) PI) (/ k 2)) k)) (/ (/ (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ k 2))) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2))))))) 1539342809.329 * * * * [misc]progress: [ 28 / 64 ] simplifiying candidate # 1539342809.329 * * * * [misc]progress: [ 29 / 64 ] simplifiying candidate # 1539342809.329 * * * * [misc]progress: [ 30 / 64 ] simplifiying candidate # 1539342809.329 * * * * [misc]progress: [ 31 / 64 ] simplifiying candidate # 1539342809.329 * * * * [misc]progress: [ 32 / 64 ] simplifiying candidate # 1539342809.330 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt k)) 1539342809.330 * * [misc]simplify: iters left: 6 (11 enodes) 1539342809.333 * * [misc]simplify: iters left: 5 (17 enodes) 1539342809.338 * * [misc]simplify: iters left: 4 (25 enodes) 1539342809.344 * * [misc]simplify: iters left: 3 (27 enodes) 1539342809.352 * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* PI n) 2))) (/ (sqrt k) (cbrt (sqrt (* (* PI n) 2))))) 1539342809.352 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (sqrt (* (* PI n) 2))) (/ (sqrt k) (cbrt (sqrt (* (* PI n) 2))))) (/ (cbrt (sqrt (* (* 2 n) PI))) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.352 * [enter]simplify: Simplifying (/ (cbrt (sqrt (* (* 2 n) PI))) (pow (* PI (* n 2)) (/ k 2))) 1539342809.352 * * [misc]simplify: iters left: 6 (13 enodes) 1539342809.356 * * [misc]simplify: iters left: 5 (18 enodes) 1539342809.361 * * [misc]simplify: iters left: 4 (22 enodes) 1539342809.367 * * [misc]simplify: iters left: 3 (24 enodes) 1539342809.373 * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (pow (* (* 2 n) PI) (/ k 2))) 1539342809.373 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt k)) (/ (cbrt (sqrt (* (* 2 n) PI))) (pow (* (* 2 n) PI) (/ k 2))))) 1539342809.373 * * * * [misc]progress: [ 33 / 64 ] simplifiying candidate # 1539342809.373 * [enter]simplify: Simplifying (/ (sqrt (* 2 n)) (sqrt k)) 1539342809.373 * * [misc]simplify: iters left: 5 (7 enodes) 1539342809.375 * * [misc]simplify: iters left: 4 (8 enodes) 1539342809.377 * [exit]simplify: Simplified to (/ (sqrt (* 2 n)) (sqrt k)) 1539342809.377 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* 2 n)) (sqrt k)) (/ (sqrt PI) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.378 * [enter]simplify: Simplifying (/ (sqrt PI) (pow (* PI (* n 2)) (/ k 2))) 1539342809.378 * * [misc]simplify: iters left: 6 (10 enodes) 1539342809.381 * * [misc]simplify: iters left: 5 (14 enodes) 1539342809.385 * * [misc]simplify: iters left: 4 (20 enodes) 1539342809.390 * * [misc]simplify: iters left: 3 (21 enodes) 1539342809.395 * [exit]simplify: Simplified to (/ (sqrt PI) (pow (* (* n 2) PI) (/ k 2))) 1539342809.395 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* 2 n)) (sqrt k)) (/ (sqrt PI) (pow (* (* n 2) PI) (/ k 2))))) 1539342809.395 * * * * [misc]progress: [ 34 / 64 ] simplifiying candidate # 1539342809.395 * [enter]simplify: Simplifying (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt k)) 1539342809.396 * * [misc]simplify: iters left: 6 (10 enodes) 1539342809.398 * * [misc]simplify: iters left: 5 (14 enodes) 1539342809.402 * * [misc]simplify: iters left: 4 (20 enodes) 1539342809.407 * * [misc]simplify: iters left: 3 (22 enodes) 1539342809.409 * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* PI 2) n))) (sqrt k)) 1539342809.409 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (sqrt (* (* PI 2) n))) (sqrt k)) (/ (sqrt (sqrt (* (* 2 n) PI))) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.410 * [enter]simplify: Simplifying (/ (sqrt (sqrt (* (* 2 n) PI))) (pow (* PI (* n 2)) (/ k 2))) 1539342809.410 * * [misc]simplify: iters left: 6 (13 enodes) 1539342809.411 * * [misc]simplify: iters left: 5 (18 enodes) 1539342809.414 * * [misc]simplify: iters left: 4 (22 enodes) 1539342809.416 * * [misc]simplify: iters left: 3 (24 enodes) 1539342809.419 * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (pow (* (* 2 n) PI) (/ k 2))) 1539342809.419 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt k)) (/ (sqrt (sqrt (* (* 2 n) PI))) (pow (* (* 2 n) PI) (/ k 2))))) 1539342809.419 * * * * [misc]progress: [ 35 / 64 ] simplifiying candidate # 1539342809.419 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1539342809.419 * * [misc]simplify: iters left: 3 (4 enodes) 1539342809.420 * * [misc]simplify: iters left: 2 (6 enodes) 1539342809.421 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1539342809.421 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt k)) (/ (sqrt (* (* 2 n) PI)) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.421 * [enter]simplify: Simplifying (/ (sqrt (* (* 2 n) PI)) (pow (* PI (* n 2)) (/ k 2))) 1539342809.421 * * [misc]simplify: iters left: 6 (12 enodes) 1539342809.423 * * [misc]simplify: iters left: 5 (17 enodes) 1539342809.425 * * [misc]simplify: iters left: 4 (21 enodes) 1539342809.427 * * [misc]simplify: iters left: 3 (22 enodes) 1539342809.430 * [exit]simplify: Simplified to (/ (sqrt (* (* PI n) 2)) (pow (* (* PI n) 2) (/ k 2))) 1539342809.430 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (/ (sqrt (* (* PI n) 2)) (pow (* (* PI n) 2) (/ k 2))))) 1539342809.430 * * * * [misc]progress: [ 36 / 64 ] simplifiying candidate # 1539342809.430 * * * * [misc]progress: [ 37 / 64 ] simplifiying candidate # 1539342809.430 * * * * [misc]progress: [ 38 / 64 ] simplifiying candidate # 1539342809.430 * * * * [misc]progress: [ 39 / 64 ] simplifiying candidate # 1539342809.430 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1539342809.430 * * [misc]simplify: iters left: 5 (8 enodes) 1539342809.431 * * [misc]simplify: iters left: 4 (12 enodes) 1539342809.433 * * [misc]simplify: iters left: 3 (18 enodes) 1539342809.435 * * [misc]simplify: iters left: 2 (20 enodes) 1539342809.437 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1539342809.438 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt (* (* 2 n) PI)) (sqrt k)) (pow (* (* 2 n) PI) (/ k 2)))) 1539342809.438 * * * * [misc]progress: [ 40 / 64 ] simplifiying candidate # 1539342809.438 * [enter]simplify: Simplifying (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342809.438 * * [misc]simplify: iters left: 6 (8 enodes) 1539342809.439 * * [misc]simplify: iters left: 5 (12 enodes) 1539342809.441 * * [misc]simplify: iters left: 4 (18 enodes) 1539342809.443 * * [misc]simplify: iters left: 3 (20 enodes) 1539342809.445 * [exit]simplify: Simplified to (* (cbrt (sqrt (* 2 (* PI n)))) (cbrt (sqrt (* 2 (* PI n))))) 1539342809.445 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (sqrt (* 2 (* PI n)))) (cbrt (sqrt (* 2 (* PI n))))) (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))))) 1539342809.445 * * * * [misc]progress: [ 41 / 64 ] simplifiying candidate # 1539342809.445 * [enter]simplify: Simplifying (sqrt (* 2 n)) 1539342809.445 * * [misc]simplify: iters left: 3 (4 enodes) 1539342809.446 * * [misc]simplify: iters left: 2 (5 enodes) 1539342809.446 * [exit]simplify: Simplified to (sqrt (* 2 n)) 1539342809.447 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* 2 n)) (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt PI)))) 1539342809.447 * * * * [misc]progress: [ 42 / 64 ] simplifiying candidate # 1539342809.447 * [enter]simplify: Simplifying (sqrt (sqrt (* (* 2 n) PI))) 1539342809.447 * * [misc]simplify: iters left: 6 (7 enodes) 1539342809.448 * * [misc]simplify: iters left: 5 (11 enodes) 1539342809.451 * * [misc]simplify: iters left: 4 (17 enodes) 1539342809.456 * * [misc]simplify: iters left: 3 (19 enodes) 1539342809.461 * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) 1539342809.461 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (sqrt (* (* 2 n) PI))) (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))))) 1539342809.461 * * * * [misc]progress: [ 43 / 64 ] simplifiying candidate # 1539342809.461 * * * * [misc]progress: [ 44 / 64 ] simplifiying candidate # 1539342809.461 * * * * [misc]progress: [ 45 / 64 ] simplifiying candidate # 1539342809.462 * * * * [misc]progress: [ 46 / 64 ] simplifiying candidate # 1539342809.462 * * * * [misc]progress: [ 47 / 64 ] simplifiying candidate # 1539342809.462 * * * * [misc]progress: [ 48 / 64 ] simplifiying candidate # 1539342809.462 * * * * [misc]progress: [ 49 / 64 ] simplifiying candidate # 1539342809.462 * * * * [misc]progress: [ 50 / 64 ] simplifiying candidate # 1539342809.462 * [enter]simplify: Simplifying (sqrt (* 2 n)) 1539342809.462 * * [misc]simplify: iters left: 3 (4 enodes) 1539342809.463 * * [misc]simplify: iters left: 2 (5 enodes) 1539342809.465 * [exit]simplify: Simplified to (sqrt (* 2 n)) 1539342809.465 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (sqrt (* 2 n)) (sqrt PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.465 * * * * [misc]progress: [ 51 / 64 ] simplifiying candidate # 1539342809.465 * * * * [misc]progress: [ 52 / 64 ] simplifiying candidate # 1539342809.465 * * * * [misc]progress: [ 53 / 64 ] simplifiying candidate # 1539342809.465 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342809.465 * * [misc]simplify: iters left: 4 (5 enodes) 1539342809.467 * * [misc]simplify: iters left: 3 (9 enodes) 1539342809.469 * * [misc]simplify: iters left: 2 (15 enodes) 1539342809.473 * * [misc]simplify: iters left: 1 (17 enodes) 1539342809.477 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342809.477 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))) 1539342809.477 * * * * [misc]progress: [ 54 / 64 ] simplifiying candidate # 1539342809.478 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342809.478 * * [misc]simplify: iters left: 4 (5 enodes) 1539342809.479 * * [misc]simplify: iters left: 3 (9 enodes) 1539342809.480 * * [misc]simplify: iters left: 2 (15 enodes) 1539342809.482 * * [misc]simplify: iters left: 1 (17 enodes) 1539342809.484 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342809.484 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))) 1539342809.484 * * * * [misc]progress: [ 55 / 64 ] simplifiying candidate # 1539342809.485 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342809.485 * * [misc]simplify: iters left: 4 (5 enodes) 1539342809.485 * * [misc]simplify: iters left: 3 (9 enodes) 1539342809.487 * * [misc]simplify: iters left: 2 (15 enodes) 1539342809.488 * * [misc]simplify: iters left: 1 (17 enodes) 1539342809.490 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342809.490 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))) 1539342809.490 * * * * [misc]progress: [ 56 / 64 ] simplifiying candidate # 1539342809.491 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342809.491 * * [misc]simplify: iters left: 4 (5 enodes) 1539342809.491 * * [misc]simplify: iters left: 3 (9 enodes) 1539342809.493 * * [misc]simplify: iters left: 2 (15 enodes) 1539342809.495 * * [misc]simplify: iters left: 1 (17 enodes) 1539342809.497 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342809.497 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.497 * * * * [misc]progress: [ 57 / 64 ] simplifiying candidate # 1539342809.497 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342809.497 * * [misc]simplify: iters left: 4 (5 enodes) 1539342809.498 * * [misc]simplify: iters left: 3 (9 enodes) 1539342809.499 * * [misc]simplify: iters left: 2 (15 enodes) 1539342809.501 * * [misc]simplify: iters left: 1 (17 enodes) 1539342809.503 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342809.503 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.503 * * * * [misc]progress: [ 58 / 64 ] simplifiying candidate # 1539342809.504 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342809.504 * * [misc]simplify: iters left: 4 (5 enodes) 1539342809.504 * * [misc]simplify: iters left: 3 (9 enodes) 1539342809.506 * * [misc]simplify: iters left: 2 (15 enodes) 1539342809.507 * * [misc]simplify: iters left: 1 (17 enodes) 1539342809.509 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342809.509 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.509 * * * * [misc]progress: [ 59 / 64 ] simplifiying candidate # 1539342809.509 * [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)))))))))))))) 1539342809.509 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539342809.509 * * * * [misc]progress: [ 60 / 64 ] simplifiying candidate # 1539342809.510 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (pow PI 3)) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (pow n 2) (pow k 3))))) (- (+ (* +nan.0 (/ (* (sqrt 2) PI) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (* (sqrt 2) (pow PI 2)) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* n (pow k 2)))))))))) 1539342809.510 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539342809.510 * * * * [misc]progress: [ 61 / 64 ] simplifiying candidate # 1539342809.510 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (pow PI 2) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) n))) (- (+ (* +nan.0 (/ PI (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ PI (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))))))) 1539342809.510 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1539342809.510 * * * * [misc]progress: [ 62 / 64 ] simplifiying candidate # 1539342809.510 * [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))))))))) 1539342809.510 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ +nan.0 (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.510 * * * * [misc]progress: [ 63 / 64 ] simplifiying candidate # 1539342809.510 * [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))))))) 1539342809.510 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ +nan.0 (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.510 * * * * [misc]progress: [ 64 / 64 ] simplifiying candidate # 1539342809.510 * [enter]simplify: Simplifying (- (+ (* +nan.0 PI) (- (+ (* +nan.0 (/ (pow PI 3) (pow n 2))) (- (* +nan.0 (/ (pow PI 2) n))))))) 1539342809.510 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ +nan.0 (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1539342809.510 * * * [misc]progress: adding candidates to table 1539342810.226 * * [misc]progress: iteration 3 / 4 1539342810.227 * * * [misc]progress: picking best candidate 1539342810.260 * * * * [misc]pick: Picked # 1539342810.260 * * * [misc]progress: localizing error 1539342810.267 * * * [misc]progress: generating rewritten candidates 1539342810.267 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1 2 1) 1539342810.269 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1) 1539342810.272 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1539342810.305 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 2) 1539342810.307 * * * [misc]progress: generating series expansions 1539342810.307 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1 2 1) 1539342810.308 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539342810.308 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539342810.308 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342810.308 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.308 * [misc]backup-simplify: Simplify 2 into 2 1539342810.308 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.308 * [misc]taylor: Taking taylor expansion of n in n 1539342810.308 * [misc]backup-simplify: Simplify 0 into 0 1539342810.308 * [misc]backup-simplify: Simplify 1 into 1 1539342810.308 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.308 * [misc]backup-simplify: Simplify PI into PI 1539342810.308 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342810.308 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.308 * [misc]backup-simplify: Simplify 2 into 2 1539342810.308 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.308 * [misc]taylor: Taking taylor expansion of n in n 1539342810.308 * [misc]backup-simplify: Simplify 0 into 0 1539342810.308 * [misc]backup-simplify: Simplify 1 into 1 1539342810.308 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.308 * [misc]backup-simplify: Simplify PI into PI 1539342810.310 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.310 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342810.310 * [misc]backup-simplify: Simplify 0 into 0 1539342810.311 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.311 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342810.312 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.313 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342810.314 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342810.314 * [misc]backup-simplify: Simplify 0 into 0 1539342810.315 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.317 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342810.317 * [misc]backup-simplify: Simplify 0 into 0 1539342810.319 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342810.321 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342810.322 * [misc]backup-simplify: Simplify 0 into 0 1539342810.324 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342810.327 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539342810.327 * [misc]backup-simplify: Simplify 0 into 0 1539342810.331 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342810.334 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539342810.334 * [misc]backup-simplify: Simplify 0 into 0 1539342810.339 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539342810.343 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539342810.343 * [misc]backup-simplify: Simplify 0 into 0 1539342810.343 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539342810.343 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539342810.344 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539342810.344 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.344 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.344 * [misc]backup-simplify: Simplify 2 into 2 1539342810.344 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.344 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.344 * [misc]backup-simplify: Simplify PI into PI 1539342810.344 * [misc]taylor: Taking taylor expansion of n in n 1539342810.344 * [misc]backup-simplify: Simplify 0 into 0 1539342810.344 * [misc]backup-simplify: Simplify 1 into 1 1539342810.344 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.344 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.344 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.344 * [misc]backup-simplify: Simplify 2 into 2 1539342810.344 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.344 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.344 * [misc]backup-simplify: Simplify PI into PI 1539342810.344 * [misc]taylor: Taking taylor expansion of n in n 1539342810.344 * [misc]backup-simplify: Simplify 0 into 0 1539342810.344 * [misc]backup-simplify: Simplify 1 into 1 1539342810.345 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.345 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.345 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.346 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.347 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342810.347 * [misc]backup-simplify: Simplify 0 into 0 1539342810.349 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.350 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.350 * [misc]backup-simplify: Simplify 0 into 0 1539342810.351 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.353 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.353 * [misc]backup-simplify: Simplify 0 into 0 1539342810.355 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.357 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342810.357 * [misc]backup-simplify: Simplify 0 into 0 1539342810.359 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.362 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342810.362 * [misc]backup-simplify: Simplify 0 into 0 1539342810.364 * [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 1539342810.368 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342810.368 * [misc]backup-simplify: Simplify 0 into 0 1539342810.368 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539342810.369 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539342810.369 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539342810.369 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.369 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.369 * [misc]backup-simplify: Simplify -2 into -2 1539342810.369 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.369 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.369 * [misc]backup-simplify: Simplify PI into PI 1539342810.369 * [misc]taylor: Taking taylor expansion of n in n 1539342810.369 * [misc]backup-simplify: Simplify 0 into 0 1539342810.369 * [misc]backup-simplify: Simplify 1 into 1 1539342810.369 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.369 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.369 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.369 * [misc]backup-simplify: Simplify -2 into -2 1539342810.369 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.369 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.369 * [misc]backup-simplify: Simplify PI into PI 1539342810.369 * [misc]taylor: Taking taylor expansion of n in n 1539342810.369 * [misc]backup-simplify: Simplify 0 into 0 1539342810.369 * [misc]backup-simplify: Simplify 1 into 1 1539342810.370 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.370 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.370 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.371 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.372 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342810.372 * [misc]backup-simplify: Simplify 0 into 0 1539342810.373 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.374 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.375 * [misc]backup-simplify: Simplify 0 into 0 1539342810.376 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.378 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.378 * [misc]backup-simplify: Simplify 0 into 0 1539342810.380 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.382 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342810.382 * [misc]backup-simplify: Simplify 0 into 0 1539342810.384 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.387 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342810.387 * [misc]backup-simplify: Simplify 0 into 0 1539342810.389 * [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 1539342810.393 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342810.393 * [misc]backup-simplify: Simplify 0 into 0 1539342810.393 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539342810.393 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1) 1539342810.393 * [misc]backup-simplify: Simplify (* (* 2 n) PI) into (* 2 (* n PI)) 1539342810.393 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539342810.393 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342810.393 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.393 * [misc]backup-simplify: Simplify 2 into 2 1539342810.393 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.394 * [misc]taylor: Taking taylor expansion of n in n 1539342810.394 * [misc]backup-simplify: Simplify 0 into 0 1539342810.394 * [misc]backup-simplify: Simplify 1 into 1 1539342810.394 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.394 * [misc]backup-simplify: Simplify PI into PI 1539342810.394 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342810.394 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.394 * [misc]backup-simplify: Simplify 2 into 2 1539342810.394 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.394 * [misc]taylor: Taking taylor expansion of n in n 1539342810.394 * [misc]backup-simplify: Simplify 0 into 0 1539342810.394 * [misc]backup-simplify: Simplify 1 into 1 1539342810.394 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.394 * [misc]backup-simplify: Simplify PI into PI 1539342810.394 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.394 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342810.395 * [misc]backup-simplify: Simplify 0 into 0 1539342810.395 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.396 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342810.396 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.397 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342810.398 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342810.398 * [misc]backup-simplify: Simplify 0 into 0 1539342810.400 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.401 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342810.401 * [misc]backup-simplify: Simplify 0 into 0 1539342810.402 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342810.403 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342810.403 * [misc]backup-simplify: Simplify 0 into 0 1539342810.405 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342810.406 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539342810.406 * [misc]backup-simplify: Simplify 0 into 0 1539342810.408 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342810.410 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539342810.410 * [misc]backup-simplify: Simplify 0 into 0 1539342810.412 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539342810.415 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539342810.415 * [misc]backup-simplify: Simplify 0 into 0 1539342810.415 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539342810.415 * [misc]backup-simplify: Simplify (* (* 2 (/ 1 n)) PI) into (* 2 (/ PI n)) 1539342810.415 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539342810.415 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.415 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.415 * [misc]backup-simplify: Simplify 2 into 2 1539342810.415 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.415 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.415 * [misc]backup-simplify: Simplify PI into PI 1539342810.415 * [misc]taylor: Taking taylor expansion of n in n 1539342810.415 * [misc]backup-simplify: Simplify 0 into 0 1539342810.415 * [misc]backup-simplify: Simplify 1 into 1 1539342810.415 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.415 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.415 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.415 * [misc]backup-simplify: Simplify 2 into 2 1539342810.415 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.415 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.415 * [misc]backup-simplify: Simplify PI into PI 1539342810.416 * [misc]taylor: Taking taylor expansion of n in n 1539342810.416 * [misc]backup-simplify: Simplify 0 into 0 1539342810.416 * [misc]backup-simplify: Simplify 1 into 1 1539342810.416 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.416 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.416 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.417 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.417 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342810.417 * [misc]backup-simplify: Simplify 0 into 0 1539342810.418 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.419 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.419 * [misc]backup-simplify: Simplify 0 into 0 1539342810.420 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.420 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.420 * [misc]backup-simplify: Simplify 0 into 0 1539342810.422 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.423 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342810.423 * [misc]backup-simplify: Simplify 0 into 0 1539342810.424 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.427 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342810.427 * [misc]backup-simplify: Simplify 0 into 0 1539342810.429 * [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 1539342810.431 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342810.431 * [misc]backup-simplify: Simplify 0 into 0 1539342810.431 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539342810.431 * [misc]backup-simplify: Simplify (* (* 2 (/ 1 (- n))) PI) into (* -2 (/ PI n)) 1539342810.431 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539342810.431 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.431 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.431 * [misc]backup-simplify: Simplify -2 into -2 1539342810.431 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.431 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.431 * [misc]backup-simplify: Simplify PI into PI 1539342810.431 * [misc]taylor: Taking taylor expansion of n in n 1539342810.431 * [misc]backup-simplify: Simplify 0 into 0 1539342810.431 * [misc]backup-simplify: Simplify 1 into 1 1539342810.431 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.431 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.431 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.431 * [misc]backup-simplify: Simplify -2 into -2 1539342810.431 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.431 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.431 * [misc]backup-simplify: Simplify PI into PI 1539342810.431 * [misc]taylor: Taking taylor expansion of n in n 1539342810.431 * [misc]backup-simplify: Simplify 0 into 0 1539342810.431 * [misc]backup-simplify: Simplify 1 into 1 1539342810.432 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.432 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.432 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.433 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.433 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342810.433 * [misc]backup-simplify: Simplify 0 into 0 1539342810.434 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.435 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.435 * [misc]backup-simplify: Simplify 0 into 0 1539342810.436 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.437 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.437 * [misc]backup-simplify: Simplify 0 into 0 1539342810.439 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.440 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342810.440 * [misc]backup-simplify: Simplify 0 into 0 1539342810.441 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.443 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342810.443 * [misc]backup-simplify: Simplify 0 into 0 1539342810.444 * [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 1539342810.446 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342810.446 * [misc]backup-simplify: Simplify 0 into 0 1539342810.446 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539342810.446 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1539342810.447 * [misc]backup-simplify: Simplify (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* 2 n) PI))) into (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) 1539342810.447 * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) in (k n) around 0 1539342810.447 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342810.447 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.447 * [misc]taylor: Taking taylor expansion of k in n 1539342810.447 * [misc]backup-simplify: Simplify k into k 1539342810.447 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.447 * [misc]backup-simplify: Simplify 2 into 2 1539342810.447 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.447 * [misc]taylor: Taking taylor expansion of n in n 1539342810.447 * [misc]backup-simplify: Simplify 0 into 0 1539342810.447 * [misc]backup-simplify: Simplify 1 into 1 1539342810.447 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.447 * [misc]backup-simplify: Simplify PI into PI 1539342810.447 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.448 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342810.448 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.449 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342810.449 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.449 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342810.449 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342810.450 * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539342810.450 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539342810.450 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.450 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.450 * [misc]backup-simplify: Simplify 2 into 2 1539342810.450 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.450 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.451 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) into (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) 1539342810.451 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in n 1539342810.451 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in n 1539342810.451 * [misc]taylor: Taking taylor expansion of k in n 1539342810.451 * [misc]backup-simplify: Simplify k into k 1539342810.451 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.451 * [misc]taylor: Taking taylor expansion of n in n 1539342810.451 * [misc]backup-simplify: Simplify 0 into 0 1539342810.451 * [misc]backup-simplify: Simplify 1 into 1 1539342810.451 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.451 * [misc]backup-simplify: Simplify PI into PI 1539342810.451 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.452 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.452 * [misc]backup-simplify: Simplify (/ k PI) into (/ k PI) 1539342810.452 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.452 * [misc]backup-simplify: Simplify (/ (/ k PI) (* 2 (sqrt 0))) into (* +nan.0 (/ k PI)) 1539342810.452 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342810.452 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.452 * [misc]taylor: Taking taylor expansion of k in k 1539342810.452 * [misc]backup-simplify: Simplify 0 into 0 1539342810.452 * [misc]backup-simplify: Simplify 1 into 1 1539342810.452 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of 2 in k 1539342810.452 * [misc]backup-simplify: Simplify 2 into 2 1539342810.452 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342810.452 * [misc]taylor: Taking taylor expansion of n in k 1539342810.452 * [misc]backup-simplify: Simplify n into n 1539342810.452 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.452 * [misc]backup-simplify: Simplify PI into PI 1539342810.452 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342810.452 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539342810.452 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539342810.452 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342810.453 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539342810.453 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342810.453 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539342810.453 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539342810.454 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539342810.454 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1/2 (log (* 2 (* n PI))))) into (* 1/2 (log (* 2 (* n PI)))) 1539342810.454 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342810.454 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342810.454 * [misc]taylor: Taking taylor expansion of 2 in k 1539342810.454 * [misc]backup-simplify: Simplify 2 into 2 1539342810.454 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.454 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.454 * [misc]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 1539342810.454 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in k 1539342810.454 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in k 1539342810.454 * [misc]taylor: Taking taylor expansion of k in k 1539342810.454 * [misc]backup-simplify: Simplify 0 into 0 1539342810.454 * [misc]backup-simplify: Simplify 1 into 1 1539342810.454 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342810.454 * [misc]taylor: Taking taylor expansion of n in k 1539342810.454 * [misc]backup-simplify: Simplify n into n 1539342810.454 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.454 * [misc]backup-simplify: Simplify PI into PI 1539342810.454 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342810.454 * [misc]backup-simplify: Simplify (/ 1 (* n PI)) into (/ 1 (* n PI)) 1539342810.455 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.455 * [misc]backup-simplify: Simplify (/ (/ 1 (* n PI)) (* 2 (sqrt 0))) into (/ +nan.0 (* n PI)) 1539342810.455 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342810.455 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.455 * [misc]taylor: Taking taylor expansion of k in k 1539342810.455 * [misc]backup-simplify: Simplify 0 into 0 1539342810.455 * [misc]backup-simplify: Simplify 1 into 1 1539342810.455 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of 2 in k 1539342810.455 * [misc]backup-simplify: Simplify 2 into 2 1539342810.455 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342810.455 * [misc]taylor: Taking taylor expansion of n in k 1539342810.455 * [misc]backup-simplify: Simplify n into n 1539342810.455 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.455 * [misc]backup-simplify: Simplify PI into PI 1539342810.455 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342810.455 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539342810.455 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539342810.455 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342810.455 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539342810.456 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342810.456 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539342810.456 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539342810.456 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539342810.457 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1/2 (log (* 2 (* n PI))))) into (* 1/2 (log (* 2 (* n PI)))) 1539342810.457 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342810.457 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342810.457 * [misc]taylor: Taking taylor expansion of 2 in k 1539342810.457 * [misc]backup-simplify: Simplify 2 into 2 1539342810.457 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.457 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.457 * [misc]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 1539342810.457 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in k 1539342810.457 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in k 1539342810.457 * [misc]taylor: Taking taylor expansion of k in k 1539342810.457 * [misc]backup-simplify: Simplify 0 into 0 1539342810.457 * [misc]backup-simplify: Simplify 1 into 1 1539342810.457 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342810.457 * [misc]taylor: Taking taylor expansion of n in k 1539342810.457 * [misc]backup-simplify: Simplify n into n 1539342810.457 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.457 * [misc]backup-simplify: Simplify PI into PI 1539342810.457 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342810.457 * [misc]backup-simplify: Simplify (/ 1 (* n PI)) into (/ 1 (* n PI)) 1539342810.457 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.458 * [misc]backup-simplify: Simplify (/ (/ 1 (* n PI)) (* 2 (sqrt 0))) into (/ +nan.0 (* n PI)) 1539342810.458 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 1539342810.458 * [misc]taylor: Taking taylor expansion of 0 in n 1539342810.458 * [misc]backup-simplify: Simplify 0 into 0 1539342810.458 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) 1539342810.458 * [misc]backup-simplify: Simplify (- (/ (* 1/2 (log (* 2 (* n PI)))) (sqrt 2)) (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) 1539342810.459 * [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))))) 1539342810.459 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (sqrt 2) (* n PI))))) in n 1539342810.459 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* n PI)))) in n 1539342810.459 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.459 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.459 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* n PI))) in n 1539342810.459 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539342810.459 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.459 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.459 * [misc]backup-simplify: Simplify 2 into 2 1539342810.459 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.459 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.459 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.459 * [misc]taylor: Taking taylor expansion of n in n 1539342810.459 * [misc]backup-simplify: Simplify 0 into 0 1539342810.459 * [misc]backup-simplify: Simplify 1 into 1 1539342810.459 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.459 * [misc]backup-simplify: Simplify PI into PI 1539342810.459 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.460 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342810.460 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.460 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539342810.461 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) PI)) into (/ 1 (* (sqrt 2) PI)) 1539342810.461 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (* (sqrt 2) PI))) into (/ +nan.0 (* (sqrt 2) PI)) 1539342810.462 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 1539342810.463 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 1539342810.463 * [misc]backup-simplify: Simplify 0 into 0 1539342810.463 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342810.463 * [misc]backup-simplify: Simplify (- (/ 0 (* n PI)) (+ (* (/ 1 (* n PI)) (/ 0 (* n PI))))) into 0 1539342810.464 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 (* n PI)) 2) (+)) (* 2 0)) into (/ +nan.0 (* (pow n 2) (pow PI 2))) 1539342810.464 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.464 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1539342810.465 * [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 1539342810.465 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1539342810.466 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1539342810.466 * [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)) 1539342810.467 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342810.468 * [misc]backup-simplify: Simplify (- (/ (* 1/8 (pow (log (* 2 (* n PI))) 2)) (sqrt 2)) (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) (/ 0 (sqrt 2))))) into (* 1/8 (/ (pow (log (* 2 (* n PI))) 2) (sqrt 2))) 1539342810.469 * [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))))))) 1539342810.469 * [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 1539342810.469 * [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 1539342810.470 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1539342810.470 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.470 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.470 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1539342810.470 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1539342810.470 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.470 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.470 * [misc]backup-simplify: Simplify 2 into 2 1539342810.470 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.470 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.470 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539342810.470 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539342810.470 * [misc]taylor: Taking taylor expansion of n in n 1539342810.470 * [misc]backup-simplify: Simplify 0 into 0 1539342810.470 * [misc]backup-simplify: Simplify 1 into 1 1539342810.470 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539342810.470 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.470 * [misc]backup-simplify: Simplify PI into PI 1539342810.471 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.471 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342810.471 * [misc]backup-simplify: Simplify (* 1 (pow PI 2)) into (pow PI 2) 1539342810.472 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342810.473 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (pow PI 2))) into (/ 1 (* (sqrt 2) (pow PI 2))) 1539342810.473 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))))) in n 1539342810.473 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI)))) in n 1539342810.473 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.473 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.473 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))) in n 1539342810.473 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342810.473 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342810.473 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.473 * [misc]backup-simplify: Simplify 2 into 2 1539342810.473 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.473 * [misc]taylor: Taking taylor expansion of n in n 1539342810.473 * [misc]backup-simplify: Simplify 0 into 0 1539342810.473 * [misc]backup-simplify: Simplify 1 into 1 1539342810.473 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.474 * [misc]backup-simplify: Simplify PI into PI 1539342810.474 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.474 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342810.475 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.475 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342810.476 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.476 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539342810.476 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.476 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.476 * [misc]backup-simplify: Simplify 2 into 2 1539342810.476 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.476 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.476 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.476 * [misc]taylor: Taking taylor expansion of n in n 1539342810.476 * [misc]backup-simplify: Simplify 0 into 0 1539342810.476 * [misc]backup-simplify: Simplify 1 into 1 1539342810.476 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.477 * [misc]backup-simplify: Simplify PI into PI 1539342810.477 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342810.477 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.478 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342810.478 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.479 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539342810.480 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342810.481 * [misc]backup-simplify: Simplify (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI)) into (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI)) 1539342810.481 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342810.482 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342810.482 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 2))) into 0 1539342810.483 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539342810.487 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) (pow PI 2))) (/ 0 (* (sqrt 2) (pow PI 2)))))) into 0 1539342810.489 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (sqrt 2) (pow PI 2))))) into 0 1539342810.490 * [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))) 1539342810.491 * [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)))))) 1539342810.493 * [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)))))) 1539342810.495 * [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)))))) 1539342810.497 * [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)))))) 1539342810.499 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342810.500 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342810.501 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1539342810.502 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))))) into 0 1539342810.503 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (sqrt 2) PI)))) into 0 1539342810.503 * [misc]backup-simplify: Simplify (- 0) into 0 1539342810.503 * [misc]backup-simplify: Simplify 0 into 0 1539342810.503 * [misc]backup-simplify: Simplify 0 into 0 1539342810.504 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.504 * [misc]backup-simplify: Simplify (- (/ 0 (* n PI)) (+ (* (/ 1 (* n PI)) (/ 0 (* n PI))) (* 0 (/ 0 (* n PI))))) into 0 1539342810.504 * [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))) 1539342810.505 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.505 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1539342810.507 * [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 1539342810.507 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539342810.508 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1539342810.509 * [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)) 1539342810.509 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342810.510 * [misc]backup-simplify: Simplify (- (/ (* 1/48 (pow (log (* 2 (* n PI))) 3)) (sqrt 2)) (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) (/ 0 (sqrt 2))) (* (* 1/8 (/ (pow (log (* 2 (* n PI))) 2) (sqrt 2))) (/ 0 (sqrt 2))))) into (* 1/48 (/ (pow (log (* 2 (* n PI))) 3) (sqrt 2))) 1539342810.511 * [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)))))))))) 1539342810.511 * [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 1539342810.511 * [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 1539342810.511 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI)))) in n 1539342810.511 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.511 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.511 * [misc]taylor: Taking taylor expansion of (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI))) in n 1539342810.511 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1539342810.512 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342810.512 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342810.512 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.512 * [misc]backup-simplify: Simplify 2 into 2 1539342810.512 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.512 * [misc]taylor: Taking taylor expansion of n in n 1539342810.512 * [misc]backup-simplify: Simplify 0 into 0 1539342810.512 * [misc]backup-simplify: Simplify 1 into 1 1539342810.512 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.512 * [misc]backup-simplify: Simplify PI into PI 1539342810.512 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.512 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342810.512 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.513 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342810.513 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.513 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342810.514 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539342810.514 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.514 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.514 * [misc]backup-simplify: Simplify 2 into 2 1539342810.514 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.514 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.514 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.514 * [misc]taylor: Taking taylor expansion of n in n 1539342810.514 * [misc]backup-simplify: Simplify 0 into 0 1539342810.514 * [misc]backup-simplify: Simplify 1 into 1 1539342810.514 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.514 * [misc]backup-simplify: Simplify PI into PI 1539342810.514 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342810.515 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342810.515 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1539342810.516 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.516 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342810.516 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.517 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539342810.517 * [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)) 1539342810.517 * [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 1539342810.517 * [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 1539342810.517 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3))))) in n 1539342810.517 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.517 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.517 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) in n 1539342810.517 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 3) (pow PI 3))) in n 1539342810.517 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.517 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.517 * [misc]backup-simplify: Simplify 2 into 2 1539342810.518 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.518 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.518 * [misc]taylor: Taking taylor expansion of (* (pow n 3) (pow PI 3)) in n 1539342810.518 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539342810.518 * [misc]taylor: Taking taylor expansion of n in n 1539342810.518 * [misc]backup-simplify: Simplify 0 into 0 1539342810.518 * [misc]backup-simplify: Simplify 1 into 1 1539342810.518 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539342810.518 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.518 * [misc]backup-simplify: Simplify PI into PI 1539342810.518 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.518 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.518 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342810.519 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342810.519 * [misc]backup-simplify: Simplify (* 1 (pow PI 3)) into (pow PI 3) 1539342810.519 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539342810.520 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (pow PI 3))) into (/ 1 (* (sqrt 2) (pow PI 3))) 1539342810.520 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))))) in n 1539342810.520 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1539342810.520 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.520 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.520 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1539342810.520 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342810.520 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342810.520 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.520 * [misc]backup-simplify: Simplify 2 into 2 1539342810.520 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.520 * [misc]taylor: Taking taylor expansion of n in n 1539342810.520 * [misc]backup-simplify: Simplify 0 into 0 1539342810.520 * [misc]backup-simplify: Simplify 1 into 1 1539342810.520 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.520 * [misc]backup-simplify: Simplify PI into PI 1539342810.520 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.520 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342810.521 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.521 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342810.522 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.522 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1539342810.522 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.522 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.522 * [misc]backup-simplify: Simplify 2 into 2 1539342810.522 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.522 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.522 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539342810.522 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539342810.522 * [misc]taylor: Taking taylor expansion of n in n 1539342810.522 * [misc]backup-simplify: Simplify 0 into 0 1539342810.522 * [misc]backup-simplify: Simplify 1 into 1 1539342810.522 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539342810.522 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.522 * [misc]backup-simplify: Simplify PI into PI 1539342810.522 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342810.523 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.523 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342810.523 * [misc]backup-simplify: Simplify (* 1 (pow PI 2)) into (pow PI 2) 1539342810.523 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342810.524 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342810.525 * [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))) 1539342810.525 * [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))) 1539342810.526 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.526 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342810.527 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 (pow PI 2)))) into 0 1539342810.528 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342810.528 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342810.528 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (pow PI 2))) into 0 1539342810.528 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539342810.529 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539342810.530 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (pow PI 3)))) into 0 1539342810.530 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 3))) into 0 1539342810.531 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342810.532 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (pow PI 3)))) into 0 1539342810.532 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 3))) into 0 1539342810.534 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) (pow PI 3))) (/ 0 (* (sqrt 2) (pow PI 3)))))) into 0 1539342810.539 * [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 1539342810.541 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (/ 1 (* (sqrt 2) (pow PI 3)))))) into 0 1539342810.544 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342810.545 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342810.548 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342810.549 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342810.550 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342810.551 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 2))) into 0 1539342810.552 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539342810.555 * [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 1539342810.556 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) (pow PI 2))))) into 0 1539342810.557 * [misc]backup-simplify: Simplify (- 0) into 0 1539342810.557 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342810.557 * [misc]backup-simplify: Simplify (- 0) into 0 1539342810.558 * [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)))))))) 1539342810.563 * [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)))))))) 1539342810.567 * [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)))))))) 1539342810.575 * [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))))))))))))))) 1539342810.576 * [misc]backup-simplify: Simplify (/ (* (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) (sqrt (* (* 2 (/ 1 n)) PI))) into (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) 1539342810.576 * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) in (k n) around 0 1539342810.576 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342810.576 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.576 * [misc]taylor: Taking taylor expansion of k in n 1539342810.576 * [misc]backup-simplify: Simplify k into k 1539342810.576 * [misc]backup-simplify: Simplify (/ 1/2 k) into (/ 1/2 k) 1539342810.576 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.576 * [misc]backup-simplify: Simplify 2 into 2 1539342810.576 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.576 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.576 * [misc]backup-simplify: Simplify PI into PI 1539342810.576 * [misc]taylor: Taking taylor expansion of n in n 1539342810.576 * [misc]backup-simplify: Simplify 0 into 0 1539342810.576 * [misc]backup-simplify: Simplify 1 into 1 1539342810.577 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.577 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.578 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.578 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.579 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342810.580 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.580 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.580 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.580 * [misc]backup-simplify: Simplify 2 into 2 1539342810.580 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.580 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.581 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 1539342810.581 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in n 1539342810.581 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in n 1539342810.581 * [misc]taylor: Taking taylor expansion of n in n 1539342810.581 * [misc]backup-simplify: Simplify 0 into 0 1539342810.581 * [misc]backup-simplify: Simplify 1 into 1 1539342810.581 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539342810.581 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.581 * [misc]backup-simplify: Simplify PI into PI 1539342810.581 * [misc]taylor: Taking taylor expansion of k in n 1539342810.581 * [misc]backup-simplify: Simplify k into k 1539342810.581 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539342810.581 * [misc]backup-simplify: Simplify (/ 1 (* PI k)) into (/ 1 (* PI k)) 1539342810.581 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.582 * [misc]backup-simplify: Simplify (/ (/ 1 (* PI k)) (* 2 (sqrt 0))) into (/ +nan.0 (* PI k)) 1539342810.582 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342810.582 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.582 * [misc]taylor: Taking taylor expansion of k in k 1539342810.582 * [misc]backup-simplify: Simplify 0 into 0 1539342810.582 * [misc]backup-simplify: Simplify 1 into 1 1539342810.582 * [misc]backup-simplify: Simplify (/ 1/2 1) into 1/2 1539342810.582 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of 2 in k 1539342810.582 * [misc]backup-simplify: Simplify 2 into 2 1539342810.582 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342810.582 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.582 * [misc]backup-simplify: Simplify PI into PI 1539342810.582 * [misc]taylor: Taking taylor expansion of n in k 1539342810.582 * [misc]backup-simplify: Simplify n into n 1539342810.582 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342810.582 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539342810.583 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539342810.583 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) 1539342810.583 * [misc]backup-simplify: Simplify (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1539342810.583 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342810.583 * [misc]taylor: Taking taylor expansion of 2 in k 1539342810.583 * [misc]backup-simplify: Simplify 2 into 2 1539342810.583 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.583 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.584 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 1539342810.584 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in k 1539342810.584 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in k 1539342810.584 * [misc]taylor: Taking taylor expansion of n in k 1539342810.584 * [misc]backup-simplify: Simplify n into n 1539342810.584 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539342810.584 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.584 * [misc]backup-simplify: Simplify PI into PI 1539342810.584 * [misc]taylor: Taking taylor expansion of k in k 1539342810.584 * [misc]backup-simplify: Simplify 0 into 0 1539342810.584 * [misc]backup-simplify: Simplify 1 into 1 1539342810.584 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539342810.585 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539342810.585 * [misc]backup-simplify: Simplify (/ n PI) into (/ n PI) 1539342810.585 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.585 * [misc]backup-simplify: Simplify (/ (/ n PI) (* 2 (sqrt 0))) into (* +nan.0 (/ n PI)) 1539342810.585 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) in k 1539342810.585 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in k 1539342810.585 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1539342810.585 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1539342810.585 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1539342810.586 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in k 1539342810.586 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342810.586 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.586 * [misc]taylor: Taking taylor expansion of k in k 1539342810.586 * [misc]backup-simplify: Simplify 0 into 0 1539342810.586 * [misc]backup-simplify: Simplify 1 into 1 1539342810.586 * [misc]backup-simplify: Simplify (/ 1/2 1) into 1/2 1539342810.586 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539342810.586 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539342810.586 * [misc]taylor: Taking taylor expansion of 2 in k 1539342810.586 * [misc]backup-simplify: Simplify 2 into 2 1539342810.586 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342810.586 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.586 * [misc]backup-simplify: Simplify PI into PI 1539342810.586 * [misc]taylor: Taking taylor expansion of n in k 1539342810.586 * [misc]backup-simplify: Simplify n into n 1539342810.586 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342810.586 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539342810.586 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539342810.586 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) 1539342810.587 * [misc]backup-simplify: Simplify (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1539342810.587 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342810.587 * [misc]taylor: Taking taylor expansion of 2 in k 1539342810.587 * [misc]backup-simplify: Simplify 2 into 2 1539342810.587 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.587 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.587 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 1539342810.587 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in k 1539342810.587 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in k 1539342810.587 * [misc]taylor: Taking taylor expansion of n in k 1539342810.587 * [misc]backup-simplify: Simplify n into n 1539342810.588 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539342810.588 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.588 * [misc]backup-simplify: Simplify PI into PI 1539342810.588 * [misc]taylor: Taking taylor expansion of k in k 1539342810.588 * [misc]backup-simplify: Simplify 0 into 0 1539342810.588 * [misc]backup-simplify: Simplify 1 into 1 1539342810.588 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539342810.589 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539342810.589 * [misc]backup-simplify: Simplify (/ n PI) into (/ n PI) 1539342810.589 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.589 * [misc]backup-simplify: Simplify (/ (/ n PI) (* 2 (sqrt 0))) into (* +nan.0 (/ n PI)) 1539342810.589 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 0) into 0 1539342810.590 * [misc]taylor: Taking taylor expansion of 0 in n 1539342810.590 * [misc]backup-simplify: Simplify 0 into 0 1539342810.590 * [misc]backup-simplify: Simplify 0 into 0 1539342810.590 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))))) into 0 1539342810.591 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (* +nan.0 (/ n PI))) (* 0 0)) into (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) (* (sqrt 2) PI)))) 1539342810.591 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) (* (sqrt 2) PI)))) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) (* (sqrt 2) PI))) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.591 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.591 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) (* (sqrt 2) PI)) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342810.591 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.591 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.591 * [misc]backup-simplify: Simplify 2 into 2 1539342810.591 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.591 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.592 * [misc]backup-simplify: Simplify PI into PI 1539342810.592 * [misc]taylor: Taking taylor expansion of n in n 1539342810.592 * [misc]backup-simplify: Simplify 0 into 0 1539342810.592 * [misc]backup-simplify: Simplify 1 into 1 1539342810.592 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.592 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.593 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.593 * [misc]taylor: Taking taylor expansion of k in n 1539342810.593 * [misc]backup-simplify: Simplify k into k 1539342810.593 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.594 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.595 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342810.595 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342810.596 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.596 * [misc]taylor: Taking taylor expansion of n in n 1539342810.596 * [misc]backup-simplify: Simplify 0 into 0 1539342810.596 * [misc]backup-simplify: Simplify 1 into 1 1539342810.596 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) PI) in n 1539342810.596 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.596 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.596 * [misc]backup-simplify: Simplify 2 into 2 1539342810.596 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.596 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.596 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.596 * [misc]backup-simplify: Simplify PI into PI 1539342810.597 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) into 0 1539342810.598 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.599 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342810.601 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342810.602 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539342810.603 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539342810.605 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342810.605 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) (* 0 0)) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.606 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1539342810.607 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) 1539342810.607 * [misc]backup-simplify: Simplify 0 into 0 1539342810.608 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1539342810.608 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)))) into 0 1539342810.609 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ n PI)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow n 2) (pow PI 2))) 1539342810.610 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342810.611 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342810.613 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) (* (sqrt 2) (pow PI 2))))) 1539342810.613 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) (* (sqrt 2) (pow PI 2))))) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) (* (sqrt 2) (pow PI 2)))) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.613 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.613 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) (* (sqrt 2) (pow PI 2))) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342810.613 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.613 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.613 * [misc]backup-simplify: Simplify 2 into 2 1539342810.613 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.613 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.613 * [misc]backup-simplify: Simplify PI into PI 1539342810.613 * [misc]taylor: Taking taylor expansion of n in n 1539342810.613 * [misc]backup-simplify: Simplify 0 into 0 1539342810.613 * [misc]backup-simplify: Simplify 1 into 1 1539342810.613 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.614 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.614 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.614 * [misc]taylor: Taking taylor expansion of k in n 1539342810.614 * [misc]backup-simplify: Simplify k into k 1539342810.615 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.616 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.616 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342810.617 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342810.617 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.617 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539342810.617 * [misc]taylor: Taking taylor expansion of n in n 1539342810.617 * [misc]backup-simplify: Simplify 0 into 0 1539342810.618 * [misc]backup-simplify: Simplify 1 into 1 1539342810.618 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in n 1539342810.618 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.618 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.618 * [misc]backup-simplify: Simplify 2 into 2 1539342810.618 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.618 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.618 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539342810.618 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.618 * [misc]backup-simplify: Simplify PI into PI 1539342810.618 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.619 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.619 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342810.620 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342810.621 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) 1539342810.622 * [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))) 1539342810.623 * [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)))) 1539342810.624 * [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)))) 1539342810.624 * [misc]backup-simplify: Simplify 0 into 0 1539342810.625 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539342810.626 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342810.627 * [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))) 1539342810.627 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342810.628 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342810.630 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) (* (sqrt 2) (pow PI 3))))) 1539342810.630 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) (* (sqrt 2) (pow PI 3))))) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) (* (sqrt 2) (pow PI 3)))) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.630 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.630 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) (* (sqrt 2) (pow PI 3))) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342810.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.630 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.630 * [misc]backup-simplify: Simplify 2 into 2 1539342810.630 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.630 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.630 * [misc]backup-simplify: Simplify PI into PI 1539342810.630 * [misc]taylor: Taking taylor expansion of n in n 1539342810.630 * [misc]backup-simplify: Simplify 0 into 0 1539342810.630 * [misc]backup-simplify: Simplify 1 into 1 1539342810.631 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.631 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.631 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.631 * [misc]taylor: Taking taylor expansion of k in n 1539342810.631 * [misc]backup-simplify: Simplify k into k 1539342810.632 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.633 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.633 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342810.634 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342810.634 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.634 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539342810.634 * [misc]taylor: Taking taylor expansion of n in n 1539342810.634 * [misc]backup-simplify: Simplify 0 into 0 1539342810.634 * [misc]backup-simplify: Simplify 1 into 1 1539342810.634 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 3)) in n 1539342810.634 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.635 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.635 * [misc]backup-simplify: Simplify 2 into 2 1539342810.635 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.635 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.635 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539342810.635 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.635 * [misc]backup-simplify: Simplify PI into PI 1539342810.635 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.635 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.636 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.636 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342810.637 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342810.637 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539342810.639 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) 1539342810.640 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.641 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.646 * [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 1539342810.647 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342810.648 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))) into 0 1539342810.650 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539342810.651 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 1) (* 0 0))) into 0 1539342810.651 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 PI)) into 0 1539342810.654 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) PI)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))))) into 0 1539342810.655 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) into 0 1539342810.655 * [misc]backup-simplify: Simplify (- 0) into 0 1539342810.655 * [misc]backup-simplify: Simplify 0 into 0 1539342810.655 * [misc]backup-simplify: Simplify 0 into 0 1539342810.656 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539342810.658 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342810.659 * [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))) 1539342810.660 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342810.661 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342810.663 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) (* (sqrt 2) (pow PI 4))))) 1539342810.663 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) (* (sqrt 2) (pow PI 4))))) in n 1539342810.663 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) (* (sqrt 2) (pow PI 4)))) in n 1539342810.663 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.663 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.663 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) (* (sqrt 2) (pow PI 4))) in n 1539342810.663 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) in n 1539342810.663 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342810.663 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342810.663 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342810.663 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.664 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342810.664 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342810.664 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.664 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.664 * [misc]backup-simplify: Simplify 2 into 2 1539342810.664 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.664 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.664 * [misc]backup-simplify: Simplify PI into PI 1539342810.664 * [misc]taylor: Taking taylor expansion of n in n 1539342810.664 * [misc]backup-simplify: Simplify 0 into 0 1539342810.664 * [misc]backup-simplify: Simplify 1 into 1 1539342810.664 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.664 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.665 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.665 * [misc]taylor: Taking taylor expansion of k in n 1539342810.665 * [misc]backup-simplify: Simplify k into k 1539342810.665 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.666 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.667 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342810.668 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342810.668 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.668 * [misc]taylor: Taking taylor expansion of (pow n 4) in n 1539342810.668 * [misc]taylor: Taking taylor expansion of n in n 1539342810.668 * [misc]backup-simplify: Simplify 0 into 0 1539342810.668 * [misc]backup-simplify: Simplify 1 into 1 1539342810.668 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 4)) in n 1539342810.668 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.668 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.668 * [misc]backup-simplify: Simplify 2 into 2 1539342810.669 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.669 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.669 * [misc]taylor: Taking taylor expansion of (pow PI 4) in n 1539342810.669 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.669 * [misc]backup-simplify: Simplify PI into PI 1539342810.669 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.669 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.670 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.670 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342810.671 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1539342810.672 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 4)) into (* (sqrt 2) (pow PI 4)) 1539342810.673 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 4))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 4))) 1539342810.674 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2)))) into (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2)))) 1539342810.676 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) 1539342810.677 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) 1539342810.679 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.681 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.688 * [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 1539342810.689 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342810.690 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 1539342810.694 * [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 1539342810.695 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539342810.696 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342810.697 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.701 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) PI)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))) (* 0 (/ 0 (* (sqrt 2) PI))))) into 0 1539342810.702 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))))) into 0 1539342810.702 * [misc]backup-simplify: Simplify (- 0) into 0 1539342810.702 * [misc]backup-simplify: Simplify 0 into 0 1539342810.702 * [misc]backup-simplify: Simplify 0 into 0 1539342810.703 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 1539342810.705 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342810.707 * [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))) 1539342810.707 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342810.710 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342810.712 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) (* (sqrt 2) (pow PI 5))))) 1539342810.713 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) (* (sqrt 2) (pow PI 5))))) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) (* (sqrt 2) (pow PI 5)))) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.713 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.713 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) (* (sqrt 2) (pow PI 5))) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342810.713 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.713 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.713 * [misc]backup-simplify: Simplify 2 into 2 1539342810.713 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.713 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.713 * [misc]backup-simplify: Simplify PI into PI 1539342810.713 * [misc]taylor: Taking taylor expansion of n in n 1539342810.713 * [misc]backup-simplify: Simplify 0 into 0 1539342810.713 * [misc]backup-simplify: Simplify 1 into 1 1539342810.713 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.714 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.714 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.714 * [misc]taylor: Taking taylor expansion of k in n 1539342810.714 * [misc]backup-simplify: Simplify k into k 1539342810.715 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.716 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.716 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342810.717 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342810.717 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.717 * [misc]taylor: Taking taylor expansion of (pow n 5) in n 1539342810.717 * [misc]taylor: Taking taylor expansion of n in n 1539342810.717 * [misc]backup-simplify: Simplify 0 into 0 1539342810.717 * [misc]backup-simplify: Simplify 1 into 1 1539342810.717 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 5)) in n 1539342810.718 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.718 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.718 * [misc]backup-simplify: Simplify 2 into 2 1539342810.718 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.718 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.718 * [misc]taylor: Taking taylor expansion of (pow PI 5) in n 1539342810.718 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.718 * [misc]backup-simplify: Simplify PI into PI 1539342810.718 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.719 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.719 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.720 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.720 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342810.721 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1539342810.721 * [misc]backup-simplify: Simplify (* PI (pow PI 4)) into (pow PI 5) 1539342810.722 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 5)) into (* (sqrt 2) (pow PI 5)) 1539342810.723 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 5))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 5))) 1539342810.723 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342810.725 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.725 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342810.728 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342810.729 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539342810.730 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539342810.731 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342810.732 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 1)) into 0 1539342810.733 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342810.734 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539342810.737 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) (pow PI 2))) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) (/ 0 (* (sqrt 2) (pow PI 2)))))) into 0 1539342810.738 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into 0 1539342810.738 * [misc]backup-simplify: Simplify (- 0) into 0 1539342810.738 * [misc]backup-simplify: Simplify 0 into 0 1539342810.739 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.741 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342810.749 * [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 1539342810.749 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342810.750 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1539342810.753 * [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 1539342810.754 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539342810.754 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342810.755 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.757 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) PI)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))) (* 0 (/ 0 (* (sqrt 2) PI))) (* 0 (/ 0 (* (sqrt 2) PI))))) into 0 1539342810.758 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))))) into 0 1539342810.758 * [misc]backup-simplify: Simplify (- 0) into 0 1539342810.758 * [misc]backup-simplify: Simplify 0 into 0 1539342810.758 * [misc]backup-simplify: Simplify 0 into 0 1539342810.759 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 1539342810.761 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342810.762 * [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))) 1539342810.763 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342810.764 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342810.765 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) (* (sqrt 2) (pow PI 6))))) 1539342810.765 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) (* (sqrt 2) (pow PI 6))))) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) (* (sqrt 2) (pow PI 6)))) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.765 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.765 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) (* (sqrt 2) (pow PI 6))) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342810.765 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342810.765 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.765 * [misc]backup-simplify: Simplify 2 into 2 1539342810.765 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.765 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.765 * [misc]backup-simplify: Simplify PI into PI 1539342810.765 * [misc]taylor: Taking taylor expansion of n in n 1539342810.765 * [misc]backup-simplify: Simplify 0 into 0 1539342810.765 * [misc]backup-simplify: Simplify 1 into 1 1539342810.766 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.766 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342810.766 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342810.766 * [misc]taylor: Taking taylor expansion of k in n 1539342810.766 * [misc]backup-simplify: Simplify k into k 1539342810.767 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.767 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342810.767 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342810.768 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342810.768 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.768 * [misc]taylor: Taking taylor expansion of (pow n 6) in n 1539342810.768 * [misc]taylor: Taking taylor expansion of n in n 1539342810.768 * [misc]backup-simplify: Simplify 0 into 0 1539342810.768 * [misc]backup-simplify: Simplify 1 into 1 1539342810.768 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 6)) in n 1539342810.768 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.768 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.768 * [misc]backup-simplify: Simplify 2 into 2 1539342810.768 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.768 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.768 * [misc]taylor: Taking taylor expansion of (pow PI 6) in n 1539342810.768 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.768 * [misc]backup-simplify: Simplify PI into PI 1539342810.769 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.769 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.769 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342810.769 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342810.769 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342810.770 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342810.770 * [misc]backup-simplify: Simplify (* (pow PI 3) (pow PI 3)) into (pow PI 6) 1539342810.770 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 6)) into (* (sqrt 2) (pow PI 6)) 1539342810.771 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 6))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 6))) 1539342810.773 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3)))) into (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3)))) 1539342810.774 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) 1539342810.775 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) 1539342810.780 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) (pow PI 3))))) (* (pow (/ 1 n) 3) (pow (/ 1 k) 2))) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) (pow PI 2))))) (* (pow (/ 1 n) 2) (/ 1 k))) (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) PI)))) (* (/ 1 n) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 2) (* (pow PI 2) k))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 3) (* (pow PI 3) (pow k 2))))))))))) 1539342810.781 * [misc]backup-simplify: Simplify (/ (* (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) (sqrt (* (* 2 (/ 1 (- n))) PI))) into (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) 1539342810.781 * [misc]approximate: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) in (k n) around 0 1539342810.781 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342810.781 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342810.781 * [misc]taylor: Taking taylor expansion of k in n 1539342810.781 * [misc]backup-simplify: Simplify k into k 1539342810.781 * [misc]backup-simplify: Simplify (/ -1/2 k) into (/ -1/2 k) 1539342810.781 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.781 * [misc]backup-simplify: Simplify -2 into -2 1539342810.781 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.781 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.781 * [misc]backup-simplify: Simplify PI into PI 1539342810.781 * [misc]taylor: Taking taylor expansion of n in n 1539342810.781 * [misc]backup-simplify: Simplify 0 into 0 1539342810.781 * [misc]backup-simplify: Simplify 1 into 1 1539342810.782 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.782 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.783 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342810.783 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342810.784 * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342810.784 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342810.784 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539342810.784 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539342810.784 * [misc]taylor: Taking taylor expansion of -1 in n 1539342810.785 * [misc]backup-simplify: Simplify -1 into -1 1539342810.785 * [misc]taylor: Taking taylor expansion of k in n 1539342810.785 * [misc]backup-simplify: Simplify k into k 1539342810.785 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539342810.785 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539342810.785 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539342810.785 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539342810.785 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342810.785 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.785 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.785 * [misc]backup-simplify: Simplify -2 into -2 1539342810.785 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.785 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.785 * [misc]backup-simplify: Simplify PI into PI 1539342810.785 * [misc]taylor: Taking taylor expansion of n in n 1539342810.785 * [misc]backup-simplify: Simplify 0 into 0 1539342810.785 * [misc]backup-simplify: Simplify 1 into 1 1539342810.785 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.786 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.786 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.787 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.787 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539342810.788 * [misc]backup-simplify: Simplify (/ (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (* +nan.0 PI)) into (* +nan.0 (/ (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) PI)) 1539342810.788 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) in k 1539342810.788 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in k 1539342810.788 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1539342810.788 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1539342810.788 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1539342810.788 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in k 1539342810.788 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342810.788 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342810.788 * [misc]taylor: Taking taylor expansion of k in k 1539342810.788 * [misc]backup-simplify: Simplify 0 into 0 1539342810.788 * [misc]backup-simplify: Simplify 1 into 1 1539342810.788 * [misc]backup-simplify: Simplify (/ -1/2 1) into -1/2 1539342810.788 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539342810.789 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342810.789 * [misc]taylor: Taking taylor expansion of -2 in k 1539342810.789 * [misc]backup-simplify: Simplify -2 into -2 1539342810.789 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342810.789 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.789 * [misc]backup-simplify: Simplify PI into PI 1539342810.789 * [misc]taylor: Taking taylor expansion of n in k 1539342810.789 * [misc]backup-simplify: Simplify n into n 1539342810.789 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342810.789 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342810.789 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539342810.789 * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) 1539342810.789 * [misc]backup-simplify: Simplify (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1539342810.789 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342810.789 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342810.789 * [misc]taylor: Taking taylor expansion of -1 in k 1539342810.789 * [misc]backup-simplify: Simplify -1 into -1 1539342810.789 * [misc]taylor: Taking taylor expansion of k in k 1539342810.789 * [misc]backup-simplify: Simplify 0 into 0 1539342810.789 * [misc]backup-simplify: Simplify 1 into 1 1539342810.789 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342810.790 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.790 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342810.790 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1539342810.790 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342810.790 * [misc]taylor: Taking taylor expansion of -2 in k 1539342810.790 * [misc]backup-simplify: Simplify -2 into -2 1539342810.790 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342810.790 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.790 * [misc]backup-simplify: Simplify PI into PI 1539342810.790 * [misc]taylor: Taking taylor expansion of n in k 1539342810.790 * [misc]backup-simplify: Simplify n into n 1539342810.790 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342810.790 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342810.791 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539342810.791 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1539342810.791 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1539342810.791 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539342810.791 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 0) into 0 1539342810.792 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1539342810.792 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (sqrt (* -2 (/ PI n)))) into (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) 1539342810.792 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) in k 1539342810.792 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in k 1539342810.792 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1539342810.792 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1539342810.792 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1539342810.792 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in k 1539342810.792 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342810.792 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342810.792 * [misc]taylor: Taking taylor expansion of k in k 1539342810.792 * [misc]backup-simplify: Simplify 0 into 0 1539342810.792 * [misc]backup-simplify: Simplify 1 into 1 1539342810.792 * [misc]backup-simplify: Simplify (/ -1/2 1) into -1/2 1539342810.792 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539342810.793 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342810.793 * [misc]taylor: Taking taylor expansion of -2 in k 1539342810.793 * [misc]backup-simplify: Simplify -2 into -2 1539342810.793 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342810.793 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.793 * [misc]backup-simplify: Simplify PI into PI 1539342810.793 * [misc]taylor: Taking taylor expansion of n in k 1539342810.793 * [misc]backup-simplify: Simplify n into n 1539342810.793 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342810.793 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342810.793 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539342810.793 * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) 1539342810.793 * [misc]backup-simplify: Simplify (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1539342810.793 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342810.793 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342810.793 * [misc]taylor: Taking taylor expansion of -1 in k 1539342810.793 * [misc]backup-simplify: Simplify -1 into -1 1539342810.793 * [misc]taylor: Taking taylor expansion of k in k 1539342810.793 * [misc]backup-simplify: Simplify 0 into 0 1539342810.793 * [misc]backup-simplify: Simplify 1 into 1 1539342810.794 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342810.794 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.794 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342810.794 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1539342810.794 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342810.794 * [misc]taylor: Taking taylor expansion of -2 in k 1539342810.794 * [misc]backup-simplify: Simplify -2 into -2 1539342810.794 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342810.794 * [misc]taylor: Taking taylor expansion of PI in k 1539342810.794 * [misc]backup-simplify: Simplify PI into PI 1539342810.794 * [misc]taylor: Taking taylor expansion of n in k 1539342810.794 * [misc]backup-simplify: Simplify n into n 1539342810.794 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342810.795 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342810.795 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539342810.795 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1539342810.795 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1539342810.795 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539342810.795 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 0) into 0 1539342810.796 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1539342810.796 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (sqrt (* -2 (/ PI n)))) into (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) 1539342810.796 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) in n 1539342810.796 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.796 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.796 * [misc]taylor: Taking taylor expansion of (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) in n 1539342810.796 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n 1539342810.796 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n 1539342810.796 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342810.796 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342810.796 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1539342810.796 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342810.797 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.797 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.797 * [misc]backup-simplify: Simplify -2 into -2 1539342810.797 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.797 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.797 * [misc]backup-simplify: Simplify PI into PI 1539342810.797 * [misc]taylor: Taking taylor expansion of n in n 1539342810.797 * [misc]backup-simplify: Simplify 0 into 0 1539342810.797 * [misc]backup-simplify: Simplify 1 into 1 1539342810.797 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.797 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.798 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342810.798 * [misc]taylor: Taking taylor expansion of k in n 1539342810.798 * [misc]backup-simplify: Simplify k into k 1539342810.799 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342810.799 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342810.800 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) 1539342810.800 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342810.801 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342810.801 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342810.801 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.801 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.801 * [misc]backup-simplify: Simplify -2 into -2 1539342810.801 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.801 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.801 * [misc]backup-simplify: Simplify PI into PI 1539342810.801 * [misc]taylor: Taking taylor expansion of n in n 1539342810.801 * [misc]backup-simplify: Simplify 0 into 0 1539342810.801 * [misc]backup-simplify: Simplify 1 into 1 1539342810.802 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.802 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.802 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.803 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.804 * [misc]backup-simplify: Simplify (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342810.804 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342810.805 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342810.806 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539342810.807 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539342810.807 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1539342810.808 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (sqrt (* -2 (/ PI n)))) (+ (* (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) (/ 0 (sqrt (* -2 (/ PI n))))))) into (- (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))))) 1539342810.808 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))))) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342810.808 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342810.808 * [misc]taylor: Taking taylor expansion of (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342810.808 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342810.808 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.808 * [misc]backup-simplify: Simplify -2 into -2 1539342810.808 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.808 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.808 * [misc]backup-simplify: Simplify PI into PI 1539342810.808 * [misc]taylor: Taking taylor expansion of n in n 1539342810.809 * [misc]backup-simplify: Simplify 0 into 0 1539342810.809 * [misc]backup-simplify: Simplify 1 into 1 1539342810.809 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.809 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.810 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342810.810 * [misc]taylor: Taking taylor expansion of k in n 1539342810.810 * [misc]backup-simplify: Simplify k into k 1539342810.810 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342810.811 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342810.812 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) 1539342810.812 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342810.813 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342810.813 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342810.813 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.813 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.813 * [misc]backup-simplify: Simplify -2 into -2 1539342810.813 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.813 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.813 * [misc]backup-simplify: Simplify PI into PI 1539342810.813 * [misc]taylor: Taking taylor expansion of n in n 1539342810.813 * [misc]backup-simplify: Simplify 0 into 0 1539342810.813 * [misc]backup-simplify: Simplify 1 into 1 1539342810.813 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.814 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.814 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.815 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.815 * [misc]backup-simplify: Simplify (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342810.816 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342810.816 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) 1539342810.817 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) 1539342810.817 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.818 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342810.819 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539342810.820 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 1539342810.820 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 1539342810.821 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342810.822 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.822 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342810.823 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342810.824 * [misc]backup-simplify: Simplify (- (/ 0 (* +nan.0 PI)) (+ (* (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) (/ (* +nan.0 (pow PI 2)) (* +nan.0 PI))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342810.825 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (* 0 (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342810.826 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342810.827 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (* (/ 1 (- n)) 1)) (+ (* (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) PI))) (* 1 (/ 1 (- k)))) (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) PI)))) 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))) n))))))) 1539342810.827 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 2) 1539342810.827 * [misc]backup-simplify: Simplify (sqrt (* (* 2 n) PI)) into (* (sqrt 2) (sqrt (* n PI))) 1539342810.827 * [misc]approximate: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in (n) around 0 1539342810.827 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1539342810.827 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.827 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.827 * [misc]backup-simplify: Simplify 2 into 2 1539342810.828 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.828 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.828 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1539342810.828 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.828 * [misc]taylor: Taking taylor expansion of n in n 1539342810.828 * [misc]backup-simplify: Simplify 0 into 0 1539342810.828 * [misc]backup-simplify: Simplify 1 into 1 1539342810.828 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.828 * [misc]backup-simplify: Simplify PI into PI 1539342810.828 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.828 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.829 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.829 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.829 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1539342810.829 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.829 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.829 * [misc]backup-simplify: Simplify 2 into 2 1539342810.829 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.829 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.829 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1539342810.829 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342810.829 * [misc]taylor: Taking taylor expansion of n in n 1539342810.829 * [misc]backup-simplify: Simplify 0 into 0 1539342810.829 * [misc]backup-simplify: Simplify 1 into 1 1539342810.829 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.829 * [misc]backup-simplify: Simplify PI into PI 1539342810.829 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342810.830 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342810.830 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.830 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.830 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342810.830 * [misc]backup-simplify: Simplify 0 into 0 1539342810.831 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342810.832 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342810.832 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342810.833 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342810.834 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342810.835 * [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)))) 1539342810.836 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1539342810.837 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342810.840 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539342810.840 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342810.842 * [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)))) 1539342810.843 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1539342810.845 * [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))))))))) 1539342810.845 * [misc]backup-simplify: Simplify (sqrt (* (* 2 (/ 1 n)) PI)) into (* (sqrt 2) (sqrt (/ PI n))) 1539342810.845 * [misc]approximate: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in (n) around 0 1539342810.845 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 1539342810.845 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.845 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.845 * [misc]backup-simplify: Simplify 2 into 2 1539342810.845 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.846 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.846 * [misc]taylor: Taking taylor expansion of (sqrt (/ PI n)) in n 1539342810.846 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.846 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.846 * [misc]backup-simplify: Simplify PI into PI 1539342810.846 * [misc]taylor: Taking taylor expansion of n in n 1539342810.846 * [misc]backup-simplify: Simplify 0 into 0 1539342810.846 * [misc]backup-simplify: Simplify 1 into 1 1539342810.846 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.846 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.846 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.846 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 1539342810.846 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342810.846 * [misc]taylor: Taking taylor expansion of 2 in n 1539342810.846 * [misc]backup-simplify: Simplify 2 into 2 1539342810.847 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342810.847 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342810.847 * [misc]taylor: Taking taylor expansion of (sqrt (/ PI n)) in n 1539342810.847 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.847 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.847 * [misc]backup-simplify: Simplify PI into PI 1539342810.847 * [misc]taylor: Taking taylor expansion of n in n 1539342810.847 * [misc]backup-simplify: Simplify 0 into 0 1539342810.847 * [misc]backup-simplify: Simplify 1 into 1 1539342810.847 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.847 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.847 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.848 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342810.848 * [misc]backup-simplify: Simplify 0 into 0 1539342810.848 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342810.849 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1539342810.850 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.850 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342810.851 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342810.853 * [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)))) 1539342810.853 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1539342810.854 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.856 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539342810.857 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342810.860 * [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)))) 1539342810.862 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 3)))) 1539342810.866 * [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))))))) 1539342810.866 * [misc]backup-simplify: Simplify (sqrt (* (* 2 (/ 1 (- n))) PI)) into (sqrt (* -2 (/ PI n))) 1539342810.866 * [misc]approximate: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in (n) around 0 1539342810.866 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342810.866 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.866 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.866 * [misc]backup-simplify: Simplify -2 into -2 1539342810.866 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.866 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.866 * [misc]backup-simplify: Simplify PI into PI 1539342810.866 * [misc]taylor: Taking taylor expansion of n in n 1539342810.867 * [misc]backup-simplify: Simplify 0 into 0 1539342810.867 * [misc]backup-simplify: Simplify 1 into 1 1539342810.867 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.867 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.867 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.868 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.868 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342810.868 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342810.868 * [misc]taylor: Taking taylor expansion of -2 in n 1539342810.868 * [misc]backup-simplify: Simplify -2 into -2 1539342810.868 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342810.868 * [misc]taylor: Taking taylor expansion of PI in n 1539342810.868 * [misc]backup-simplify: Simplify PI into PI 1539342810.868 * [misc]taylor: Taking taylor expansion of n in n 1539342810.868 * [misc]backup-simplify: Simplify 0 into 0 1539342810.868 * [misc]backup-simplify: Simplify 1 into 1 1539342810.869 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342810.869 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342810.869 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342810.870 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342810.870 * [misc]backup-simplify: Simplify 0 into 0 1539342810.870 * [misc]backup-simplify: Simplify (* +nan.0 PI) into (* +nan.0 PI) 1539342810.871 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342810.872 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342810.873 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342810.874 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 2)) into (* +nan.0 (pow PI 2)) 1539342810.875 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342810.876 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342810.879 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539342810.880 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 3)) into (* +nan.0 (pow PI 3)) 1539342810.881 * [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))))))) 1539342810.881 * * * [misc]progress: simplifying candidates 1539342810.881 * * * * [misc]progress: [ 1 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 2 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 3 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 4 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 5 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 6 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 7 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 8 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 9 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 10 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 11 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 12 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 13 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 14 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 15 / 64 ] simplifiying candidate # 1539342810.882 * * * * [misc]progress: [ 16 / 64 ] simplifiying candidate # 1539342810.883 * * * * [misc]progress: [ 17 / 64 ] simplifiying candidate # 1539342810.883 * * * * [misc]progress: [ 18 / 64 ] simplifiying candidate # 1539342810.883 * * * * [misc]progress: [ 19 / 64 ] simplifiying candidate # 1539342810.883 * * * * [misc]progress: [ 20 / 64 ] simplifiying candidate # 1539342810.883 * [enter]simplify: Simplifying (- (+ (log (sqrt k)) (* (log (* PI (* n 2))) (/ k 2))) (log (sqrt (* (* 2 n) PI)))) 1539342810.883 * * [misc]simplify: iters left: 6 (17 enodes) 1539342810.889 * * [misc]simplify: iters left: 5 (33 enodes) 1539342810.899 * * [misc]simplify: iters left: 4 (60 enodes) 1539342810.920 * * [misc]simplify: iters left: 3 (132 enodes) 1539342810.966 * * [misc]simplify: iters left: 2 (272 enodes) 1539342811.087 * [exit]simplify: Simplified to (- (+ (+ (log (sqrt k)) (* (/ k 2) (log n))) (* (/ k 2) (log (* PI 2)))) (log (sqrt (* (* PI 2) n)))) 1539342811.087 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (+ (+ (log (sqrt k)) (* (/ k 2) (log n))) (* (/ k 2) (log (* PI 2)))) (log (sqrt (* (* PI 2) n))))))) 1539342811.087 * * * * [misc]progress: [ 21 / 64 ] simplifiying candidate # 1539342811.087 * [enter]simplify: Simplifying (- (+ (log (sqrt k)) (* (log (* PI (* n 2))) (/ k 2))) (log (sqrt (* (* 2 n) PI)))) 1539342811.087 * * [misc]simplify: iters left: 6 (17 enodes) 1539342811.090 * * [misc]simplify: iters left: 5 (33 enodes) 1539342811.097 * * [misc]simplify: iters left: 4 (60 enodes) 1539342811.107 * * [misc]simplify: iters left: 3 (132 enodes) 1539342811.147 * * [misc]simplify: iters left: 2 (272 enodes) 1539342811.232 * [exit]simplify: Simplified to (- (+ (+ (log (sqrt k)) (* (/ k 2) (log n))) (* (/ k 2) (log (* PI 2)))) (log (sqrt (* (* PI 2) n)))) 1539342811.232 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (+ (+ (log (sqrt k)) (* (/ k 2) (log n))) (* (/ k 2) (log (* PI 2)))) (log (sqrt (* (* PI 2) n))))))) 1539342811.232 * * * * [misc]progress: [ 22 / 64 ] simplifiying candidate # 1539342811.233 * [enter]simplify: Simplifying (- (+ (log (sqrt k)) (log (pow (* PI (* n 2)) (/ k 2)))) (log (sqrt (* (* 2 n) PI)))) 1539342811.233 * * [misc]simplify: iters left: 6 (17 enodes) 1539342811.235 * * [misc]simplify: iters left: 5 (29 enodes) 1539342811.244 * * [misc]simplify: iters left: 4 (53 enodes) 1539342811.252 * * [misc]simplify: iters left: 3 (105 enodes) 1539342811.282 * * [misc]simplify: iters left: 2 (244 enodes) 1539342811.367 * [exit]simplify: Simplified to (- (+ (+ (* (log PI) (/ k 2)) (log (sqrt k))) (* (log (* n 2)) (/ k 2))) (log (sqrt (* (* PI n) 2)))) 1539342811.367 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (+ (+ (* (log PI) (/ k 2)) (log (sqrt k))) (* (log (* n 2)) (/ k 2))) (log (sqrt (* (* PI n) 2))))))) 1539342811.367 * * * * [misc]progress: [ 23 / 64 ] simplifiying candidate # 1539342811.368 * [enter]simplify: Simplifying (- (log (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))) (log (sqrt (* (* 2 n) PI)))) 1539342811.368 * * [misc]simplify: iters left: 6 (16 enodes) 1539342811.372 * * [misc]simplify: iters left: 5 (28 enodes) 1539342811.376 * * [misc]simplify: iters left: 4 (40 enodes) 1539342811.383 * * [misc]simplify: iters left: 3 (65 enodes) 1539342811.401 * * [misc]simplify: iters left: 2 (128 enodes) 1539342811.473 * * [misc]simplify: iters left: 1 (360 enodes) 1539342811.604 * [exit]simplify: Simplified to (- (+ (* (log (* 2 PI)) (/ k 2)) (+ (* (log n) (/ k 2)) (log (sqrt k)))) (log (sqrt (* PI (* n 2))))) 1539342811.604 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (+ (* (log (* 2 PI)) (/ k 2)) (+ (* (log n) (/ k 2)) (log (sqrt k)))) (log (sqrt (* PI (* n 2)))))))) 1539342811.604 * * * * [misc]progress: [ 24 / 64 ] simplifiying candidate # 1539342811.604 * * * * [misc]progress: [ 25 / 64 ] simplifiying candidate # 1539342811.604 * * * * [misc]progress: [ 26 / 64 ] simplifiying candidate # 1539342811.604 * [enter]simplify: Simplifying (/ (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* PI (* n 2)) (/ k 2)) (pow (* PI (* n 2)) (/ k 2))) (pow (* PI (* n 2)) (/ k 2)))) (* (* (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI))) (sqrt (* (* 2 n) PI)))) 1539342811.604 * * [misc]simplify: iters left: 6 (20 enodes) 1539342811.608 * * [misc]simplify: iters left: 5 (40 enodes) 1539342811.617 * * [misc]simplify: iters left: 4 (210 enodes) 1539342811.798 * [exit]simplify: Simplified to (* (/ (/ (/ (sqrt k) (/ 2 k)) (* PI n)) (sqrt (* (* 2 PI) n))) (pow (pow (* (* 2 PI) n) (/ k 2)) 3)) 1539342811.798 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (* (/ (/ (/ (sqrt k) (/ 2 k)) (* PI n)) (sqrt (* (* 2 PI) n))) (pow (pow (* (* 2 PI) n) (/ k 2)) 3))))) 1539342811.798 * * * * [misc]progress: [ 27 / 64 ] simplifiying candidate # 1539342811.798 * [enter]simplify: Simplifying (/ (* (* (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))) (* (* (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI))) (sqrt (* (* 2 n) PI)))) 1539342811.798 * * [misc]simplify: iters left: 6 (18 enodes) 1539342811.804 * * [misc]simplify: iters left: 5 (39 enodes) 1539342811.822 * * [misc]simplify: iters left: 4 (190 enodes) 1539342812.045 * [exit]simplify: Simplified to (* (/ (* k (pow (* n (* 2 PI)) (/ k 2))) (* n (* 2 PI))) (/ (* (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (* n (* 2 PI))) (sqrt k)))) 1539342812.046 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (* (/ (* k (pow (* n (* 2 PI)) (/ k 2))) (* n (* 2 PI))) (/ (* (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (* n (* 2 PI))) (sqrt k))))))) 1539342812.046 * * * * [misc]progress: [ 28 / 64 ] simplifiying candidate # 1539342812.046 * * * * [misc]progress: [ 29 / 64 ] simplifiying candidate # 1539342812.046 * * * * [misc]progress: [ 30 / 64 ] simplifiying candidate # 1539342812.046 * * * * [misc]progress: [ 31 / 64 ] simplifiying candidate # 1539342812.046 * * * * [misc]progress: [ 32 / 64 ] simplifiying candidate # 1539342812.046 * [enter]simplify: Simplifying (/ (sqrt k) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) 1539342812.046 * * [misc]simplify: iters left: 6 (11 enodes) 1539342812.050 * * [misc]simplify: iters left: 5 (17 enodes) 1539342812.055 * * [misc]simplify: iters left: 4 (23 enodes) 1539342812.061 * * [misc]simplify: iters left: 3 (24 enodes) 1539342812.066 * [exit]simplify: Simplified to (/ (sqrt k) (* (cbrt (sqrt (* (* n PI) 2))) (cbrt (sqrt (* (* n PI) 2))))) 1539342812.066 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt k) (* (cbrt (sqrt (* (* n PI) 2))) (cbrt (sqrt (* (* n PI) 2))))) (/ (pow (* PI (* n 2)) (/ k 2)) (cbrt (sqrt (* (* 2 n) PI))))))) 1539342812.067 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (cbrt (sqrt (* (* 2 n) PI)))) 1539342812.067 * * [misc]simplify: iters left: 6 (13 enodes) 1539342812.071 * * [misc]simplify: iters left: 5 (18 enodes) 1539342812.076 * * [misc]simplify: iters left: 4 (22 enodes) 1539342812.082 * * [misc]simplify: iters left: 3 (23 enodes) 1539342812.087 * [exit]simplify: Simplified to (/ (pow (* PI (* 2 n)) (/ k 2)) (cbrt (sqrt (* PI (* 2 n))))) 1539342812.087 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (pow (* PI (* 2 n)) (/ k 2)) (cbrt (sqrt (* PI (* 2 n)))))))) 1539342812.087 * * * * [misc]progress: [ 33 / 64 ] simplifiying candidate # 1539342812.088 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (* 2 n))) 1539342812.088 * * [misc]simplify: iters left: 5 (7 enodes) 1539342812.090 * * [misc]simplify: iters left: 4 (8 enodes) 1539342812.092 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (* 2 n))) 1539342812.092 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt k) (sqrt (* 2 n))) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt PI))))) 1539342812.092 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt PI)) 1539342812.092 * * [misc]simplify: iters left: 6 (10 enodes) 1539342812.095 * * [misc]simplify: iters left: 5 (14 enodes) 1539342812.099 * * [misc]simplify: iters left: 4 (20 enodes) 1539342812.105 * * [misc]simplify: iters left: 3 (22 enodes) 1539342812.110 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt PI)) 1539342812.110 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (sqrt (* 2 n))) (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt PI))))) 1539342812.111 * * * * [misc]progress: [ 34 / 64 ] simplifiying candidate # 1539342812.111 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (sqrt (* (* 2 n) PI)))) 1539342812.111 * * [misc]simplify: iters left: 6 (10 enodes) 1539342812.114 * * [misc]simplify: iters left: 5 (14 enodes) 1539342812.121 * * [misc]simplify: iters left: 4 (20 enodes) 1539342812.125 * * [misc]simplify: iters left: 3 (22 enodes) 1539342812.127 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (* n (* 2 PI))))) 1539342812.127 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt k) (sqrt (sqrt (* n (* 2 PI))))) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI))))))) 1539342812.128 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))) 1539342812.128 * * [misc]simplify: iters left: 6 (13 enodes) 1539342812.130 * * [misc]simplify: iters left: 5 (18 enodes) 1539342812.132 * * [misc]simplify: iters left: 4 (22 enodes) 1539342812.135 * * [misc]simplify: iters left: 3 (23 enodes) 1539342812.138 * [exit]simplify: Simplified to (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (sqrt (* PI (* 2 n))))) 1539342812.138 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (sqrt (sqrt (* (* 2 n) PI)))) (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (sqrt (* PI (* 2 n)))))))) 1539342812.138 * * * * [misc]progress: [ 35 / 64 ] simplifiying candidate # 1539342812.138 * [enter]simplify: Simplifying (/ (sqrt k) 1) 1539342812.138 * * [misc]simplify: iters left: 3 (4 enodes) 1539342812.139 * * [misc]simplify: iters left: 2 (6 enodes) 1539342812.140 * * [misc]simplify: iters left: 1 (8 enodes) 1539342812.141 * [exit]simplify: Simplified to (sqrt k) 1539342812.141 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI)))))) 1539342812.141 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342812.141 * * [misc]simplify: iters left: 6 (12 enodes) 1539342812.143 * * [misc]simplify: iters left: 5 (17 enodes) 1539342812.145 * * [misc]simplify: iters left: 4 (21 enodes) 1539342812.147 * * [misc]simplify: iters left: 3 (22 enodes) 1539342812.150 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342812.150 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt (* (* 2 n) PI)))))) 1539342812.150 * * * * [misc]progress: [ 36 / 64 ] simplifiying candidate # 1539342812.150 * * * * [misc]progress: [ 37 / 64 ] simplifiying candidate # 1539342812.150 * * * * [misc]progress: [ 38 / 64 ] simplifiying candidate # 1539342812.150 * * * * [misc]progress: [ 39 / 64 ] simplifiying candidate # 1539342812.150 * [enter]simplify: Simplifying (cbrt (sqrt (* (* 2 n) PI))) 1539342812.150 * * [misc]simplify: iters left: 6 (7 enodes) 1539342812.151 * * [misc]simplify: iters left: 5 (11 enodes) 1539342812.153 * * [misc]simplify: iters left: 4 (17 enodes) 1539342812.155 * * [misc]simplify: iters left: 3 (19 enodes) 1539342812.157 * [exit]simplify: Simplified to (cbrt (sqrt (* (* 2 n) PI))) 1539342812.157 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) (cbrt (sqrt (* (* 2 n) PI)))))) 1539342812.157 * * * * [misc]progress: [ 40 / 64 ] simplifiying candidate # 1539342812.157 * [enter]simplify: Simplifying (sqrt PI) 1539342812.157 * * [misc]simplify: iters left: 1 (2 enodes) 1539342812.157 * [exit]simplify: Simplified to (sqrt PI) 1539342812.157 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (* 2 n))) (sqrt PI)))) 1539342812.157 * * * * [misc]progress: [ 41 / 64 ] simplifiying candidate # 1539342812.158 * [enter]simplify: Simplifying (sqrt (sqrt (* (* 2 n) PI))) 1539342812.158 * * [misc]simplify: iters left: 6 (7 enodes) 1539342812.159 * * [misc]simplify: iters left: 5 (11 enodes) 1539342812.160 * * [misc]simplify: iters left: 4 (17 enodes) 1539342812.162 * * [misc]simplify: iters left: 3 (19 enodes) 1539342812.164 * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) 1539342812.164 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) (sqrt (sqrt (* (* 2 n) PI)))))) 1539342812.164 * * * * [misc]progress: [ 42 / 64 ] simplifiying candidate # 1539342812.164 * [enter]simplify: Simplifying (sqrt (* (* 2 n) PI)) 1539342812.165 * * [misc]simplify: iters left: 5 (6 enodes) 1539342812.165 * * [misc]simplify: iters left: 4 (10 enodes) 1539342812.167 * * [misc]simplify: iters left: 3 (16 enodes) 1539342812.169 * * [misc]simplify: iters left: 2 (18 enodes) 1539342812.171 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539342812.171 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) 1) (sqrt (* (* 2 n) PI))))) 1539342812.171 * * * * [misc]progress: [ 43 / 64 ] simplifiying candidate # 1539342812.171 * [enter]simplify: Simplifying (sqrt k) 1539342812.171 * * [misc]simplify: iters left: 1 (2 enodes) 1539342812.171 * [exit]simplify: Simplified to (sqrt k) 1539342812.171 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (/ (sqrt (* (* 2 n) PI)) (pow (* PI (* n 2)) (/ k 2)))))) 1539342812.171 * * * * [misc]progress: [ 44 / 64 ] simplifiying candidate # 1539342812.171 * * * * [misc]progress: [ 45 / 64 ] simplifiying candidate # 1539342812.171 * * * * [misc]progress: [ 46 / 64 ] simplifiying candidate # 1539342812.171 * * * * [misc]progress: [ 47 / 64 ] simplifiying candidate # 1539342812.171 * * * * [misc]progress: [ 48 / 64 ] simplifiying candidate # 1539342812.171 * * * * [misc]progress: [ 49 / 64 ] simplifiying candidate # 1539342812.171 * * * * [misc]progress: [ 50 / 64 ] simplifiying candidate # 1539342812.172 * [enter]simplify: Simplifying (sqrt (* 2 n)) 1539342812.172 * * [misc]simplify: iters left: 3 (4 enodes) 1539342812.172 * * [misc]simplify: iters left: 2 (5 enodes) 1539342812.173 * [exit]simplify: Simplified to (sqrt (* 2 n)) 1539342812.173 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (* (sqrt (* 2 n)) (sqrt PI))))) 1539342812.173 * * * * [misc]progress: [ 51 / 64 ] simplifiying candidate # 1539342812.173 * * * * [misc]progress: [ 52 / 64 ] simplifiying candidate # 1539342812.173 * * * * [misc]progress: [ 53 / 64 ] simplifiying candidate # 1539342812.173 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342812.173 * * [misc]simplify: iters left: 4 (5 enodes) 1539342812.174 * * [misc]simplify: iters left: 3 (9 enodes) 1539342812.175 * * [misc]simplify: iters left: 2 (15 enodes) 1539342812.177 * * [misc]simplify: iters left: 1 (17 enodes) 1539342812.179 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342812.179 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))) (sqrt (* (* 2 n) PI))))) 1539342812.179 * * * * [misc]progress: [ 54 / 64 ] simplifiying candidate # 1539342812.179 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342812.179 * * [misc]simplify: iters left: 4 (5 enodes) 1539342812.180 * * [misc]simplify: iters left: 3 (9 enodes) 1539342812.181 * * [misc]simplify: iters left: 2 (15 enodes) 1539342812.183 * * [misc]simplify: iters left: 1 (17 enodes) 1539342812.185 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342812.185 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))) (sqrt (* (* 2 n) PI))))) 1539342812.185 * * * * [misc]progress: [ 55 / 64 ] simplifiying candidate # 1539342812.185 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342812.185 * * [misc]simplify: iters left: 4 (5 enodes) 1539342812.186 * * [misc]simplify: iters left: 3 (9 enodes) 1539342812.187 * * [misc]simplify: iters left: 2 (15 enodes) 1539342812.189 * * [misc]simplify: iters left: 1 (17 enodes) 1539342812.191 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342812.191 * [misc]simplify: Simplified (2 2 1 2 1) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))) (sqrt (* (* 2 n) PI))))) 1539342812.191 * * * * [misc]progress: [ 56 / 64 ] simplifiying candidate # 1539342812.191 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342812.191 * * [misc]simplify: iters left: 4 (5 enodes) 1539342812.192 * * [misc]simplify: iters left: 3 (9 enodes) 1539342812.194 * * [misc]simplify: iters left: 2 (15 enodes) 1539342812.196 * * [misc]simplify: iters left: 1 (17 enodes) 1539342812.197 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342812.197 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* PI n) 2))))) 1539342812.198 * * * * [misc]progress: [ 57 / 64 ] simplifiying candidate # 1539342812.198 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342812.198 * * [misc]simplify: iters left: 4 (5 enodes) 1539342812.199 * * [misc]simplify: iters left: 3 (9 enodes) 1539342812.200 * * [misc]simplify: iters left: 2 (15 enodes) 1539342812.202 * * [misc]simplify: iters left: 1 (17 enodes) 1539342812.204 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342812.204 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* PI n) 2))))) 1539342812.204 * * * * [misc]progress: [ 58 / 64 ] simplifiying candidate # 1539342812.204 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342812.204 * * [misc]simplify: iters left: 4 (5 enodes) 1539342812.205 * * [misc]simplify: iters left: 3 (9 enodes) 1539342812.206 * * [misc]simplify: iters left: 2 (15 enodes) 1539342812.208 * * [misc]simplify: iters left: 1 (17 enodes) 1539342812.209 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342812.209 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* PI n) 2))))) 1539342812.209 * * * * [misc]progress: [ 59 / 64 ] simplifiying candidate # 1539342812.210 * [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))))))))))))))) 1539342812.210 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539342812.210 * * * * [misc]progress: [ 60 / 64 ] simplifiying candidate # 1539342812.210 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 2) (* (pow PI 2) k))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 3) (* (pow PI 3) (pow k 2))))))))))) 1539342812.210 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539342812.210 * * * * [misc]progress: [ 61 / 64 ] simplifiying candidate # 1539342812.210 * [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))) n))))))) 1539342812.210 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539342812.210 * * * * [misc]progress: [ 62 / 64 ] simplifiying candidate # 1539342812.210 * [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))))))))) 1539342812.210 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) +nan.0))) 1539342812.210 * * * * [misc]progress: [ 63 / 64 ] simplifiying candidate # 1539342812.210 * [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))))))) 1539342812.210 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) +nan.0))) 1539342812.210 * * * * [misc]progress: [ 64 / 64 ] simplifiying candidate # 1539342812.211 * [enter]simplify: Simplifying (- (+ (* +nan.0 PI) (- (+ (* +nan.0 (/ (pow PI 3) (pow n 2))) (- (* +nan.0 (/ (pow PI 2) n))))))) 1539342812.211 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) +nan.0))) 1539342812.211 * * * [misc]progress: adding candidates to table 1539342812.999 * * [misc]progress: iteration 4 / 4 1539342812.999 * * * [misc]progress: picking best candidate 1539342813.057 * * * * [misc]pick: Picked # 1539342813.057 * * * [misc]progress: localizing error 1539342813.080 * * * [misc]progress: generating rewritten candidates 1539342813.080 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) 1539342813.100 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1 1) 1539342813.104 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 2 2 1) 1539342813.109 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 2) 1539342813.125 * * * [misc]progress: generating series expansions 1539342813.125 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) 1539342813.125 * [misc]backup-simplify: Simplify (* (sqrt k) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI)))) into (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) 1539342813.125 * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) in (k n) around 0 1539342813.125 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) in n 1539342813.125 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in n 1539342813.125 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1539342813.125 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1539342813.125 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1539342813.125 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342813.125 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.125 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.125 * [misc]taylor: Taking taylor expansion of k in n 1539342813.125 * [misc]backup-simplify: Simplify k into k 1539342813.125 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342813.125 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.125 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.126 * [misc]backup-simplify: Simplify 2 into 2 1539342813.126 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.126 * [misc]taylor: Taking taylor expansion of n in n 1539342813.126 * [misc]backup-simplify: Simplify 0 into 0 1539342813.126 * [misc]backup-simplify: Simplify 1 into 1 1539342813.126 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.126 * [misc]backup-simplify: Simplify PI into PI 1539342813.127 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.127 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342813.127 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.128 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342813.129 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.129 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342813.129 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.130 * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539342813.130 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539342813.130 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.130 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.131 * [misc]backup-simplify: Simplify 2 into 2 1539342813.131 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.131 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.132 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) into (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) 1539342813.132 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in n 1539342813.132 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in n 1539342813.132 * [misc]taylor: Taking taylor expansion of k in n 1539342813.132 * [misc]backup-simplify: Simplify k into k 1539342813.132 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.132 * [misc]taylor: Taking taylor expansion of n in n 1539342813.132 * [misc]backup-simplify: Simplify 0 into 0 1539342813.132 * [misc]backup-simplify: Simplify 1 into 1 1539342813.132 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.132 * [misc]backup-simplify: Simplify PI into PI 1539342813.132 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.133 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.133 * [misc]backup-simplify: Simplify (/ k PI) into (/ k PI) 1539342813.133 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.133 * [misc]backup-simplify: Simplify (/ (/ k PI) (* 2 (sqrt 0))) into (* +nan.0 (/ k PI)) 1539342813.133 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) in k 1539342813.133 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in k 1539342813.133 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1539342813.133 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1539342813.133 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1539342813.133 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342813.134 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.134 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.134 * [misc]taylor: Taking taylor expansion of k in k 1539342813.134 * [misc]backup-simplify: Simplify 0 into 0 1539342813.134 * [misc]backup-simplify: Simplify 1 into 1 1539342813.134 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539342813.134 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539342813.134 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.134 * [misc]backup-simplify: Simplify 2 into 2 1539342813.134 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342813.134 * [misc]taylor: Taking taylor expansion of n in k 1539342813.134 * [misc]backup-simplify: Simplify n into n 1539342813.134 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.134 * [misc]backup-simplify: Simplify PI into PI 1539342813.134 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342813.134 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539342813.134 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539342813.134 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342813.134 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539342813.135 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342813.135 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539342813.136 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539342813.136 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539342813.136 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1/2 (log (* 2 (* n PI))))) into (* 1/2 (log (* 2 (* n PI)))) 1539342813.136 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342813.136 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.136 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.136 * [misc]backup-simplify: Simplify 2 into 2 1539342813.137 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.137 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.137 * [misc]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 1539342813.137 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in k 1539342813.137 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in k 1539342813.137 * [misc]taylor: Taking taylor expansion of k in k 1539342813.137 * [misc]backup-simplify: Simplify 0 into 0 1539342813.137 * [misc]backup-simplify: Simplify 1 into 1 1539342813.137 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342813.137 * [misc]taylor: Taking taylor expansion of n in k 1539342813.137 * [misc]backup-simplify: Simplify n into n 1539342813.137 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.137 * [misc]backup-simplify: Simplify PI into PI 1539342813.137 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342813.137 * [misc]backup-simplify: Simplify (/ 1 (* n PI)) into (/ 1 (* n PI)) 1539342813.138 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.138 * [misc]backup-simplify: Simplify (/ (/ 1 (* n PI)) (* 2 (sqrt 0))) into (/ +nan.0 (* n PI)) 1539342813.138 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ k (* n PI)))) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.138 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.138 * [misc]taylor: Taking taylor expansion of k in k 1539342813.138 * [misc]backup-simplify: Simplify 0 into 0 1539342813.138 * [misc]backup-simplify: Simplify 1 into 1 1539342813.138 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.138 * [misc]backup-simplify: Simplify 2 into 2 1539342813.138 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342813.138 * [misc]taylor: Taking taylor expansion of n in k 1539342813.138 * [misc]backup-simplify: Simplify n into n 1539342813.138 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.138 * [misc]backup-simplify: Simplify PI into PI 1539342813.138 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342813.139 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539342813.139 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539342813.139 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342813.139 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539342813.139 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342813.139 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539342813.140 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539342813.140 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539342813.141 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1/2 (log (* 2 (* n PI))))) into (* 1/2 (log (* 2 (* n PI)))) 1539342813.141 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342813.141 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.141 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.141 * [misc]backup-simplify: Simplify 2 into 2 1539342813.141 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.141 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.142 * [misc]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 1539342813.142 * [misc]taylor: Taking taylor expansion of (sqrt (/ k (* n PI))) in k 1539342813.142 * [misc]taylor: Taking taylor expansion of (/ k (* n PI)) in k 1539342813.142 * [misc]taylor: Taking taylor expansion of k in k 1539342813.142 * [misc]backup-simplify: Simplify 0 into 0 1539342813.142 * [misc]backup-simplify: Simplify 1 into 1 1539342813.142 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342813.142 * [misc]taylor: Taking taylor expansion of n in k 1539342813.142 * [misc]backup-simplify: Simplify n into n 1539342813.142 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.142 * [misc]backup-simplify: Simplify PI into PI 1539342813.142 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342813.142 * [misc]backup-simplify: Simplify (/ 1 (* n PI)) into (/ 1 (* n PI)) 1539342813.142 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.142 * [misc]backup-simplify: Simplify (/ (/ 1 (* n PI)) (* 2 (sqrt 0))) into (/ +nan.0 (* n PI)) 1539342813.143 * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 1539342813.143 * [misc]taylor: Taking taylor expansion of 0 in n 1539342813.143 * [misc]backup-simplify: Simplify 0 into 0 1539342813.143 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) 1539342813.144 * [misc]backup-simplify: Simplify (- (/ (* 1/2 (log (* 2 (* n PI)))) (sqrt 2)) (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) 1539342813.144 * [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))))) 1539342813.144 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (* (sqrt 2) (* n PI))))) in n 1539342813.144 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* n PI)))) in n 1539342813.145 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.145 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.145 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* n PI))) in n 1539342813.145 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539342813.145 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.145 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.145 * [misc]backup-simplify: Simplify 2 into 2 1539342813.145 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.145 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.145 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.145 * [misc]taylor: Taking taylor expansion of n in n 1539342813.145 * [misc]backup-simplify: Simplify 0 into 0 1539342813.145 * [misc]backup-simplify: Simplify 1 into 1 1539342813.145 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.145 * [misc]backup-simplify: Simplify PI into PI 1539342813.146 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.146 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342813.146 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.147 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539342813.148 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) PI)) into (/ 1 (* (sqrt 2) PI)) 1539342813.149 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (* (sqrt 2) PI))) into (/ +nan.0 (* (sqrt 2) PI)) 1539342813.150 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 1539342813.151 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 1539342813.151 * [misc]backup-simplify: Simplify 0 into 0 1539342813.152 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342813.152 * [misc]backup-simplify: Simplify (- (/ 0 (* n PI)) (+ (* (/ 1 (* n PI)) (/ 0 (* n PI))))) into 0 1539342813.152 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 (* n PI)) 2) (+)) (* 2 0)) into (/ +nan.0 (* (pow n 2) (pow PI 2))) 1539342813.153 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.153 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1539342813.155 * [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 1539342813.155 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1539342813.156 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1539342813.157 * [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)) 1539342813.158 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342813.159 * [misc]backup-simplify: Simplify (- (/ (* 1/8 (pow (log (* 2 (* n PI))) 2)) (sqrt 2)) (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) (/ 0 (sqrt 2))))) into (* 1/8 (/ (pow (log (* 2 (* n PI))) 2) (sqrt 2))) 1539342813.160 * [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))))))) 1539342813.161 * [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 1539342813.161 * [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 1539342813.161 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1539342813.161 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.161 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.161 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1539342813.161 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1539342813.161 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.161 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.161 * [misc]backup-simplify: Simplify 2 into 2 1539342813.161 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.161 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.161 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539342813.161 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539342813.161 * [misc]taylor: Taking taylor expansion of n in n 1539342813.161 * [misc]backup-simplify: Simplify 0 into 0 1539342813.162 * [misc]backup-simplify: Simplify 1 into 1 1539342813.162 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539342813.162 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.162 * [misc]backup-simplify: Simplify PI into PI 1539342813.162 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.162 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.163 * [misc]backup-simplify: Simplify (* 1 (pow PI 2)) into (pow PI 2) 1539342813.163 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342813.164 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (pow PI 2))) into (/ 1 (* (sqrt 2) (pow PI 2))) 1539342813.164 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))))) in n 1539342813.164 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI)))) in n 1539342813.164 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.164 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.164 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))) in n 1539342813.164 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342813.164 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.164 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.164 * [misc]backup-simplify: Simplify 2 into 2 1539342813.164 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.165 * [misc]taylor: Taking taylor expansion of n in n 1539342813.165 * [misc]backup-simplify: Simplify 0 into 0 1539342813.165 * [misc]backup-simplify: Simplify 1 into 1 1539342813.165 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.165 * [misc]backup-simplify: Simplify PI into PI 1539342813.165 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.165 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342813.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.166 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342813.167 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.167 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539342813.167 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.167 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.167 * [misc]backup-simplify: Simplify 2 into 2 1539342813.167 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.167 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.167 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.167 * [misc]taylor: Taking taylor expansion of n in n 1539342813.167 * [misc]backup-simplify: Simplify 0 into 0 1539342813.167 * [misc]backup-simplify: Simplify 1 into 1 1539342813.167 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.167 * [misc]backup-simplify: Simplify PI into PI 1539342813.168 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.168 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.169 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342813.169 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.170 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539342813.171 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.171 * [misc]backup-simplify: Simplify (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI)) into (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) PI)) 1539342813.172 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342813.172 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342813.173 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 2))) into 0 1539342813.174 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539342813.177 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) (pow PI 2))) (/ 0 (* (sqrt 2) (pow PI 2)))))) into 0 1539342813.178 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (sqrt 2) (pow PI 2))))) into 0 1539342813.178 * [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))) 1539342813.179 * [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)))))) 1539342813.180 * [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)))))) 1539342813.182 * [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)))))) 1539342813.183 * [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)))))) 1539342813.184 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342813.185 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342813.185 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 PI) (* 0 0))) into 0 1539342813.187 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))))) into 0 1539342813.188 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (* (sqrt 2) PI)))) into 0 1539342813.188 * [misc]backup-simplify: Simplify (- 0) into 0 1539342813.188 * [misc]backup-simplify: Simplify 0 into 0 1539342813.188 * [misc]backup-simplify: Simplify 0 into 0 1539342813.188 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.188 * [misc]backup-simplify: Simplify (- (/ 0 (* n PI)) (+ (* (/ 1 (* n PI)) (/ 0 (* n PI))) (* 0 (/ 0 (* n PI))))) into 0 1539342813.189 * [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))) 1539342813.190 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.190 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1539342813.191 * [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 1539342813.192 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539342813.192 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1539342813.193 * [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)) 1539342813.193 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342813.194 * [misc]backup-simplify: Simplify (- (/ (* 1/48 (pow (log (* 2 (* n PI))) 3)) (sqrt 2)) (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* (* 1/2 (/ (log (* 2 (* n PI))) (sqrt 2))) (/ 0 (sqrt 2))) (* (* 1/8 (/ (pow (log (* 2 (* n PI))) 2) (sqrt 2))) (/ 0 (sqrt 2))))) into (* 1/48 (/ (pow (log (* 2 (* n PI))) 3) (sqrt 2))) 1539342813.196 * [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)))))))))) 1539342813.196 * [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 1539342813.196 * [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 1539342813.196 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI)))) in n 1539342813.196 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.196 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.196 * [misc]taylor: Taking taylor expansion of (/ (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI))) in n 1539342813.196 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1539342813.196 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342813.196 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.196 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.196 * [misc]backup-simplify: Simplify 2 into 2 1539342813.196 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.196 * [misc]taylor: Taking taylor expansion of n in n 1539342813.196 * [misc]backup-simplify: Simplify 0 into 0 1539342813.196 * [misc]backup-simplify: Simplify 1 into 1 1539342813.196 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.196 * [misc]backup-simplify: Simplify PI into PI 1539342813.196 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.196 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342813.197 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.197 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342813.197 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.198 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.198 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1539342813.198 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.198 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.198 * [misc]backup-simplify: Simplify 2 into 2 1539342813.198 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.198 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.198 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.198 * [misc]taylor: Taking taylor expansion of n in n 1539342813.198 * [misc]backup-simplify: Simplify 0 into 0 1539342813.198 * [misc]backup-simplify: Simplify 1 into 1 1539342813.198 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.198 * [misc]backup-simplify: Simplify PI into PI 1539342813.199 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.199 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.200 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1539342813.200 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.200 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1539342813.200 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.201 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) PI) (* 0 0)) into (* (sqrt 2) PI) 1539342813.202 * [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)) 1539342813.202 * [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 1539342813.202 * [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 1539342813.202 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3))))) in n 1539342813.202 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.202 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.202 * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (* (pow n 3) (pow PI 3)))) in n 1539342813.202 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 3) (pow PI 3))) in n 1539342813.202 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.202 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.202 * [misc]backup-simplify: Simplify 2 into 2 1539342813.202 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.202 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.202 * [misc]taylor: Taking taylor expansion of (* (pow n 3) (pow PI 3)) in n 1539342813.202 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539342813.202 * [misc]taylor: Taking taylor expansion of n in n 1539342813.202 * [misc]backup-simplify: Simplify 0 into 0 1539342813.202 * [misc]backup-simplify: Simplify 1 into 1 1539342813.202 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539342813.202 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.202 * [misc]backup-simplify: Simplify PI into PI 1539342813.202 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.202 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.203 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.203 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342813.203 * [misc]backup-simplify: Simplify (* 1 (pow PI 3)) into (pow PI 3) 1539342813.204 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539342813.208 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (pow PI 3))) into (/ 1 (* (sqrt 2) (pow PI 3))) 1539342813.208 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))))) in n 1539342813.208 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1539342813.208 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.208 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.208 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (* n PI))) (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1539342813.209 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342813.209 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.209 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.209 * [misc]backup-simplify: Simplify 2 into 2 1539342813.209 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.209 * [misc]taylor: Taking taylor expansion of n in n 1539342813.209 * [misc]backup-simplify: Simplify 0 into 0 1539342813.209 * [misc]backup-simplify: Simplify 1 into 1 1539342813.209 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.209 * [misc]backup-simplify: Simplify PI into PI 1539342813.209 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.209 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342813.210 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.211 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342813.211 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.211 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1539342813.211 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.211 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.211 * [misc]backup-simplify: Simplify 2 into 2 1539342813.212 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.212 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.212 * [misc]taylor: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1539342813.212 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539342813.212 * [misc]taylor: Taking taylor expansion of n in n 1539342813.212 * [misc]backup-simplify: Simplify 0 into 0 1539342813.212 * [misc]backup-simplify: Simplify 1 into 1 1539342813.212 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539342813.212 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.212 * [misc]backup-simplify: Simplify PI into PI 1539342813.213 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.213 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.213 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.214 * [misc]backup-simplify: Simplify (* 1 (pow PI 2)) into (pow PI 2) 1539342813.215 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342813.215 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.216 * [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))) 1539342813.218 * [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))) 1539342813.219 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.220 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342813.222 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 (pow PI 2)))) into 0 1539342813.222 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342813.222 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342813.223 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (pow PI 2))) into 0 1539342813.223 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539342813.224 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 1))) into 0 1539342813.225 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (pow PI 3)))) into 0 1539342813.226 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 3))) into 0 1539342813.228 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342813.230 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 (pow PI 3)))) into 0 1539342813.231 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 3))) into 0 1539342813.235 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* (sqrt 2) (pow PI 3))) (/ 0 (* (sqrt 2) (pow PI 3)))))) into 0 1539342813.240 * [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 1539342813.242 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (/ 1 (* (sqrt 2) (pow PI 3)))))) into 0 1539342813.243 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342813.244 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342813.247 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342813.248 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342813.248 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342813.249 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (pow PI 2))) into 0 1539342813.250 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539342813.253 * [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 1539342813.254 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (+ (log n) (log (* 2 PI))) (* (sqrt 2) (pow PI 2))))) into 0 1539342813.254 * [misc]backup-simplify: Simplify (- 0) into 0 1539342813.254 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342813.255 * [misc]backup-simplify: Simplify (- 0) into 0 1539342813.256 * [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)))))))) 1539342813.258 * [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)))))))) 1539342813.261 * [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)))))))) 1539342813.266 * [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))))))))))))))) 1539342813.266 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (/ (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) (sqrt (* (* 2 (/ 1 n)) PI)))) into (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) 1539342813.266 * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) in (k n) around 0 1539342813.266 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.266 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.266 * [misc]taylor: Taking taylor expansion of k in n 1539342813.266 * [misc]backup-simplify: Simplify k into k 1539342813.266 * [misc]backup-simplify: Simplify (/ 1/2 k) into (/ 1/2 k) 1539342813.266 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.266 * [misc]backup-simplify: Simplify 2 into 2 1539342813.266 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.266 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.266 * [misc]backup-simplify: Simplify PI into PI 1539342813.266 * [misc]taylor: Taking taylor expansion of n in n 1539342813.266 * [misc]backup-simplify: Simplify 0 into 0 1539342813.266 * [misc]backup-simplify: Simplify 1 into 1 1539342813.267 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.267 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.267 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.268 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.268 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.268 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.268 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.268 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.268 * [misc]backup-simplify: Simplify 2 into 2 1539342813.269 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.269 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.269 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 1539342813.269 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in n 1539342813.269 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in n 1539342813.269 * [misc]taylor: Taking taylor expansion of n in n 1539342813.269 * [misc]backup-simplify: Simplify 0 into 0 1539342813.269 * [misc]backup-simplify: Simplify 1 into 1 1539342813.269 * [misc]taylor: Taking taylor expansion of (* PI k) in n 1539342813.269 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.269 * [misc]backup-simplify: Simplify PI into PI 1539342813.269 * [misc]taylor: Taking taylor expansion of k in n 1539342813.269 * [misc]backup-simplify: Simplify k into k 1539342813.269 * [misc]backup-simplify: Simplify (* PI k) into (* PI k) 1539342813.269 * [misc]backup-simplify: Simplify (/ 1 (* PI k)) into (/ 1 (* PI k)) 1539342813.269 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.270 * [misc]backup-simplify: Simplify (/ (/ 1 (* PI k)) (* 2 (sqrt 0))) into (/ +nan.0 (* PI k)) 1539342813.270 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.270 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.270 * [misc]taylor: Taking taylor expansion of k in k 1539342813.270 * [misc]backup-simplify: Simplify 0 into 0 1539342813.270 * [misc]backup-simplify: Simplify 1 into 1 1539342813.270 * [misc]backup-simplify: Simplify (/ 1/2 1) into 1/2 1539342813.270 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.270 * [misc]backup-simplify: Simplify 2 into 2 1539342813.270 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.270 * [misc]backup-simplify: Simplify PI into PI 1539342813.270 * [misc]taylor: Taking taylor expansion of n in k 1539342813.270 * [misc]backup-simplify: Simplify n into n 1539342813.270 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.270 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539342813.270 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539342813.270 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) 1539342813.270 * [misc]backup-simplify: Simplify (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1539342813.270 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.270 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.270 * [misc]backup-simplify: Simplify 2 into 2 1539342813.271 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.271 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.271 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 1539342813.271 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in k 1539342813.271 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in k 1539342813.271 * [misc]taylor: Taking taylor expansion of n in k 1539342813.271 * [misc]backup-simplify: Simplify n into n 1539342813.271 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539342813.271 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.271 * [misc]backup-simplify: Simplify PI into PI 1539342813.271 * [misc]taylor: Taking taylor expansion of k in k 1539342813.271 * [misc]backup-simplify: Simplify 0 into 0 1539342813.271 * [misc]backup-simplify: Simplify 1 into 1 1539342813.271 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539342813.272 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539342813.272 * [misc]backup-simplify: Simplify (/ n PI) into (/ n PI) 1539342813.272 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.272 * [misc]backup-simplify: Simplify (/ (/ n PI) (* 2 (sqrt 0))) into (* +nan.0 (/ n PI)) 1539342813.272 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n (* PI k)))) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.272 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.272 * [misc]taylor: Taking taylor expansion of k in k 1539342813.272 * [misc]backup-simplify: Simplify 0 into 0 1539342813.272 * [misc]backup-simplify: Simplify 1 into 1 1539342813.272 * [misc]backup-simplify: Simplify (/ 1/2 1) into 1/2 1539342813.272 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.272 * [misc]backup-simplify: Simplify 2 into 2 1539342813.272 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.272 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.272 * [misc]backup-simplify: Simplify PI into PI 1539342813.272 * [misc]taylor: Taking taylor expansion of n in k 1539342813.272 * [misc]backup-simplify: Simplify n into n 1539342813.272 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.273 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539342813.273 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539342813.273 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) 1539342813.273 * [misc]backup-simplify: Simplify (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1539342813.273 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.273 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.273 * [misc]backup-simplify: Simplify 2 into 2 1539342813.273 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.273 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.273 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 1539342813.273 * [misc]taylor: Taking taylor expansion of (sqrt (/ n (* PI k))) in k 1539342813.273 * [misc]taylor: Taking taylor expansion of (/ n (* PI k)) in k 1539342813.273 * [misc]taylor: Taking taylor expansion of n in k 1539342813.273 * [misc]backup-simplify: Simplify n into n 1539342813.273 * [misc]taylor: Taking taylor expansion of (* PI k) in k 1539342813.273 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.273 * [misc]backup-simplify: Simplify PI into PI 1539342813.273 * [misc]taylor: Taking taylor expansion of k in k 1539342813.273 * [misc]backup-simplify: Simplify 0 into 0 1539342813.273 * [misc]backup-simplify: Simplify 1 into 1 1539342813.274 * [misc]backup-simplify: Simplify (* PI 0) into 0 1539342813.274 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1539342813.274 * [misc]backup-simplify: Simplify (/ n PI) into (/ n PI) 1539342813.274 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.274 * [misc]backup-simplify: Simplify (/ (/ n PI) (* 2 (sqrt 0))) into (* +nan.0 (/ n PI)) 1539342813.274 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 0) into 0 1539342813.275 * [misc]taylor: Taking taylor expansion of 0 in n 1539342813.275 * [misc]backup-simplify: Simplify 0 into 0 1539342813.275 * [misc]backup-simplify: Simplify 0 into 0 1539342813.275 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))))) into 0 1539342813.275 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (* +nan.0 (/ n PI))) (* 0 0)) into (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) (* (sqrt 2) PI)))) 1539342813.275 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) (* (sqrt 2) PI)))) in n 1539342813.275 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) (* (sqrt 2) PI))) in n 1539342813.275 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.275 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.275 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) (* (sqrt 2) PI)) in n 1539342813.275 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) in n 1539342813.276 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342813.276 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342813.276 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.276 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.276 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342813.276 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.276 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.276 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.276 * [misc]backup-simplify: Simplify 2 into 2 1539342813.276 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.276 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.276 * [misc]backup-simplify: Simplify PI into PI 1539342813.276 * [misc]taylor: Taking taylor expansion of n in n 1539342813.276 * [misc]backup-simplify: Simplify 0 into 0 1539342813.276 * [misc]backup-simplify: Simplify 1 into 1 1539342813.276 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.276 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.276 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.276 * [misc]taylor: Taking taylor expansion of k in n 1539342813.276 * [misc]backup-simplify: Simplify k into k 1539342813.277 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.277 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.278 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342813.278 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.278 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.278 * [misc]taylor: Taking taylor expansion of n in n 1539342813.278 * [misc]backup-simplify: Simplify 0 into 0 1539342813.278 * [misc]backup-simplify: Simplify 1 into 1 1539342813.278 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) PI) in n 1539342813.278 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.278 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.278 * [misc]backup-simplify: Simplify 2 into 2 1539342813.279 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.279 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.279 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.279 * [misc]backup-simplify: Simplify PI into PI 1539342813.279 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) into 0 1539342813.280 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.280 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342813.282 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342813.282 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539342813.282 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539342813.283 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342813.284 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) (* 0 0)) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.284 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1539342813.285 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) 1539342813.285 * [misc]backup-simplify: Simplify 0 into 0 1539342813.285 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0 1539342813.286 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)))) into 0 1539342813.286 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ n PI)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow n 2) (pow PI 2))) 1539342813.287 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342813.287 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342813.288 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) (* (sqrt 2) (pow PI 2))))) 1539342813.288 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) (* (sqrt 2) (pow PI 2))))) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) (* (sqrt 2) (pow PI 2)))) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.288 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.288 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) (* (sqrt 2) (pow PI 2))) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 2)) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.288 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.288 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.288 * [misc]backup-simplify: Simplify 2 into 2 1539342813.288 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.288 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.288 * [misc]backup-simplify: Simplify PI into PI 1539342813.288 * [misc]taylor: Taking taylor expansion of n in n 1539342813.288 * [misc]backup-simplify: Simplify 0 into 0 1539342813.288 * [misc]backup-simplify: Simplify 1 into 1 1539342813.289 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.289 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.289 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.289 * [misc]taylor: Taking taylor expansion of k in n 1539342813.289 * [misc]backup-simplify: Simplify k into k 1539342813.289 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.290 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.290 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342813.291 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.291 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.291 * [misc]taylor: Taking taylor expansion of (pow n 2) in n 1539342813.291 * [misc]taylor: Taking taylor expansion of n in n 1539342813.291 * [misc]backup-simplify: Simplify 0 into 0 1539342813.291 * [misc]backup-simplify: Simplify 1 into 1 1539342813.291 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in n 1539342813.291 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.291 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.291 * [misc]backup-simplify: Simplify 2 into 2 1539342813.291 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.291 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.291 * [misc]taylor: Taking taylor expansion of (pow PI 2) in n 1539342813.291 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.291 * [misc]backup-simplify: Simplify PI into PI 1539342813.291 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.292 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.292 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.293 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342813.293 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) 1539342813.294 * [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))) 1539342813.295 * [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)))) 1539342813.296 * [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)))) 1539342813.296 * [misc]backup-simplify: Simplify 0 into 0 1539342813.296 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539342813.297 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342813.297 * [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))) 1539342813.298 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342813.298 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342813.299 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) (* (sqrt 2) (pow PI 3))))) 1539342813.299 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) (* (sqrt 2) (pow PI 3))))) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) (* (sqrt 2) (pow PI 3)))) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.299 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.299 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) (* (sqrt 2) (pow PI 3))) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 3)) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.299 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.299 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.299 * [misc]backup-simplify: Simplify 2 into 2 1539342813.299 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.299 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.299 * [misc]backup-simplify: Simplify PI into PI 1539342813.299 * [misc]taylor: Taking taylor expansion of n in n 1539342813.299 * [misc]backup-simplify: Simplify 0 into 0 1539342813.299 * [misc]backup-simplify: Simplify 1 into 1 1539342813.299 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.300 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.300 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.300 * [misc]taylor: Taking taylor expansion of k in n 1539342813.300 * [misc]backup-simplify: Simplify k into k 1539342813.300 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.301 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.301 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342813.301 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.302 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.302 * [misc]taylor: Taking taylor expansion of (pow n 3) in n 1539342813.302 * [misc]taylor: Taking taylor expansion of n in n 1539342813.302 * [misc]backup-simplify: Simplify 0 into 0 1539342813.302 * [misc]backup-simplify: Simplify 1 into 1 1539342813.302 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 3)) in n 1539342813.302 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.302 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.302 * [misc]backup-simplify: Simplify 2 into 2 1539342813.302 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.302 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.302 * [misc]taylor: Taking taylor expansion of (pow PI 3) in n 1539342813.302 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.302 * [misc]backup-simplify: Simplify PI into PI 1539342813.302 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.303 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.303 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.303 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.303 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342813.304 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539342813.305 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) 1539342813.305 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.306 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.309 * [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 1539342813.309 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342813.310 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))) into 0 1539342813.311 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539342813.312 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 1) (* 0 0))) into 0 1539342813.312 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 PI)) into 0 1539342813.313 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) PI)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))))) into 0 1539342813.314 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) into 0 1539342813.314 * [misc]backup-simplify: Simplify (- 0) into 0 1539342813.314 * [misc]backup-simplify: Simplify 0 into 0 1539342813.314 * [misc]backup-simplify: Simplify 0 into 0 1539342813.315 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539342813.316 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342813.316 * [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))) 1539342813.317 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342813.318 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342813.319 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) (* (sqrt 2) (pow PI 4))))) 1539342813.319 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) (* (sqrt 2) (pow PI 4))))) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) (* (sqrt 2) (pow PI 4)))) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.319 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.319 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) (* (sqrt 2) (pow PI 4))) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 4)) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.319 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.319 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.319 * [misc]backup-simplify: Simplify 2 into 2 1539342813.319 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.319 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.319 * [misc]backup-simplify: Simplify PI into PI 1539342813.319 * [misc]taylor: Taking taylor expansion of n in n 1539342813.319 * [misc]backup-simplify: Simplify 0 into 0 1539342813.319 * [misc]backup-simplify: Simplify 1 into 1 1539342813.320 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.320 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.320 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.320 * [misc]taylor: Taking taylor expansion of k in n 1539342813.320 * [misc]backup-simplify: Simplify k into k 1539342813.321 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.321 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.321 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342813.322 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.322 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.322 * [misc]taylor: Taking taylor expansion of (pow n 4) in n 1539342813.322 * [misc]taylor: Taking taylor expansion of n in n 1539342813.322 * [misc]backup-simplify: Simplify 0 into 0 1539342813.322 * [misc]backup-simplify: Simplify 1 into 1 1539342813.322 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 4)) in n 1539342813.322 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.322 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.322 * [misc]backup-simplify: Simplify 2 into 2 1539342813.322 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.322 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.322 * [misc]taylor: Taking taylor expansion of (pow PI 4) in n 1539342813.322 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.322 * [misc]backup-simplify: Simplify PI into PI 1539342813.323 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.323 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.323 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.323 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.324 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1539342813.324 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 4)) into (* (sqrt 2) (pow PI 4)) 1539342813.325 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 4))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 4))) 1539342813.326 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2)))) into (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2)))) 1539342813.327 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) 1539342813.329 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) 1539342813.330 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.331 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.335 * [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 1539342813.336 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342813.336 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 1539342813.338 * [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 1539342813.339 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1539342813.340 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342813.340 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.342 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) PI)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))) (* 0 (/ 0 (* (sqrt 2) PI))))) into 0 1539342813.343 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))))) into 0 1539342813.343 * [misc]backup-simplify: Simplify (- 0) into 0 1539342813.343 * [misc]backup-simplify: Simplify 0 into 0 1539342813.343 * [misc]backup-simplify: Simplify 0 into 0 1539342813.344 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 1539342813.345 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342813.346 * [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))) 1539342813.347 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342813.347 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342813.349 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) (* (sqrt 2) (pow PI 5))))) 1539342813.349 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) (* (sqrt 2) (pow PI 5))))) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) (* (sqrt 2) (pow PI 5)))) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.349 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.349 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) (* (sqrt 2) (pow PI 5))) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 5)) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.349 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.349 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.349 * [misc]backup-simplify: Simplify 2 into 2 1539342813.349 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.349 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.349 * [misc]backup-simplify: Simplify PI into PI 1539342813.349 * [misc]taylor: Taking taylor expansion of n in n 1539342813.349 * [misc]backup-simplify: Simplify 0 into 0 1539342813.349 * [misc]backup-simplify: Simplify 1 into 1 1539342813.349 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.349 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.350 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.350 * [misc]taylor: Taking taylor expansion of k in n 1539342813.350 * [misc]backup-simplify: Simplify k into k 1539342813.350 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.351 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.351 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342813.351 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.352 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.352 * [misc]taylor: Taking taylor expansion of (pow n 5) in n 1539342813.352 * [misc]taylor: Taking taylor expansion of n in n 1539342813.352 * [misc]backup-simplify: Simplify 0 into 0 1539342813.352 * [misc]backup-simplify: Simplify 1 into 1 1539342813.352 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 5)) in n 1539342813.352 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.352 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.352 * [misc]backup-simplify: Simplify 2 into 2 1539342813.352 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.352 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.352 * [misc]taylor: Taking taylor expansion of (pow PI 5) in n 1539342813.352 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.352 * [misc]backup-simplify: Simplify PI into PI 1539342813.352 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.352 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.352 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.353 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.353 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.353 * [misc]backup-simplify: Simplify (* (pow PI 2) (pow PI 2)) into (pow PI 4) 1539342813.354 * [misc]backup-simplify: Simplify (* PI (pow PI 4)) into (pow PI 5) 1539342813.354 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 5)) into (* (sqrt 2) (pow PI 5)) 1539342813.355 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 5))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 5))) 1539342813.355 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 1)) into 0 1539342813.356 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.356 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342813.358 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342813.358 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 1539342813.359 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 1539342813.360 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342813.361 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (* 0 1)) into 0 1539342813.362 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 PI)) into 0 1539342813.362 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (pow PI 2))) into 0 1539342813.366 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) (pow PI 2))) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) (/ 0 (* (sqrt 2) (pow PI 2)))))) into 0 1539342813.367 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into 0 1539342813.367 * [misc]backup-simplify: Simplify (- 0) into 0 1539342813.367 * [misc]backup-simplify: Simplify 0 into 0 1539342813.369 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.371 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342813.385 * [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 1539342813.386 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342813.388 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 1539342813.394 * [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 1539342813.395 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 1539342813.395 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342813.397 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.402 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) PI)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))) (* 0 (/ 0 (* (sqrt 2) PI))) (* 0 (/ 0 (* (sqrt 2) PI))))) into 0 1539342813.404 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))))) into 0 1539342813.404 * [misc]backup-simplify: Simplify (- 0) into 0 1539342813.404 * [misc]backup-simplify: Simplify 0 into 0 1539342813.404 * [misc]backup-simplify: Simplify 0 into 0 1539342813.406 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 1539342813.408 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342813.410 * [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))) 1539342813.412 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342813.414 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342813.416 * [misc]backup-simplify: Simplify (+ (* (/ (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 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) (* (sqrt 2) (pow PI 6))))) 1539342813.416 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) (* (sqrt 2) (pow PI 6))))) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) (* (sqrt 2) (pow PI 6)))) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.416 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.416 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) (* (sqrt 2) (pow PI 6))) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (pow n 6)) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.416 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.416 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.416 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.417 * [misc]backup-simplify: Simplify 2 into 2 1539342813.417 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.417 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.417 * [misc]backup-simplify: Simplify PI into PI 1539342813.417 * [misc]taylor: Taking taylor expansion of n in n 1539342813.417 * [misc]backup-simplify: Simplify 0 into 0 1539342813.417 * [misc]backup-simplify: Simplify 1 into 1 1539342813.417 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.417 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.418 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.418 * [misc]taylor: Taking taylor expansion of k in n 1539342813.418 * [misc]backup-simplify: Simplify k into k 1539342813.418 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.419 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.420 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) 1539342813.420 * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.421 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.421 * [misc]taylor: Taking taylor expansion of (pow n 6) in n 1539342813.421 * [misc]taylor: Taking taylor expansion of n in n 1539342813.421 * [misc]backup-simplify: Simplify 0 into 0 1539342813.421 * [misc]backup-simplify: Simplify 1 into 1 1539342813.421 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 6)) in n 1539342813.421 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.421 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.421 * [misc]backup-simplify: Simplify 2 into 2 1539342813.421 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.421 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.421 * [misc]taylor: Taking taylor expansion of (pow PI 6) in n 1539342813.421 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.422 * [misc]backup-simplify: Simplify PI into PI 1539342813.422 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.422 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.422 * [misc]backup-simplify: Simplify (* 1 1) into 1 1539342813.423 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.423 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.423 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342813.424 * [misc]backup-simplify: Simplify (* (pow PI 3) (pow PI 3)) into (pow PI 6) 1539342813.425 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 6)) into (* (sqrt 2) (pow PI 6)) 1539342813.426 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 6))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 6))) 1539342813.427 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3)))) into (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3)))) 1539342813.429 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) 1539342813.430 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) 1539342813.435 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) (pow PI 3))))) (* (pow (/ 1 n) 3) (pow (/ 1 k) 2))) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) (pow PI 2))))) (* (pow (/ 1 n) 2) (/ 1 k))) (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) PI)))) (* (/ 1 n) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 2) (* (pow PI 2) k))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 3) (* (pow PI 3) (pow k 2))))))))))) 1539342813.435 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (- k))) (/ (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) (sqrt (* (* 2 (/ 1 (- n))) PI)))) into (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) 1539342813.435 * [misc]approximate: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) in (k n) around 0 1539342813.435 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) in n 1539342813.435 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in n 1539342813.435 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1539342813.435 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1539342813.435 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1539342813.435 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in n 1539342813.436 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342813.436 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.436 * [misc]taylor: Taking taylor expansion of k in n 1539342813.436 * [misc]backup-simplify: Simplify k into k 1539342813.436 * [misc]backup-simplify: Simplify (/ -1/2 k) into (/ -1/2 k) 1539342813.436 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342813.436 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.436 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.436 * [misc]backup-simplify: Simplify -2 into -2 1539342813.436 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.436 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.436 * [misc]backup-simplify: Simplify PI into PI 1539342813.436 * [misc]taylor: Taking taylor expansion of n in n 1539342813.436 * [misc]backup-simplify: Simplify 0 into 0 1539342813.436 * [misc]backup-simplify: Simplify 1 into 1 1539342813.436 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.437 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.437 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342813.438 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.438 * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342813.439 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342813.439 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1539342813.439 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1539342813.439 * [misc]taylor: Taking taylor expansion of -1 in n 1539342813.439 * [misc]backup-simplify: Simplify -1 into -1 1539342813.439 * [misc]taylor: Taking taylor expansion of k in n 1539342813.439 * [misc]backup-simplify: Simplify k into k 1539342813.439 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1539342813.439 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1539342813.439 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1539342813.439 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1539342813.439 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342813.440 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.440 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.440 * [misc]backup-simplify: Simplify -2 into -2 1539342813.440 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.440 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.440 * [misc]backup-simplify: Simplify PI into PI 1539342813.440 * [misc]taylor: Taking taylor expansion of n in n 1539342813.440 * [misc]backup-simplify: Simplify 0 into 0 1539342813.440 * [misc]backup-simplify: Simplify 1 into 1 1539342813.440 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.440 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.440 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.441 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342813.442 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) into (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539342813.443 * [misc]backup-simplify: Simplify (/ (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (* +nan.0 PI)) into (* +nan.0 (/ (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) PI)) 1539342813.443 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342813.443 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.443 * [misc]taylor: Taking taylor expansion of k in k 1539342813.443 * [misc]backup-simplify: Simplify 0 into 0 1539342813.443 * [misc]backup-simplify: Simplify 1 into 1 1539342813.443 * [misc]backup-simplify: Simplify (/ -1/2 1) into -1/2 1539342813.443 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.443 * [misc]backup-simplify: Simplify -2 into -2 1539342813.443 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.443 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.443 * [misc]backup-simplify: Simplify PI into PI 1539342813.443 * [misc]taylor: Taking taylor expansion of n in k 1539342813.443 * [misc]backup-simplify: Simplify n into n 1539342813.443 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.443 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342813.444 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539342813.444 * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) 1539342813.444 * [misc]backup-simplify: Simplify (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1539342813.444 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342813.444 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342813.444 * [misc]taylor: Taking taylor expansion of -1 in k 1539342813.444 * [misc]backup-simplify: Simplify -1 into -1 1539342813.444 * [misc]taylor: Taking taylor expansion of k in k 1539342813.444 * [misc]backup-simplify: Simplify 0 into 0 1539342813.444 * [misc]backup-simplify: Simplify 1 into 1 1539342813.444 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342813.444 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.444 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342813.444 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1539342813.444 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342813.444 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.444 * [misc]backup-simplify: Simplify -2 into -2 1539342813.444 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.444 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.444 * [misc]backup-simplify: Simplify PI into PI 1539342813.444 * [misc]taylor: Taking taylor expansion of n in k 1539342813.444 * [misc]backup-simplify: Simplify n into n 1539342813.444 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.445 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342813.445 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539342813.445 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1539342813.445 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1539342813.445 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539342813.445 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 0) into 0 1539342813.445 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1539342813.445 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (sqrt (* -2 (/ PI n)))) into (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) 1539342813.445 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) (sqrt (* -2 (/ PI n)))) in k 1539342813.445 * [misc]taylor: Taking taylor expansion of (* (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (/ -1 k))) in k 1539342813.445 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1539342813.445 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1539342813.445 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1539342813.445 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in k 1539342813.446 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342813.446 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.446 * [misc]taylor: Taking taylor expansion of k in k 1539342813.446 * [misc]backup-simplify: Simplify 0 into 0 1539342813.446 * [misc]backup-simplify: Simplify 1 into 1 1539342813.446 * [misc]backup-simplify: Simplify (/ -1/2 1) into -1/2 1539342813.446 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539342813.446 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342813.446 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.446 * [misc]backup-simplify: Simplify -2 into -2 1539342813.446 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.446 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.446 * [misc]backup-simplify: Simplify PI into PI 1539342813.446 * [misc]taylor: Taking taylor expansion of n in k 1539342813.446 * [misc]backup-simplify: Simplify n into n 1539342813.446 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.446 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342813.446 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539342813.446 * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) 1539342813.446 * [misc]backup-simplify: Simplify (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1539342813.446 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1539342813.446 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1539342813.446 * [misc]taylor: Taking taylor expansion of -1 in k 1539342813.446 * [misc]backup-simplify: Simplify -1 into -1 1539342813.446 * [misc]taylor: Taking taylor expansion of k in k 1539342813.446 * [misc]backup-simplify: Simplify 0 into 0 1539342813.446 * [misc]backup-simplify: Simplify 1 into 1 1539342813.446 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1539342813.446 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.447 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1539342813.447 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1539342813.447 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342813.447 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.447 * [misc]backup-simplify: Simplify -2 into -2 1539342813.447 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.447 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.447 * [misc]backup-simplify: Simplify PI into PI 1539342813.447 * [misc]taylor: Taking taylor expansion of n in k 1539342813.447 * [misc]backup-simplify: Simplify n into n 1539342813.447 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.447 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342813.447 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539342813.447 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1539342813.447 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1539342813.447 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539342813.447 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 0) into 0 1539342813.448 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1539342813.448 * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (sqrt (* -2 (/ PI n)))) into (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) 1539342813.448 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) in n 1539342813.448 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.448 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.448 * [misc]taylor: Taking taylor expansion of (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) in n 1539342813.448 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n 1539342813.448 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n 1539342813.448 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342813.448 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.448 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1539342813.448 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342813.448 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.448 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.448 * [misc]backup-simplify: Simplify -2 into -2 1539342813.448 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.448 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.448 * [misc]backup-simplify: Simplify PI into PI 1539342813.448 * [misc]taylor: Taking taylor expansion of n in n 1539342813.448 * [misc]backup-simplify: Simplify 0 into 0 1539342813.448 * [misc]backup-simplify: Simplify 1 into 1 1539342813.448 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.448 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.449 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342813.449 * [misc]taylor: Taking taylor expansion of k in n 1539342813.449 * [misc]backup-simplify: Simplify k into k 1539342813.449 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.450 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.450 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) 1539342813.451 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342813.451 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342813.451 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342813.451 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.451 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.451 * [misc]backup-simplify: Simplify -2 into -2 1539342813.451 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.451 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.451 * [misc]backup-simplify: Simplify PI into PI 1539342813.451 * [misc]taylor: Taking taylor expansion of n in n 1539342813.451 * [misc]backup-simplify: Simplify 0 into 0 1539342813.451 * [misc]backup-simplify: Simplify 1 into 1 1539342813.451 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.451 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.452 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.452 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342813.452 * [misc]backup-simplify: Simplify (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.453 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.453 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.453 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1539342813.454 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1539342813.454 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1539342813.455 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (sqrt (* -2 (/ PI n)))) (+ (* (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) (/ 0 (sqrt (* -2 (/ PI n))))))) into (- (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))))) 1539342813.455 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))))) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n))))) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1539342813.455 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.455 * [misc]taylor: Taking taylor expansion of (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342813.455 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.455 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.455 * [misc]backup-simplify: Simplify -2 into -2 1539342813.455 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.455 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.455 * [misc]backup-simplify: Simplify PI into PI 1539342813.455 * [misc]taylor: Taking taylor expansion of n in n 1539342813.455 * [misc]backup-simplify: Simplify 0 into 0 1539342813.455 * [misc]backup-simplify: Simplify 1 into 1 1539342813.455 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.455 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.456 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342813.456 * [misc]taylor: Taking taylor expansion of k in n 1539342813.456 * [misc]backup-simplify: Simplify k into k 1539342813.456 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.457 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.457 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) 1539342813.457 * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342813.458 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342813.458 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342813.458 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.458 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.458 * [misc]backup-simplify: Simplify -2 into -2 1539342813.458 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.458 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.458 * [misc]backup-simplify: Simplify PI into PI 1539342813.458 * [misc]taylor: Taking taylor expansion of n in n 1539342813.458 * [misc]backup-simplify: Simplify 0 into 0 1539342813.458 * [misc]backup-simplify: Simplify 1 into 1 1539342813.458 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.458 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.458 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.459 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342813.459 * [misc]backup-simplify: Simplify (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.459 * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.460 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) 1539342813.460 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) 1539342813.461 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.461 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342813.464 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539342813.464 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 1539342813.465 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 1539342813.466 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342813.467 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.467 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342813.468 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342813.469 * [misc]backup-simplify: Simplify (- (/ 0 (* +nan.0 PI)) (+ (* (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) (/ (* +nan.0 (pow PI 2)) (* +nan.0 PI))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342813.470 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (* 0 (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342813.470 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342813.472 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (* (/ 1 (- n)) 1)) (+ (* (- (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) PI))) (* 1 (/ 1 (- k)))) (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) PI)))) 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))) n))))))) 1539342813.472 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1 1) 1539342813.473 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1539342813.473 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539342813.473 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.473 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.473 * [misc]backup-simplify: Simplify 2 into 2 1539342813.473 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.473 * [misc]taylor: Taking taylor expansion of n in n 1539342813.473 * [misc]backup-simplify: Simplify 0 into 0 1539342813.473 * [misc]backup-simplify: Simplify 1 into 1 1539342813.473 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.473 * [misc]backup-simplify: Simplify PI into PI 1539342813.473 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.473 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.473 * [misc]backup-simplify: Simplify 2 into 2 1539342813.473 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.473 * [misc]taylor: Taking taylor expansion of n in n 1539342813.473 * [misc]backup-simplify: Simplify 0 into 0 1539342813.473 * [misc]backup-simplify: Simplify 1 into 1 1539342813.473 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.473 * [misc]backup-simplify: Simplify PI into PI 1539342813.474 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.474 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342813.474 * [misc]backup-simplify: Simplify 0 into 0 1539342813.474 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.475 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342813.475 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.476 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342813.477 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342813.477 * [misc]backup-simplify: Simplify 0 into 0 1539342813.479 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.480 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342813.481 * [misc]backup-simplify: Simplify 0 into 0 1539342813.483 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342813.485 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342813.485 * [misc]backup-simplify: Simplify 0 into 0 1539342813.487 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342813.490 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539342813.490 * [misc]backup-simplify: Simplify 0 into 0 1539342813.494 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342813.497 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539342813.497 * [misc]backup-simplify: Simplify 0 into 0 1539342813.501 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539342813.506 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539342813.506 * [misc]backup-simplify: Simplify 0 into 0 1539342813.506 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539342813.506 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1539342813.506 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539342813.506 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.506 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.506 * [misc]backup-simplify: Simplify 2 into 2 1539342813.507 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.507 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.507 * [misc]backup-simplify: Simplify PI into PI 1539342813.507 * [misc]taylor: Taking taylor expansion of n in n 1539342813.507 * [misc]backup-simplify: Simplify 0 into 0 1539342813.507 * [misc]backup-simplify: Simplify 1 into 1 1539342813.507 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.507 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.507 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.507 * [misc]backup-simplify: Simplify 2 into 2 1539342813.507 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.507 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.507 * [misc]backup-simplify: Simplify PI into PI 1539342813.507 * [misc]taylor: Taking taylor expansion of n in n 1539342813.507 * [misc]backup-simplify: Simplify 0 into 0 1539342813.507 * [misc]backup-simplify: Simplify 1 into 1 1539342813.507 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.508 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.508 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.509 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.510 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342813.510 * [misc]backup-simplify: Simplify 0 into 0 1539342813.511 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.512 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.512 * [misc]backup-simplify: Simplify 0 into 0 1539342813.514 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.516 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.516 * [misc]backup-simplify: Simplify 0 into 0 1539342813.518 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.520 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342813.520 * [misc]backup-simplify: Simplify 0 into 0 1539342813.522 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.525 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342813.525 * [misc]backup-simplify: Simplify 0 into 0 1539342813.527 * [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 1539342813.531 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342813.531 * [misc]backup-simplify: Simplify 0 into 0 1539342813.531 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539342813.531 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1539342813.531 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539342813.531 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.531 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.531 * [misc]backup-simplify: Simplify -2 into -2 1539342813.531 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.531 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.531 * [misc]backup-simplify: Simplify PI into PI 1539342813.531 * [misc]taylor: Taking taylor expansion of n in n 1539342813.531 * [misc]backup-simplify: Simplify 0 into 0 1539342813.531 * [misc]backup-simplify: Simplify 1 into 1 1539342813.532 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.532 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.532 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.532 * [misc]backup-simplify: Simplify -2 into -2 1539342813.532 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.532 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.532 * [misc]backup-simplify: Simplify PI into PI 1539342813.532 * [misc]taylor: Taking taylor expansion of n in n 1539342813.532 * [misc]backup-simplify: Simplify 0 into 0 1539342813.532 * [misc]backup-simplify: Simplify 1 into 1 1539342813.532 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.533 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.533 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.534 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.535 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342813.535 * [misc]backup-simplify: Simplify 0 into 0 1539342813.536 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.537 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.537 * [misc]backup-simplify: Simplify 0 into 0 1539342813.539 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.540 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.540 * [misc]backup-simplify: Simplify 0 into 0 1539342813.541 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.542 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342813.542 * [misc]backup-simplify: Simplify 0 into 0 1539342813.544 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.545 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342813.545 * [misc]backup-simplify: Simplify 0 into 0 1539342813.547 * [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 1539342813.549 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342813.549 * [misc]backup-simplify: Simplify 0 into 0 1539342813.549 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539342813.549 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 2 2 1) 1539342813.549 * [misc]backup-simplify: Simplify (* (* 2 n) PI) into (* 2 (* n PI)) 1539342813.549 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1539342813.549 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.549 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.549 * [misc]backup-simplify: Simplify 2 into 2 1539342813.549 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.549 * [misc]taylor: Taking taylor expansion of n in n 1539342813.549 * [misc]backup-simplify: Simplify 0 into 0 1539342813.549 * [misc]backup-simplify: Simplify 1 into 1 1539342813.549 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.550 * [misc]backup-simplify: Simplify PI into PI 1539342813.550 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.550 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.550 * [misc]backup-simplify: Simplify 2 into 2 1539342813.550 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.550 * [misc]taylor: Taking taylor expansion of n in n 1539342813.550 * [misc]backup-simplify: Simplify 0 into 0 1539342813.550 * [misc]backup-simplify: Simplify 1 into 1 1539342813.550 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.550 * [misc]backup-simplify: Simplify PI into PI 1539342813.550 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.550 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342813.550 * [misc]backup-simplify: Simplify 0 into 0 1539342813.550 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.551 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342813.551 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.552 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342813.552 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342813.552 * [misc]backup-simplify: Simplify 0 into 0 1539342813.554 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.555 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342813.555 * [misc]backup-simplify: Simplify 0 into 0 1539342813.556 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342813.557 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1539342813.557 * [misc]backup-simplify: Simplify 0 into 0 1539342813.559 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342813.560 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1539342813.560 * [misc]backup-simplify: Simplify 0 into 0 1539342813.562 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342813.564 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1539342813.565 * [misc]backup-simplify: Simplify 0 into 0 1539342813.567 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1539342813.570 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1539342813.570 * [misc]backup-simplify: Simplify 0 into 0 1539342813.570 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1539342813.570 * [misc]backup-simplify: Simplify (* (* 2 (/ 1 n)) PI) into (* 2 (/ PI n)) 1539342813.570 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1539342813.570 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.570 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.570 * [misc]backup-simplify: Simplify 2 into 2 1539342813.570 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.570 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.570 * [misc]backup-simplify: Simplify PI into PI 1539342813.570 * [misc]taylor: Taking taylor expansion of n in n 1539342813.570 * [misc]backup-simplify: Simplify 0 into 0 1539342813.570 * [misc]backup-simplify: Simplify 1 into 1 1539342813.571 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.571 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.571 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.571 * [misc]backup-simplify: Simplify 2 into 2 1539342813.571 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.571 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.571 * [misc]backup-simplify: Simplify PI into PI 1539342813.571 * [misc]taylor: Taking taylor expansion of n in n 1539342813.571 * [misc]backup-simplify: Simplify 0 into 0 1539342813.571 * [misc]backup-simplify: Simplify 1 into 1 1539342813.571 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.571 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.571 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.572 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.573 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342813.573 * [misc]backup-simplify: Simplify 0 into 0 1539342813.574 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.574 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.574 * [misc]backup-simplify: Simplify 0 into 0 1539342813.575 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.577 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.577 * [misc]backup-simplify: Simplify 0 into 0 1539342813.579 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.581 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342813.581 * [misc]backup-simplify: Simplify 0 into 0 1539342813.583 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.585 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342813.585 * [misc]backup-simplify: Simplify 0 into 0 1539342813.587 * [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 1539342813.589 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342813.589 * [misc]backup-simplify: Simplify 0 into 0 1539342813.589 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1539342813.589 * [misc]backup-simplify: Simplify (* (* 2 (/ 1 (- n))) PI) into (* -2 (/ PI n)) 1539342813.589 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1539342813.590 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.590 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.590 * [misc]backup-simplify: Simplify -2 into -2 1539342813.590 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.590 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.590 * [misc]backup-simplify: Simplify PI into PI 1539342813.590 * [misc]taylor: Taking taylor expansion of n in n 1539342813.590 * [misc]backup-simplify: Simplify 0 into 0 1539342813.590 * [misc]backup-simplify: Simplify 1 into 1 1539342813.590 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.590 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.590 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.590 * [misc]backup-simplify: Simplify -2 into -2 1539342813.590 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.590 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.590 * [misc]backup-simplify: Simplify PI into PI 1539342813.590 * [misc]taylor: Taking taylor expansion of n in n 1539342813.590 * [misc]backup-simplify: Simplify 0 into 0 1539342813.590 * [misc]backup-simplify: Simplify 1 into 1 1539342813.590 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.590 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.591 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.591 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.592 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342813.592 * [misc]backup-simplify: Simplify 0 into 0 1539342813.592 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.593 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.593 * [misc]backup-simplify: Simplify 0 into 0 1539342813.594 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.595 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.595 * [misc]backup-simplify: Simplify 0 into 0 1539342813.596 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.597 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1539342813.597 * [misc]backup-simplify: Simplify 0 into 0 1539342813.599 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.600 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1539342813.600 * [misc]backup-simplify: Simplify 0 into 0 1539342813.602 * [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 1539342813.604 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1539342813.604 * [misc]backup-simplify: Simplify 0 into 0 1539342813.604 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1539342813.604 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 2) 1539342813.604 * [misc]backup-simplify: Simplify (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))) into (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ 1 (* n PI)))) 1539342813.604 * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ 1 (* n PI)))) in (n k) around 0 1539342813.604 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ 1 (* n PI)))) in k 1539342813.604 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in k 1539342813.604 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1539342813.604 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1539342813.604 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1539342813.604 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1539342813.604 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.604 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.604 * [misc]taylor: Taking taylor expansion of k in k 1539342813.605 * [misc]backup-simplify: Simplify 0 into 0 1539342813.605 * [misc]backup-simplify: Simplify 1 into 1 1539342813.605 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1539342813.605 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1539342813.605 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.605 * [misc]backup-simplify: Simplify 2 into 2 1539342813.605 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342813.605 * [misc]taylor: Taking taylor expansion of n in k 1539342813.605 * [misc]backup-simplify: Simplify n into n 1539342813.605 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.605 * [misc]backup-simplify: Simplify PI into PI 1539342813.605 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342813.605 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1539342813.605 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1539342813.605 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342813.605 * [misc]backup-simplify: Simplify (* 0 (log (* 2 (* n PI)))) into 0 1539342813.605 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342813.605 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1539342813.606 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1539342813.606 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1539342813.606 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1/2 (log (* 2 (* n PI))))) into (* 1/2 (log (* 2 (* n PI)))) 1539342813.606 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342813.606 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.606 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.606 * [misc]backup-simplify: Simplify 2 into 2 1539342813.606 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.606 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.607 * [misc]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) 1539342813.607 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in k 1539342813.607 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in k 1539342813.607 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1539342813.607 * [misc]taylor: Taking taylor expansion of n in k 1539342813.607 * [misc]backup-simplify: Simplify n into n 1539342813.607 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.607 * [misc]backup-simplify: Simplify PI into PI 1539342813.607 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1539342813.607 * [misc]backup-simplify: Simplify (/ 1 (* n PI)) into (/ 1 (* n PI)) 1539342813.607 * [misc]backup-simplify: Simplify (sqrt (/ 1 (* n PI))) into (sqrt (/ 1 (* n PI))) 1539342813.607 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1539342813.607 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (* n PI)) (/ 0 (* n PI))))) into 0 1539342813.607 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 (* n PI))))) into 0 1539342813.607 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ 1 (* n PI)))) in n 1539342813.607 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in n 1539342813.607 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1539342813.607 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1539342813.607 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1539342813.607 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342813.607 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.607 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.607 * [misc]taylor: Taking taylor expansion of k in n 1539342813.607 * [misc]backup-simplify: Simplify k into k 1539342813.608 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342813.608 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.608 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.608 * [misc]backup-simplify: Simplify 2 into 2 1539342813.608 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.608 * [misc]taylor: Taking taylor expansion of n in n 1539342813.608 * [misc]backup-simplify: Simplify 0 into 0 1539342813.608 * [misc]backup-simplify: Simplify 1 into 1 1539342813.608 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.608 * [misc]backup-simplify: Simplify PI into PI 1539342813.608 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.608 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342813.608 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.609 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342813.609 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.609 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342813.610 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.610 * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539342813.610 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539342813.610 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.610 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.610 * [misc]backup-simplify: Simplify 2 into 2 1539342813.610 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.611 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.611 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) into (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) 1539342813.611 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1539342813.611 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1539342813.611 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.611 * [misc]taylor: Taking taylor expansion of n in n 1539342813.611 * [misc]backup-simplify: Simplify 0 into 0 1539342813.611 * [misc]backup-simplify: Simplify 1 into 1 1539342813.611 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.611 * [misc]backup-simplify: Simplify PI into PI 1539342813.611 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.612 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.612 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1539342813.612 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.613 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1539342813.613 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) (sqrt (/ 1 (* n PI)))) in n 1539342813.613 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in n 1539342813.613 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1539342813.613 * [misc]taylor: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1539342813.613 * [misc]taylor: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1539342813.613 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1539342813.613 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.613 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.613 * [misc]taylor: Taking taylor expansion of k in n 1539342813.613 * [misc]backup-simplify: Simplify k into k 1539342813.613 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1539342813.613 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1539342813.614 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.614 * [misc]backup-simplify: Simplify 2 into 2 1539342813.614 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.614 * [misc]taylor: Taking taylor expansion of n in n 1539342813.614 * [misc]backup-simplify: Simplify 0 into 0 1539342813.614 * [misc]backup-simplify: Simplify 1 into 1 1539342813.614 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.614 * [misc]backup-simplify: Simplify PI into PI 1539342813.614 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.614 * [misc]backup-simplify: Simplify (* 2 0) into 0 1539342813.615 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.616 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1539342813.616 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.616 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1539342813.617 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.617 * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) 1539342813.618 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1539342813.618 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.618 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.618 * [misc]backup-simplify: Simplify 2 into 2 1539342813.618 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.618 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.619 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) into (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) 1539342813.619 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1539342813.619 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1539342813.619 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1539342813.619 * [misc]taylor: Taking taylor expansion of n in n 1539342813.619 * [misc]backup-simplify: Simplify 0 into 0 1539342813.619 * [misc]backup-simplify: Simplify 1 into 1 1539342813.619 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.619 * [misc]backup-simplify: Simplify PI into PI 1539342813.620 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1539342813.620 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1539342813.621 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1539342813.621 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.621 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1539342813.622 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) 0) into 0 1539342813.622 * [misc]taylor: Taking taylor expansion of 0 in k 1539342813.622 * [misc]backup-simplify: Simplify 0 into 0 1539342813.622 * [misc]backup-simplify: Simplify 0 into 0 1539342813.623 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342813.625 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1539342813.628 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342813.628 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1539342813.628 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.629 * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1539342813.631 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342813.632 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) (/ 0 (sqrt 2))))) into 0 1539342813.633 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) (/ +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (* PI (sqrt 2))))) 1539342813.633 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (* PI (sqrt 2))))) in k 1539342813.633 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (* PI (sqrt 2)))) in k 1539342813.633 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342813.633 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.633 * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (* PI (sqrt 2))) in k 1539342813.633 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1539342813.633 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1539342813.633 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.633 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.633 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1539342813.633 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539342813.633 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342813.633 * [misc]taylor: Taking taylor expansion of n in k 1539342813.633 * [misc]backup-simplify: Simplify n into n 1539342813.634 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342813.634 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342813.634 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342813.634 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.634 * [misc]backup-simplify: Simplify 2 into 2 1539342813.634 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.634 * [misc]backup-simplify: Simplify PI into PI 1539342813.634 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.635 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.635 * [misc]taylor: Taking taylor expansion of k in k 1539342813.635 * [misc]backup-simplify: Simplify 0 into 0 1539342813.635 * [misc]backup-simplify: Simplify 1 into 1 1539342813.635 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.636 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539342813.636 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342813.637 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539342813.637 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342813.640 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342813.640 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342813.641 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1539342813.642 * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1539342813.642 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342813.642 * [misc]taylor: Taking taylor expansion of (* PI (sqrt 2)) in k 1539342813.642 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.642 * [misc]backup-simplify: Simplify PI into PI 1539342813.642 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.642 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.642 * [misc]backup-simplify: Simplify 2 into 2 1539342813.642 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.642 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.643 * [misc]backup-simplify: Simplify (* PI (sqrt 2)) into (* (sqrt 2) PI) 1539342813.644 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) PI)) into (/ 1 (* (sqrt 2) PI)) 1539342813.645 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (* (sqrt 2) PI))) into (/ +nan.0 (* (sqrt 2) PI)) 1539342813.646 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 1539342813.647 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) into (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))) 1539342813.647 * [misc]backup-simplify: Simplify 0 into 0 1539342813.648 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1539342813.650 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1539342813.651 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1539342813.653 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.654 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1539342813.660 * [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 1539342813.660 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1539342813.661 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.662 * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1539342813.664 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539342813.666 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342813.667 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342813.669 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (sqrt 2)) (/ +nan.0 (pow PI 2))) (+ (* 0 (/ +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (* (pow PI 2) (sqrt 2))))) 1539342813.669 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (* (pow PI 2) (sqrt 2))))) in k 1539342813.669 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (* (pow PI 2) (sqrt 2)))) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342813.670 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.670 * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (* (pow PI 2) (sqrt 2))) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.670 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.670 * [misc]taylor: Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of n in k 1539342813.670 * [misc]backup-simplify: Simplify n into n 1539342813.670 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342813.670 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342813.670 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.670 * [misc]backup-simplify: Simplify 2 into 2 1539342813.670 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.670 * [misc]backup-simplify: Simplify PI into PI 1539342813.670 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.671 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.671 * [misc]taylor: Taking taylor expansion of k in k 1539342813.671 * [misc]backup-simplify: Simplify 0 into 0 1539342813.671 * [misc]backup-simplify: Simplify 1 into 1 1539342813.671 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1539342813.672 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 1539342813.672 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1539342813.673 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1539342813.674 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342813.676 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342813.677 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1539342813.677 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) 1539342813.678 * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1539342813.678 * [misc]backup-simplify: Simplify (exp 0) into 1 1539342813.678 * [misc]taylor: Taking taylor expansion of (* (pow PI 2) (sqrt 2)) in k 1539342813.678 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539342813.678 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.678 * [misc]backup-simplify: Simplify PI into PI 1539342813.678 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.678 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.678 * [misc]backup-simplify: Simplify 2 into 2 1539342813.678 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.679 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.679 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.680 * [misc]backup-simplify: Simplify (* (pow PI 2) (sqrt 2)) into (* (sqrt 2) (pow PI 2)) 1539342813.681 * [misc]backup-simplify: Simplify (/ 1 (* (sqrt 2) (pow PI 2))) into (/ 1 (* (sqrt 2) (pow PI 2))) 1539342813.682 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2)))) into (/ +nan.0 (* (sqrt 2) (pow PI 2))) 1539342813.683 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) 1539342813.685 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) 1539342813.686 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1539342813.687 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 (sqrt 2))) into 0 1539342813.690 * [misc]backup-simplify: Simplify (- (/ (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (* (sqrt 2) PI)) (+ (* (/ 1 (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))))) into (+ (* 1/2 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (* 1/2 (/ (log n) (* (sqrt 2) PI)))) 1539342813.693 * [misc]backup-simplify: Simplify (+ (* +nan.0 (+ (* 1/2 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (* 1/2 (/ (log n) (* (sqrt 2) PI))))) (* 0 (/ 1 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) 1539342813.695 * [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)))))) 1539342813.697 * [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)))))) 1539342813.703 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (log (* 2 PI)) (* (sqrt 2) PI))) (- (* +nan.0 (/ (log n) (* (sqrt 2) PI)))))) (* k 1)) (+ (* (- (* +nan.0 (/ 1 (* (sqrt 2) (pow PI 2))))) (* 1 n)) (- (* +nan.0 (/ 1 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (/ (* (log n) k) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ n (* (sqrt 2) (pow PI 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (* +nan.0 (/ (* k (log (* 2 PI))) (* (sqrt 2) PI)))))))))) 1539342813.703 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) (sqrt (* (* 2 (/ 1 n)) PI))) into (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n PI))) 1539342813.703 * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n PI))) in (n k) around 0 1539342813.703 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n PI))) in k 1539342813.703 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in k 1539342813.703 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1539342813.703 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1539342813.703 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1539342813.703 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in k 1539342813.703 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.703 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.703 * [misc]taylor: Taking taylor expansion of k in k 1539342813.703 * [misc]backup-simplify: Simplify 0 into 0 1539342813.703 * [misc]backup-simplify: Simplify 1 into 1 1539342813.704 * [misc]backup-simplify: Simplify (/ 1/2 1) into 1/2 1539342813.704 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1539342813.704 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1539342813.704 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.704 * [misc]backup-simplify: Simplify 2 into 2 1539342813.704 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.704 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.704 * [misc]backup-simplify: Simplify PI into PI 1539342813.704 * [misc]taylor: Taking taylor expansion of n in k 1539342813.704 * [misc]backup-simplify: Simplify n into n 1539342813.704 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.704 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1539342813.704 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1539342813.704 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) 1539342813.704 * [misc]backup-simplify: Simplify (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1539342813.704 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.704 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.704 * [misc]backup-simplify: Simplify 2 into 2 1539342813.705 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.705 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.705 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) (sqrt 2)) 1539342813.705 * [misc]taylor: Taking taylor expansion of (sqrt (/ n PI)) in k 1539342813.705 * [misc]taylor: Taking taylor expansion of (/ n PI) in k 1539342813.705 * [misc]taylor: Taking taylor expansion of n in k 1539342813.705 * [misc]backup-simplify: Simplify n into n 1539342813.705 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.705 * [misc]backup-simplify: Simplify PI into PI 1539342813.705 * [misc]backup-simplify: Simplify (/ n PI) into (/ n PI) 1539342813.705 * [misc]backup-simplify: Simplify (sqrt (/ n PI)) into (sqrt (/ n PI)) 1539342813.706 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ n PI) (/ 0 PI)))) into 0 1539342813.706 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ n PI)))) into 0 1539342813.706 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n PI))) in n 1539342813.706 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in n 1539342813.706 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1539342813.706 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1539342813.706 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1539342813.706 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in n 1539342813.706 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.706 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.707 * [misc]taylor: Taking taylor expansion of k in n 1539342813.707 * [misc]backup-simplify: Simplify k into k 1539342813.707 * [misc]backup-simplify: Simplify (/ 1/2 k) into (/ 1/2 k) 1539342813.707 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.707 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.707 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.707 * [misc]backup-simplify: Simplify 2 into 2 1539342813.707 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.707 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.707 * [misc]backup-simplify: Simplify PI into PI 1539342813.707 * [misc]taylor: Taking taylor expansion of n in n 1539342813.707 * [misc]backup-simplify: Simplify 0 into 0 1539342813.707 * [misc]backup-simplify: Simplify 1 into 1 1539342813.707 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.708 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.708 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.709 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.709 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.710 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.710 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.710 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.710 * [misc]backup-simplify: Simplify 2 into 2 1539342813.710 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.711 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.711 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 1539342813.711 * [misc]taylor: Taking taylor expansion of (sqrt (/ n PI)) in n 1539342813.712 * [misc]taylor: Taking taylor expansion of (/ n PI) in n 1539342813.712 * [misc]taylor: Taking taylor expansion of n in n 1539342813.712 * [misc]backup-simplify: Simplify 0 into 0 1539342813.712 * [misc]backup-simplify: Simplify 1 into 1 1539342813.712 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.712 * [misc]backup-simplify: Simplify PI into PI 1539342813.712 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1539342813.712 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.713 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1539342813.713 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) (sqrt (/ n PI))) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of (/ 1/2 k) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of 1/2 in n 1539342813.713 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.713 * [misc]taylor: Taking taylor expansion of k in n 1539342813.713 * [misc]backup-simplify: Simplify k into k 1539342813.713 * [misc]backup-simplify: Simplify (/ 1/2 k) into (/ 1/2 k) 1539342813.713 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.713 * [misc]backup-simplify: Simplify 2 into 2 1539342813.713 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.713 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.713 * [misc]backup-simplify: Simplify PI into PI 1539342813.713 * [misc]taylor: Taking taylor expansion of n in n 1539342813.713 * [misc]backup-simplify: Simplify 0 into 0 1539342813.713 * [misc]backup-simplify: Simplify 1 into 1 1539342813.714 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.714 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.714 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.715 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.715 * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) 1539342813.716 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.716 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1539342813.716 * [misc]taylor: Taking taylor expansion of 2 in n 1539342813.716 * [misc]backup-simplify: Simplify 2 into 2 1539342813.716 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.716 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.717 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 1539342813.717 * [misc]taylor: Taking taylor expansion of (sqrt (/ n PI)) in n 1539342813.717 * [misc]taylor: Taking taylor expansion of (/ n PI) in n 1539342813.717 * [misc]taylor: Taking taylor expansion of n in n 1539342813.717 * [misc]backup-simplify: Simplify 0 into 0 1539342813.717 * [misc]backup-simplify: Simplify 1 into 1 1539342813.717 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.717 * [misc]backup-simplify: Simplify PI into PI 1539342813.717 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1539342813.717 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.717 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1539342813.718 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) 0) into 0 1539342813.718 * [misc]taylor: Taking taylor expansion of 0 in k 1539342813.718 * [misc]backup-simplify: Simplify 0 into 0 1539342813.718 * [misc]backup-simplify: Simplify 0 into 0 1539342813.719 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.719 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1539342813.721 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1539342813.721 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)))) into 0 1539342813.721 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.722 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1539342813.723 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342813.723 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (/ 0 (sqrt 2))))) into 0 1539342813.724 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (/ +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) 1539342813.724 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI))) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342813.724 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.724 * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.724 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.724 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342813.724 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.724 * [misc]backup-simplify: Simplify 2 into 2 1539342813.724 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.724 * [misc]backup-simplify: Simplify PI into PI 1539342813.724 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.725 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.725 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342813.725 * [misc]taylor: Taking taylor expansion of n in k 1539342813.725 * [misc]backup-simplify: Simplify n into n 1539342813.725 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342813.725 * [misc]taylor: Taking taylor expansion of k in k 1539342813.725 * [misc]backup-simplify: Simplify 0 into 0 1539342813.725 * [misc]backup-simplify: Simplify 1 into 1 1539342813.725 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342813.725 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342813.726 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342813.726 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342813.726 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.726 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) PI) in k 1539342813.726 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.726 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.726 * [misc]backup-simplify: Simplify 2 into 2 1539342813.726 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.727 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.727 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.727 * [misc]backup-simplify: Simplify PI into PI 1539342813.727 * [misc]backup-simplify: Simplify (* (sqrt 2) PI) into (* (sqrt 2) PI) 1539342813.728 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) 1539342813.728 * [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))) 1539342813.729 * [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)))) 1539342813.730 * [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)))) 1539342813.730 * [misc]backup-simplify: Simplify 0 into 0 1539342813.731 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1539342813.732 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1539342813.733 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.734 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.737 * [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 1539342813.737 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342813.737 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.738 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1539342813.739 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539342813.740 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1539342813.741 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342813.742 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (/ +nan.0 (pow PI 2))) (+ (* 0 (/ +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) 1539342813.742 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2)))) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342813.742 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.742 * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.742 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.742 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342813.742 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.742 * [misc]backup-simplify: Simplify 2 into 2 1539342813.742 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.742 * [misc]backup-simplify: Simplify PI into PI 1539342813.742 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.743 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.743 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342813.743 * [misc]taylor: Taking taylor expansion of n in k 1539342813.743 * [misc]backup-simplify: Simplify n into n 1539342813.743 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342813.743 * [misc]taylor: Taking taylor expansion of k in k 1539342813.743 * [misc]backup-simplify: Simplify 0 into 0 1539342813.743 * [misc]backup-simplify: Simplify 1 into 1 1539342813.743 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342813.743 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342813.743 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342813.744 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342813.744 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.744 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in k 1539342813.744 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.744 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.744 * [misc]backup-simplify: Simplify 2 into 2 1539342813.744 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.745 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.745 * [misc]taylor: Taking taylor expansion of (pow PI 2) in k 1539342813.745 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.745 * [misc]backup-simplify: Simplify PI into PI 1539342813.745 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.745 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 2)) into (* (sqrt 2) (pow PI 2)) 1539342813.746 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))) 1539342813.747 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2)))) into (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2)))) 1539342813.748 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) 1539342813.748 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 2))))) 1539342813.749 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 PI)) into 0 1539342813.750 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt 2) PI)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)) (/ 0 (* (sqrt 2) PI))))) into 0 1539342813.751 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) PI)))) into 0 1539342813.751 * [misc]backup-simplify: Simplify (- 0) into 0 1539342813.752 * [misc]backup-simplify: Simplify 0 into 0 1539342813.752 * [misc]backup-simplify: Simplify 0 into 0 1539342813.753 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ 1 PI) (/ 0 PI)) (* 0 (/ 0 PI)))) into 0 1539342813.755 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (/ +nan.0 PI) (/ +nan.0 (pow PI 2)))))) (* 2 0)) into (/ +nan.0 (pow PI 3)) 1539342813.756 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.757 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1539342813.762 * [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 1539342813.762 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ 1/2 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342813.762 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1539342813.763 * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1539342813.765 * [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 1539342813.765 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 2))) into 0 1539342813.766 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt 2)) (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 1539342813.768 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)) (/ +nan.0 (pow PI 3))) (+ (* 0 (/ +nan.0 (pow PI 2))) (+ (* 0 (/ +nan.0 PI)) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) 1539342813.768 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) in k 1539342813.768 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3)))) in k 1539342813.768 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342813.768 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.768 * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) in k 1539342813.768 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 1539342813.768 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 1539342813.768 * [misc]taylor: Taking taylor expansion of 1/2 in k 1539342813.768 * [misc]backup-simplify: Simplify 1/2 into 1/2 1539342813.768 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 1539342813.769 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1539342813.769 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1539342813.769 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1539342813.769 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.769 * [misc]backup-simplify: Simplify 2 into 2 1539342813.769 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.769 * [misc]backup-simplify: Simplify PI into PI 1539342813.769 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1539342813.769 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1539342813.769 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342813.769 * [misc]taylor: Taking taylor expansion of n in k 1539342813.769 * [misc]backup-simplify: Simplify n into n 1539342813.769 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342813.769 * [misc]taylor: Taking taylor expansion of k in k 1539342813.769 * [misc]backup-simplify: Simplify 0 into 0 1539342813.769 * [misc]backup-simplify: Simplify 1 into 1 1539342813.769 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342813.770 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1539342813.770 * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) 1539342813.770 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) 1539342813.771 * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1539342813.771 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow PI 3)) in k 1539342813.771 * [misc]taylor: Taking taylor expansion of (sqrt 2) in k 1539342813.771 * [misc]taylor: Taking taylor expansion of 2 in k 1539342813.771 * [misc]backup-simplify: Simplify 2 into 2 1539342813.771 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1539342813.771 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1539342813.771 * [misc]taylor: Taking taylor expansion of (pow PI 3) in k 1539342813.771 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.771 * [misc]backup-simplify: Simplify PI into PI 1539342813.771 * [misc]backup-simplify: Simplify (* PI PI) into (pow PI 2) 1539342813.772 * [misc]backup-simplify: Simplify (* PI (pow PI 2)) into (pow PI 3) 1539342813.772 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow PI 3)) into (* (sqrt 2) (pow PI 3)) 1539342813.773 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) into (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))) 1539342813.773 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3)))) into (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3)))) 1539342813.774 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) 1539342813.775 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* (sqrt 2) (pow PI 3))))) 1539342813.780 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) (pow PI 3))))) (pow (* 1 (/ 1 n)) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) (pow PI 2))))) (pow (* 1 (/ 1 n)) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (* (sqrt 2) PI)))) (* 1 (/ 1 n))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 3) (pow PI 3)))))))))) 1539342813.780 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) (sqrt (* (* 2 (/ 1 (- n))) PI))) into (/ (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (* -2 (/ PI n)))) 1539342813.780 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (* -2 (/ PI n)))) in (n k) around 0 1539342813.780 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (* -2 (/ PI n)))) in k 1539342813.780 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1539342813.780 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1539342813.780 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1539342813.780 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in k 1539342813.780 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342813.780 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.780 * [misc]taylor: Taking taylor expansion of k in k 1539342813.780 * [misc]backup-simplify: Simplify 0 into 0 1539342813.780 * [misc]backup-simplify: Simplify 1 into 1 1539342813.781 * [misc]backup-simplify: Simplify (/ -1/2 1) into -1/2 1539342813.781 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1539342813.781 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342813.781 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.781 * [misc]backup-simplify: Simplify -2 into -2 1539342813.781 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.781 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.781 * [misc]backup-simplify: Simplify PI into PI 1539342813.781 * [misc]taylor: Taking taylor expansion of n in k 1539342813.781 * [misc]backup-simplify: Simplify n into n 1539342813.781 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.781 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342813.781 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1539342813.781 * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) 1539342813.781 * [misc]backup-simplify: Simplify (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1539342813.781 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1539342813.781 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1539342813.781 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.781 * [misc]backup-simplify: Simplify -2 into -2 1539342813.781 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1539342813.782 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.782 * [misc]backup-simplify: Simplify PI into PI 1539342813.782 * [misc]taylor: Taking taylor expansion of n in k 1539342813.782 * [misc]backup-simplify: Simplify n into n 1539342813.782 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1539342813.782 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1539342813.782 * [misc]backup-simplify: Simplify (sqrt (* -2 (/ PI n))) into (sqrt (* -2 (/ PI n))) 1539342813.782 * [misc]backup-simplify: Simplify (- (/ 0 n) (+ (* (/ PI n) (/ 0 n)))) into 0 1539342813.782 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 (/ PI n))) into 0 1539342813.782 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* -2 (/ PI n))))) into 0 1539342813.783 * [misc]backup-simplify: Simplify (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) into (/ (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (sqrt (* -2 (/ PI n)))) 1539342813.783 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (* -2 (/ PI n)))) in n 1539342813.783 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1539342813.783 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1539342813.783 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1539342813.783 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in n 1539342813.783 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342813.783 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.783 * [misc]taylor: Taking taylor expansion of k in n 1539342813.783 * [misc]backup-simplify: Simplify k into k 1539342813.783 * [misc]backup-simplify: Simplify (/ -1/2 k) into (/ -1/2 k) 1539342813.783 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342813.783 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.783 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.783 * [misc]backup-simplify: Simplify -2 into -2 1539342813.783 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.783 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.783 * [misc]backup-simplify: Simplify PI into PI 1539342813.783 * [misc]taylor: Taking taylor expansion of n in n 1539342813.783 * [misc]backup-simplify: Simplify 0 into 0 1539342813.783 * [misc]backup-simplify: Simplify 1 into 1 1539342813.783 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.784 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.784 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342813.785 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.785 * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342813.786 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342813.786 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342813.786 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.786 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.786 * [misc]backup-simplify: Simplify -2 into -2 1539342813.786 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.786 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.786 * [misc]backup-simplify: Simplify PI into PI 1539342813.786 * [misc]taylor: Taking taylor expansion of n in n 1539342813.786 * [misc]backup-simplify: Simplify 0 into 0 1539342813.786 * [misc]backup-simplify: Simplify 1 into 1 1539342813.786 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.787 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.787 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.788 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342813.788 * [misc]backup-simplify: Simplify (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.788 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (/ -1/2 k)) (sqrt (* -2 (/ PI n)))) in n 1539342813.788 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1539342813.789 * [misc]taylor: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1539342813.789 * [misc]taylor: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1539342813.789 * [misc]taylor: Taking taylor expansion of (/ -1/2 k) in n 1539342813.789 * [misc]taylor: Taking taylor expansion of -1/2 in n 1539342813.789 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.789 * [misc]taylor: Taking taylor expansion of k in n 1539342813.789 * [misc]backup-simplify: Simplify k into k 1539342813.789 * [misc]backup-simplify: Simplify (/ -1/2 k) into (/ -1/2 k) 1539342813.789 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1539342813.789 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.789 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.789 * [misc]backup-simplify: Simplify -2 into -2 1539342813.789 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.789 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.789 * [misc]backup-simplify: Simplify PI into PI 1539342813.789 * [misc]taylor: Taking taylor expansion of n in n 1539342813.789 * [misc]backup-simplify: Simplify 0 into 0 1539342813.789 * [misc]backup-simplify: Simplify 1 into 1 1539342813.789 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.790 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.790 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342813.791 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.791 * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) 1539342813.792 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342813.792 * [misc]taylor: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1539342813.792 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1539342813.792 * [misc]taylor: Taking taylor expansion of -2 in n 1539342813.792 * [misc]backup-simplify: Simplify -2 into -2 1539342813.792 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1539342813.792 * [misc]taylor: Taking taylor expansion of PI in n 1539342813.792 * [misc]backup-simplify: Simplify PI into PI 1539342813.792 * [misc]taylor: Taking taylor expansion of n in n 1539342813.792 * [misc]backup-simplify: Simplify 0 into 0 1539342813.792 * [misc]backup-simplify: Simplify 1 into 1 1539342813.792 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1539342813.793 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.793 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1539342813.794 * [misc]backup-simplify: Simplify (/ (* -2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) 1539342813.794 * [misc]backup-simplify: Simplify (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (* +nan.0 PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.794 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) in k 1539342813.794 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342813.795 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.795 * [misc]taylor: Taking taylor expansion of (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI) in k 1539342813.795 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539342813.795 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539342813.795 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342813.795 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.795 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539342813.795 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539342813.795 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539342813.795 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539342813.795 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.795 * [misc]backup-simplify: Simplify -2 into -2 1539342813.795 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.795 * [misc]backup-simplify: Simplify PI into PI 1539342813.795 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.796 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342813.796 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342813.796 * [misc]taylor: Taking taylor expansion of n in k 1539342813.796 * [misc]backup-simplify: Simplify n into n 1539342813.796 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342813.796 * [misc]taylor: Taking taylor expansion of k in k 1539342813.796 * [misc]backup-simplify: Simplify 0 into 0 1539342813.796 * [misc]backup-simplify: Simplify 1 into 1 1539342813.796 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342813.796 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539342813.797 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539342813.797 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) 1539342813.798 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342813.798 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.798 * [misc]backup-simplify: Simplify PI into PI 1539342813.799 * [misc]backup-simplify: Simplify (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI) into (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI) 1539342813.799 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.800 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) into (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.801 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.802 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342813.804 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1539342813.805 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1/2 k) (/ 0 k)))) into 0 1539342813.805 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.806 * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1539342813.807 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 1539342813.808 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1539342813.809 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1539342813.810 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1539342813.813 * [misc]backup-simplify: Simplify (- (/ 0 (* +nan.0 PI)) (+ (* (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) (/ (* +nan.0 (pow PI 2)) (* +nan.0 PI))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342813.813 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k 1539342813.813 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 1539342813.813 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342813.813 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.813 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539342813.813 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539342813.813 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342813.813 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.813 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539342813.813 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539342813.813 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539342813.813 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539342813.813 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.813 * [misc]backup-simplify: Simplify -2 into -2 1539342813.813 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.813 * [misc]backup-simplify: Simplify PI into PI 1539342813.814 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.814 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342813.814 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342813.814 * [misc]taylor: Taking taylor expansion of n in k 1539342813.814 * [misc]backup-simplify: Simplify n into n 1539342813.814 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342813.814 * [misc]taylor: Taking taylor expansion of k in k 1539342813.814 * [misc]backup-simplify: Simplify 0 into 0 1539342813.814 * [misc]backup-simplify: Simplify 1 into 1 1539342813.814 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342813.815 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539342813.815 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539342813.816 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) 1539342813.817 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342813.817 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1539342813.818 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342813.819 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1539342813.820 * [misc]backup-simplify: Simplify (- (/ 0 PI) (+ (* (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI) (/ 0 PI)))) into 0 1539342813.821 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into 0 1539342813.821 * [misc]backup-simplify: Simplify 0 into 0 1539342813.822 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.823 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.828 * [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 1539342813.828 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1/2 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1539342813.829 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1539342813.830 * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1539342813.832 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1539342813.833 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1539342813.834 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1539342813.837 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3)) 1539342813.841 * [misc]backup-simplify: Simplify (- (/ 0 (* +nan.0 PI)) (+ (* (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) (/ (* +nan.0 (pow PI 3)) (* +nan.0 PI))) (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (* +nan.0 (pow PI 2)) (* +nan.0 PI))))) into (- (* +nan.0 (* PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) 1539342813.841 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) in k 1539342813.841 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k 1539342813.841 * [misc]taylor: Taking taylor expansion of +nan.0 in k 1539342813.841 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1539342813.841 * [misc]taylor: Taking taylor expansion of (* PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 1539342813.841 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.841 * [misc]backup-simplify: Simplify PI into PI 1539342813.841 * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 1539342813.842 * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 1539342813.842 * [misc]taylor: Taking taylor expansion of -1/2 in k 1539342813.842 * [misc]backup-simplify: Simplify -1/2 into -1/2 1539342813.842 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 1539342813.842 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1539342813.842 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1539342813.842 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1539342813.842 * [misc]taylor: Taking taylor expansion of -2 in k 1539342813.842 * [misc]backup-simplify: Simplify -2 into -2 1539342813.842 * [misc]taylor: Taking taylor expansion of PI in k 1539342813.842 * [misc]backup-simplify: Simplify PI into PI 1539342813.842 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1539342813.843 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1539342813.843 * [misc]taylor: Taking taylor expansion of (log n) in k 1539342813.843 * [misc]taylor: Taking taylor expansion of n in k 1539342813.843 * [misc]backup-simplify: Simplify n into n 1539342813.843 * [misc]backup-simplify: Simplify (log n) into (log n) 1539342813.843 * [misc]taylor: Taking taylor expansion of k in k 1539342813.843 * [misc]backup-simplify: Simplify 0 into 0 1539342813.843 * [misc]backup-simplify: Simplify 1 into 1 1539342813.843 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1539342813.843 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1539342813.844 * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) 1539342813.844 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) 1539342813.845 * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1539342813.846 * [misc]backup-simplify: Simplify (* PI (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI) 1539342813.846 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) into (* +nan.0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI)) 1539342813.847 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) 1539342813.848 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) PI))) 1539342813.850 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) PI))) (pow (* 1 (/ 1 (- n))) 2)) (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (* 1 (/ 1 (- n)))) (* +nan.0 (/ (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) PI)))) 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) (pow n 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) n))))))) 1539342813.850 * * * [misc]progress: simplifying candidates 1539342813.850 * * * * [misc]progress: [ 1 / 107 ] simplifiying candidate # 1539342813.850 * [enter]simplify: Simplifying (* (sqrt k) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI)))) 1539342813.851 * * [misc]simplify: iters left: 6 (14 enodes) 1539342813.855 * * [misc]simplify: iters left: 5 (23 enodes) 1539342813.861 * * [misc]simplify: iters left: 4 (31 enodes) 1539342813.870 * * [misc]simplify: iters left: 3 (35 enodes) 1539342813.878 * * [misc]simplify: iters left: 2 (37 enodes) 1539342813.885 * * [misc]simplify: iters left: 1 (38 enodes) 1539342813.894 * [exit]simplify: Simplified to (/ (sqrt k) (/ (sqrt (* n (* 2 PI))) (pow (* n (* 2 PI)) (/ k 2)))) 1539342813.894 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (pow (/ (sqrt k) (/ (sqrt (* n (* 2 PI))) (pow (* n (* 2 PI)) (/ k 2)))) 1))) 1539342813.894 * * * * [misc]progress: [ 2 / 107 ] simplifiying candidate # 1539342813.894 * * * * [misc]progress: [ 3 / 107 ] simplifiying candidate # 1539342813.894 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (* (log (* PI (* n 2))) (/ k 2)) (log (sqrt (* (* 2 n) PI))))) 1539342813.895 * * [misc]simplify: iters left: 6 (17 enodes) 1539342813.900 * * [misc]simplify: iters left: 5 (33 enodes) 1539342813.911 * * [misc]simplify: iters left: 4 (59 enodes) 1539342813.932 * * [misc]simplify: iters left: 3 (130 enodes) 1539342813.975 * * [misc]simplify: iters left: 2 (278 enodes) 1539342814.057 * [exit]simplify: Simplified to (- (+ (+ (log (sqrt k)) (* (/ k 2) (log n))) (* (log (* PI 2)) (/ k 2))) (log (sqrt (* n (* PI 2))))) 1539342814.057 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (+ (+ (log (sqrt k)) (* (/ k 2) (log n))) (* (log (* PI 2)) (/ k 2))) (log (sqrt (* n (* PI 2)))))))) 1539342814.057 * * * * [misc]progress: [ 4 / 107 ] simplifiying candidate # 1539342814.058 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (* (log (* PI (* n 2))) (/ k 2)) (log (sqrt (* (* 2 n) PI))))) 1539342814.058 * * [misc]simplify: iters left: 6 (17 enodes) 1539342814.062 * * [misc]simplify: iters left: 5 (33 enodes) 1539342814.068 * * [misc]simplify: iters left: 4 (59 enodes) 1539342814.078 * * [misc]simplify: iters left: 3 (130 enodes) 1539342814.100 * * [misc]simplify: iters left: 2 (278 enodes) 1539342814.217 * [exit]simplify: Simplified to (- (+ (+ (log (sqrt k)) (* (/ k 2) (log n))) (* (log (* PI 2)) (/ k 2))) (log (sqrt (* n (* PI 2))))) 1539342814.217 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (+ (+ (log (sqrt k)) (* (/ k 2) (log n))) (* (log (* PI 2)) (/ k 2))) (log (sqrt (* n (* PI 2)))))))) 1539342814.217 * * * * [misc]progress: [ 5 / 107 ] simplifiying candidate # 1539342814.217 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (log (pow (* PI (* n 2)) (/ k 2))) (log (sqrt (* (* 2 n) PI))))) 1539342814.218 * * [misc]simplify: iters left: 6 (17 enodes) 1539342814.223 * * [misc]simplify: iters left: 5 (29 enodes) 1539342814.232 * * [misc]simplify: iters left: 4 (53 enodes) 1539342814.242 * * [misc]simplify: iters left: 3 (109 enodes) 1539342814.267 * * [misc]simplify: iters left: 2 (243 enodes) 1539342814.363 * [exit]simplify: Simplified to (- (+ (+ (* (log PI) (/ k 2)) (log (sqrt k))) (* (/ k 2) (log (* n 2)))) (log (sqrt (* (* PI n) 2)))) 1539342814.363 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (+ (+ (* (log PI) (/ k 2)) (log (sqrt k))) (* (/ k 2) (log (* n 2)))) (log (sqrt (* (* PI n) 2))))))) 1539342814.363 * * * * [misc]progress: [ 6 / 107 ] simplifiying candidate # 1539342814.364 * [enter]simplify: Simplifying (+ (log (sqrt k)) (log (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))))) 1539342814.364 * * [misc]simplify: iters left: 6 (16 enodes) 1539342814.369 * * [misc]simplify: iters left: 5 (25 enodes) 1539342814.376 * * [misc]simplify: iters left: 4 (37 enodes) 1539342814.387 * * [misc]simplify: iters left: 3 (63 enodes) 1539342814.405 * * [misc]simplify: iters left: 2 (134 enodes) 1539342814.449 * * [misc]simplify: iters left: 1 (342 enodes) 1539342814.658 * [exit]simplify: Simplified to (- (+ (+ (log (sqrt k)) (/ (log n) (/ 2 k))) (/ (log (* PI 2)) (/ 2 k))) (log (sqrt (* 2 (* PI n))))) 1539342814.658 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (+ (+ (log (sqrt k)) (/ (log n) (/ 2 k))) (/ (log (* PI 2)) (/ 2 k))) (log (sqrt (* 2 (* PI n)))))))) 1539342814.658 * * * * [misc]progress: [ 7 / 107 ] simplifiying candidate # 1539342814.658 * * * * [misc]progress: [ 8 / 107 ] simplifiying candidate # 1539342814.658 * * * * [misc]progress: [ 9 / 107 ] simplifiying candidate # 1539342814.658 * [enter]simplify: Simplifying (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (/ (* (* (pow (* PI (* n 2)) (/ k 2)) (pow (* PI (* n 2)) (/ k 2))) (pow (* PI (* n 2)) (/ k 2))) (* (* (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI))) (sqrt (* (* 2 n) PI))))) 1539342814.659 * * [misc]simplify: iters left: 6 (20 enodes) 1539342814.666 * * [misc]simplify: iters left: 5 (41 enodes) 1539342814.682 * * [misc]simplify: iters left: 4 (163 enodes) 1539342814.782 * [exit]simplify: Simplified to (* (* (/ (pow (* (* n 2) PI) (/ k 2)) (* (* n 2) PI)) (* (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (* k (sqrt k)) (sqrt (* (* n 2) PI)))) 1539342814.782 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (* (* (/ (pow (* (* n 2) PI) (/ k 2)) (* (* n 2) PI)) (* (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (* k (sqrt k)) (sqrt (* (* n 2) PI))))))) 1539342814.782 * * * * [misc]progress: [ 10 / 107 ] simplifiying candidate # 1539342814.782 * [enter]simplify: Simplifying (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI)))) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))))) 1539342814.782 * * [misc]simplify: iters left: 6 (18 enodes) 1539342814.787 * * [misc]simplify: iters left: 5 (37 enodes) 1539342814.800 * * [misc]simplify: iters left: 4 (92 enodes) 1539342814.837 * * [misc]simplify: iters left: 3 (232 enodes) 1539342814.970 * [exit]simplify: Simplified to (* (/ (* k (pow (* (* n 2) PI) (/ k 2))) (/ (* (* n 2) PI) (pow (* (* n 2) PI) (/ k 2)))) (* (sqrt k) (/ (pow (* (* n 2) PI) (/ k 2)) (sqrt (* (* n 2) PI))))) 1539342814.970 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (* (/ (* k (pow (* (* n 2) PI) (/ k 2))) (/ (* (* n 2) PI) (pow (* (* n 2) PI) (/ k 2)))) (* (sqrt k) (/ (pow (* (* n 2) PI) (/ k 2)) (sqrt (* (* n 2) PI)))))))) 1539342814.970 * * * * [misc]progress: [ 11 / 107 ] simplifiying candidate # 1539342814.970 * * * * [misc]progress: [ 12 / 107 ] simplifiying candidate # 1539342814.970 * * * * [misc]progress: [ 13 / 107 ] simplifiying candidate # 1539342814.970 * * * * [misc]progress: [ 14 / 107 ] simplifiying candidate # 1539342814.970 * * * * [misc]progress: [ 15 / 107 ] simplifiying candidate # 1539342814.970 * [enter]simplify: Simplifying (cbrt (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI)))) 1539342814.971 * * [misc]simplify: iters left: 6 (13 enodes) 1539342814.972 * * [misc]simplify: iters left: 5 (18 enodes) 1539342814.975 * * [misc]simplify: iters left: 4 (22 enodes) 1539342814.977 * * [misc]simplify: iters left: 3 (23 enodes) 1539342814.980 * [exit]simplify: Simplified to (cbrt (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (* PI (* 2 n))))) 1539342814.980 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (* (cbrt (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI)))) (cbrt (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI)))))) (cbrt (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (* PI (* 2 n)))))))) 1539342814.980 * * * * [misc]progress: [ 16 / 107 ] simplifiying candidate # 1539342814.980 * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI)))) 1539342814.980 * * [misc]simplify: iters left: 6 (13 enodes) 1539342814.982 * * [misc]simplify: iters left: 5 (18 enodes) 1539342814.985 * * [misc]simplify: iters left: 4 (22 enodes) 1539342814.987 * * [misc]simplify: iters left: 3 (23 enodes) 1539342814.990 * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (* PI (* 2 n))))) 1539342814.990 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (sqrt (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))))) (sqrt (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (* PI (* 2 n)))))))) 1539342814.990 * * * * [misc]progress: [ 17 / 107 ] simplifiying candidate # 1539342814.990 * [enter]simplify: Simplifying (/ (pow (* n 2) (/ k 2)) (cbrt (sqrt (* (* 2 n) PI)))) 1539342814.990 * * [misc]simplify: iters left: 6 (12 enodes) 1539342814.992 * * [misc]simplify: iters left: 5 (15 enodes) 1539342814.994 * * [misc]simplify: iters left: 4 (21 enodes) 1539342814.997 * * [misc]simplify: iters left: 3 (22 enodes) 1539342815.000 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ k 2)) (cbrt (sqrt (* n (* 2 PI))))) 1539342815.000 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (pow PI (/ k 2)) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))))) (/ (pow (* n 2) (/ k 2)) (cbrt (sqrt (* n (* 2 PI)))))))) 1539342815.000 * * * * [misc]progress: [ 18 / 107 ] simplifiying candidate # 1539342815.000 * [enter]simplify: Simplifying (/ (pow (* n 2) (/ k 2)) (sqrt PI)) 1539342815.000 * * [misc]simplify: iters left: 5 (9 enodes) 1539342815.002 * * [misc]simplify: iters left: 4 (10 enodes) 1539342815.003 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ k 2)) (sqrt PI)) 1539342815.003 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (pow PI (/ k 2)) (sqrt (* 2 n)))) (/ (pow (* n 2) (/ k 2)) (sqrt PI))))) 1539342815.003 * * * * [misc]progress: [ 19 / 107 ] simplifiying candidate # 1539342815.003 * [enter]simplify: Simplifying (/ (pow (* n 2) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))) 1539342815.003 * * [misc]simplify: iters left: 6 (12 enodes) 1539342815.005 * * [misc]simplify: iters left: 5 (15 enodes) 1539342815.007 * * [misc]simplify: iters left: 4 (21 enodes) 1539342815.010 * * [misc]simplify: iters left: 3 (22 enodes) 1539342815.016 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ k 2)) (sqrt (sqrt (* n (* 2 PI))))) 1539342815.016 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (pow PI (/ k 2)) (sqrt (sqrt (* (* 2 n) PI))))) (/ (pow (* n 2) (/ k 2)) (sqrt (sqrt (* n (* 2 PI)))))))) 1539342815.016 * * * * [misc]progress: [ 20 / 107 ] simplifiying candidate # 1539342815.016 * [enter]simplify: Simplifying (/ (pow (* n 2) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342815.016 * * [misc]simplify: iters left: 6 (11 enodes) 1539342815.018 * * [misc]simplify: iters left: 5 (14 enodes) 1539342815.020 * * [misc]simplify: iters left: 4 (20 enodes) 1539342815.023 * * [misc]simplify: iters left: 3 (22 enodes) 1539342815.026 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ k 2)) (sqrt (* (* PI n) 2))) 1539342815.026 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (pow PI (/ k 2)) 1)) (/ (pow (* n 2) (/ k 2)) (sqrt (* (* PI n) 2)))))) 1539342815.026 * * * * [misc]progress: [ 21 / 107 ] simplifiying candidate # 1539342815.026 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342815.026 * * [misc]simplify: iters left: 6 (14 enodes) 1539342815.028 * * [misc]simplify: iters left: 5 (20 enodes) 1539342815.033 * * [misc]simplify: iters left: 4 (24 enodes) 1539342815.036 * * [misc]simplify: iters left: 3 (25 enodes) 1539342815.038 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342815.038 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))))) (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI))))))) 1539342815.039 * * * * [misc]progress: [ 22 / 107 ] simplifiying candidate # 1539342815.039 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt PI)) 1539342815.039 * * [misc]simplify: iters left: 6 (11 enodes) 1539342815.040 * * [misc]simplify: iters left: 5 (15 enodes) 1539342815.042 * * [misc]simplify: iters left: 4 (21 enodes) 1539342815.045 * * [misc]simplify: iters left: 3 (22 enodes) 1539342815.048 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt PI)) 1539342815.048 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (* 2 n)))) (/ (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt PI))))) 1539342815.048 * * * * [misc]progress: [ 23 / 107 ] simplifiying candidate # 1539342815.048 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342815.048 * * [misc]simplify: iters left: 6 (14 enodes) 1539342815.050 * * [misc]simplify: iters left: 5 (20 enodes) 1539342815.052 * * [misc]simplify: iters left: 4 (24 enodes) 1539342815.055 * * [misc]simplify: iters left: 3 (25 enodes) 1539342815.061 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342815.061 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt (* (* 2 n) PI))))) (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI))))))) 1539342815.061 * * * * [misc]progress: [ 24 / 107 ] simplifiying candidate # 1539342815.061 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* 2 n) PI))) 1539342815.062 * * [misc]simplify: iters left: 6 (13 enodes) 1539342815.066 * * [misc]simplify: iters left: 5 (19 enodes) 1539342815.071 * * [misc]simplify: iters left: 4 (23 enodes) 1539342815.076 * * [misc]simplify: iters left: 3 (24 enodes) 1539342815.082 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* (* 2 n) PI))) 1539342815.082 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) 1)) (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* (* 2 n) PI)))))) 1539342815.082 * * * * [misc]progress: [ 25 / 107 ] simplifiying candidate # 1539342815.082 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342815.082 * * [misc]simplify: iters left: 6 (14 enodes) 1539342815.087 * * [misc]simplify: iters left: 5 (20 enodes) 1539342815.092 * * [misc]simplify: iters left: 4 (24 enodes) 1539342815.098 * * [misc]simplify: iters left: 3 (25 enodes) 1539342815.104 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342815.104 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI))))))) 1539342815.104 * * * * [misc]progress: [ 26 / 107 ] simplifiying candidate # 1539342815.105 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt PI)) 1539342815.105 * * [misc]simplify: iters left: 6 (11 enodes) 1539342815.108 * * [misc]simplify: iters left: 5 (15 enodes) 1539342815.112 * * [misc]simplify: iters left: 4 (21 enodes) 1539342815.118 * * [misc]simplify: iters left: 3 (22 enodes) 1539342815.123 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt PI)) 1539342815.123 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* 2 n)))) (/ (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt PI))))) 1539342815.123 * * * * [misc]progress: [ 27 / 107 ] simplifiying candidate # 1539342815.123 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342815.123 * * [misc]simplify: iters left: 6 (14 enodes) 1539342815.128 * * [misc]simplify: iters left: 5 (20 enodes) 1539342815.133 * * [misc]simplify: iters left: 4 (24 enodes) 1539342815.139 * * [misc]simplify: iters left: 3 (25 enodes) 1539342815.144 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342815.145 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI))))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI))))))) 1539342815.145 * * * * [misc]progress: [ 28 / 107 ] simplifiying candidate # 1539342815.145 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* 2 n) PI))) 1539342815.145 * * [misc]simplify: iters left: 6 (13 enodes) 1539342815.149 * * [misc]simplify: iters left: 5 (19 enodes) 1539342815.155 * * [misc]simplify: iters left: 4 (23 enodes) 1539342815.160 * * [misc]simplify: iters left: 3 (24 enodes) 1539342815.166 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* (* 2 n) PI))) 1539342815.166 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) 1)) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* (* 2 n) PI)))))) 1539342815.166 * * * * [misc]progress: [ 29 / 107 ] simplifiying candidate # 1539342815.166 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (cbrt (sqrt (* (* 2 n) PI)))) 1539342815.166 * * [misc]simplify: iters left: 6 (13 enodes) 1539342815.170 * * [misc]simplify: iters left: 5 (18 enodes) 1539342815.175 * * [misc]simplify: iters left: 4 (22 enodes) 1539342815.181 * * [misc]simplify: iters left: 3 (23 enodes) 1539342815.186 * [exit]simplify: Simplified to (/ (pow (* PI (* 2 n)) (/ k 2)) (cbrt (sqrt (* PI (* 2 n))))) 1539342815.186 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ 1 (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))))) (/ (pow (* PI (* 2 n)) (/ k 2)) (cbrt (sqrt (* PI (* 2 n)))))))) 1539342815.186 * * * * [misc]progress: [ 30 / 107 ] simplifiying candidate # 1539342815.186 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt PI)) 1539342815.187 * * [misc]simplify: iters left: 6 (10 enodes) 1539342815.190 * * [misc]simplify: iters left: 5 (14 enodes) 1539342815.194 * * [misc]simplify: iters left: 4 (20 enodes) 1539342815.199 * * [misc]simplify: iters left: 3 (22 enodes) 1539342815.205 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt PI)) 1539342815.205 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ 1 (sqrt (* 2 n)))) (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt PI))))) 1539342815.205 * * * * [misc]progress: [ 31 / 107 ] simplifiying candidate # 1539342815.205 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))) 1539342815.205 * * [misc]simplify: iters left: 6 (13 enodes) 1539342815.210 * * [misc]simplify: iters left: 5 (18 enodes) 1539342815.214 * * [misc]simplify: iters left: 4 (22 enodes) 1539342815.220 * * [misc]simplify: iters left: 3 (23 enodes) 1539342815.225 * [exit]simplify: Simplified to (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (sqrt (* PI (* 2 n))))) 1539342815.225 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ 1 (sqrt (sqrt (* (* 2 n) PI))))) (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (sqrt (* PI (* 2 n)))))))) 1539342815.225 * * * * [misc]progress: [ 32 / 107 ] simplifiying candidate # 1539342815.226 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342815.226 * * [misc]simplify: iters left: 6 (12 enodes) 1539342815.229 * * [misc]simplify: iters left: 5 (17 enodes) 1539342815.234 * * [misc]simplify: iters left: 4 (21 enodes) 1539342815.239 * * [misc]simplify: iters left: 3 (22 enodes) 1539342815.244 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342815.244 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ 1 1)) (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt (* (* 2 n) PI)))))) 1539342815.244 * * * * [misc]progress: [ 33 / 107 ] simplifiying candidate # 1539342815.245 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342815.245 * * [misc]simplify: iters left: 6 (12 enodes) 1539342815.248 * * [misc]simplify: iters left: 5 (17 enodes) 1539342815.253 * * [misc]simplify: iters left: 4 (21 enodes) 1539342815.258 * * [misc]simplify: iters left: 3 (22 enodes) 1539342815.264 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342815.264 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) 1) (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt (* (* 2 n) PI)))))) 1539342815.264 * * * * [misc]progress: [ 34 / 107 ] simplifiying candidate # 1539342815.264 * [enter]simplify: Simplifying (/ 1 (sqrt (* (* 2 n) PI))) 1539342815.264 * * [misc]simplify: iters left: 6 (8 enodes) 1539342815.267 * * [misc]simplify: iters left: 5 (14 enodes) 1539342815.271 * * [misc]simplify: iters left: 4 (20 enodes) 1539342815.277 * * [misc]simplify: iters left: 3 (21 enodes) 1539342815.281 * [exit]simplify: Simplified to (/ 1 (sqrt (* (* PI n) 2))) 1539342815.282 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (/ 1 (sqrt (* (* PI n) 2)))))) 1539342815.282 * * * * [misc]progress: [ 35 / 107 ] simplifiying candidate # 1539342815.282 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1539342815.282 * * [misc]simplify: iters left: 4 (4 enodes) 1539342815.283 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1539342815.283 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (sqrt k)) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))))))) 1539342815.283 * * * * [misc]progress: [ 36 / 107 ] simplifiying candidate # 1539342815.284 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1539342815.284 * * [misc]simplify: iters left: 2 (3 enodes) 1539342815.284 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1539342815.284 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (* (sqrt (sqrt k)) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))))))) 1539342815.285 * * * * [misc]progress: [ 37 / 107 ] simplifiying candidate # 1539342815.285 * * * * [misc]progress: [ 38 / 107 ] simplifiying candidate # 1539342815.285 * [enter]simplify: Simplifying (sqrt (* (* 2 n) PI)) 1539342815.285 * * [misc]simplify: iters left: 5 (6 enodes) 1539342815.287 * * [misc]simplify: iters left: 4 (10 enodes) 1539342815.290 * * [misc]simplify: iters left: 3 (16 enodes) 1539342815.294 * * [misc]simplify: iters left: 2 (18 enodes) 1539342815.298 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539342815.298 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* 2 n) PI))))) 1539342815.298 * * * * [misc]progress: [ 39 / 107 ] simplifiying candidate # 1539342815.298 * * * * [misc]progress: [ 40 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 41 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 42 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 43 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 44 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 45 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 46 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 47 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 48 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 49 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 50 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 51 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 52 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 53 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 54 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 55 / 107 ] simplifiying candidate # 1539342815.299 * * * * [misc]progress: [ 56 / 107 ] simplifiying candidate # 1539342815.300 * * * * [misc]progress: [ 57 / 107 ] simplifiying candidate # 1539342815.300 * * * * [misc]progress: [ 58 / 107 ] simplifiying candidate # 1539342815.300 * * * * [misc]progress: [ 59 / 107 ] simplifiying candidate # 1539342815.300 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (/ k 2)) (log (sqrt (* (* 2 n) PI)))) 1539342815.300 * * [misc]simplify: iters left: 6 (14 enodes) 1539342815.305 * * [misc]simplify: iters left: 5 (28 enodes) 1539342815.314 * * [misc]simplify: iters left: 4 (48 enodes) 1539342815.330 * * [misc]simplify: iters left: 3 (101 enodes) 1539342815.363 * * [misc]simplify: iters left: 2 (189 enodes) 1539342815.421 * * [misc]simplify: iters left: 1 (299 enodes) 1539342815.473 * [exit]simplify: Simplified to (- (/ (log (* (* 2 n) PI)) (/ 2 k)) (log (sqrt (* (* 2 n) PI)))) 1539342815.473 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (exp (- (/ (log (* (* 2 n) PI)) (/ 2 k)) (log (sqrt (* (* 2 n) PI)))))))) 1539342815.473 * * * * [misc]progress: [ 60 / 107 ] simplifiying candidate # 1539342815.473 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (/ k 2)) (log (sqrt (* (* 2 n) PI)))) 1539342815.473 * * [misc]simplify: iters left: 6 (14 enodes) 1539342815.475 * * [misc]simplify: iters left: 5 (28 enodes) 1539342815.479 * * [misc]simplify: iters left: 4 (48 enodes) 1539342815.489 * * [misc]simplify: iters left: 3 (101 enodes) 1539342815.506 * * [misc]simplify: iters left: 2 (189 enodes) 1539342815.561 * * [misc]simplify: iters left: 1 (299 enodes) 1539342815.654 * [exit]simplify: Simplified to (- (/ (log (* (* 2 n) PI)) (/ 2 k)) (log (sqrt (* (* 2 n) PI)))) 1539342815.655 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (exp (- (/ (log (* (* 2 n) PI)) (/ 2 k)) (log (sqrt (* (* 2 n) PI)))))))) 1539342815.655 * * * * [misc]progress: [ 61 / 107 ] simplifiying candidate # 1539342815.655 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (/ k 2))) (log (sqrt (* (* 2 n) PI)))) 1539342815.655 * * [misc]simplify: iters left: 6 (14 enodes) 1539342815.660 * * [misc]simplify: iters left: 5 (24 enodes) 1539342815.667 * * [misc]simplify: iters left: 4 (41 enodes) 1539342815.680 * * [misc]simplify: iters left: 3 (86 enodes) 1539342815.714 * * [misc]simplify: iters left: 2 (167 enodes) 1539342815.776 * * [misc]simplify: iters left: 1 (304 enodes) 1539342815.885 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (/ k 2)) (log (sqrt (* (* 2 n) PI)))) 1539342815.885 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (exp (- (* (log (* (* 2 n) PI)) (/ k 2)) (log (sqrt (* (* 2 n) PI)))))))) 1539342815.885 * * * * [misc]progress: [ 62 / 107 ] simplifiying candidate # 1539342815.885 * * * * [misc]progress: [ 63 / 107 ] simplifiying candidate # 1539342815.885 * * * * [misc]progress: [ 64 / 107 ] simplifiying candidate # 1539342815.885 * [enter]simplify: Simplifying (/ (* (* (pow (* PI (* n 2)) (/ k 2)) (pow (* PI (* n 2)) (/ k 2))) (pow (* PI (* n 2)) (/ k 2))) (* (* (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI))) (sqrt (* (* 2 n) PI)))) 1539342815.885 * * [misc]simplify: iters left: 6 (16 enodes) 1539342815.891 * * [misc]simplify: iters left: 5 (30 enodes) 1539342815.901 * * [misc]simplify: iters left: 4 (105 enodes) 1539342815.930 * * [misc]simplify: iters left: 3 (398 enodes) 1539342816.261 * [exit]simplify: Simplified to (pow (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (* PI (* 2 n)))) 3) 1539342816.261 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (cbrt (pow (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (* PI (* 2 n)))) 3))))) 1539342816.261 * * * * [misc]progress: [ 65 / 107 ] simplifiying candidate # 1539342816.261 * * * * [misc]progress: [ 66 / 107 ] simplifiying candidate # 1539342816.261 * * * * [misc]progress: [ 67 / 107 ] simplifiying candidate # 1539342816.261 * * * * [misc]progress: [ 68 / 107 ] simplifiying candidate # 1539342816.262 * * * * [misc]progress: [ 69 / 107 ] simplifiying candidate # 1539342816.262 * [enter]simplify: Simplifying (/ (pow PI (/ k 2)) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) 1539342816.262 * * [misc]simplify: iters left: 6 (12 enodes) 1539342816.264 * * [misc]simplify: iters left: 5 (18 enodes) 1539342816.266 * * [misc]simplify: iters left: 4 (24 enodes) 1539342816.269 * * [misc]simplify: iters left: 3 (25 enodes) 1539342816.272 * [exit]simplify: Simplified to (/ (/ (pow PI (/ k 2)) (cbrt (sqrt (* n (* PI 2))))) (cbrt (sqrt (* n (* PI 2))))) 1539342816.272 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (/ (pow PI (/ k 2)) (cbrt (sqrt (* n (* PI 2))))) (cbrt (sqrt (* n (* PI 2))))) (/ (pow (* n 2) (/ k 2)) (cbrt (sqrt (* (* 2 n) PI)))))))) 1539342816.272 * [enter]simplify: Simplifying (/ (pow (* n 2) (/ k 2)) (cbrt (sqrt (* (* 2 n) PI)))) 1539342816.272 * * [misc]simplify: iters left: 6 (12 enodes) 1539342816.275 * * [misc]simplify: iters left: 5 (15 enodes) 1539342816.279 * * [misc]simplify: iters left: 4 (21 enodes) 1539342816.284 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.290 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ k 2)) (cbrt (sqrt (* n (* 2 PI))))) 1539342816.290 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (pow PI (/ k 2)) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (pow (* n 2) (/ k 2)) (cbrt (sqrt (* n (* 2 PI))))))))) 1539342816.290 * * * * [misc]progress: [ 70 / 107 ] simplifiying candidate # 1539342816.290 * [enter]simplify: Simplifying (/ (pow PI (/ k 2)) (sqrt (* 2 n))) 1539342816.290 * * [misc]simplify: iters left: 5 (9 enodes) 1539342816.293 * * [misc]simplify: iters left: 4 (10 enodes) 1539342816.295 * [exit]simplify: Simplified to (/ (pow PI (/ k 2)) (sqrt (* 2 n))) 1539342816.295 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (pow PI (/ k 2)) (sqrt (* 2 n))) (/ (pow (* n 2) (/ k 2)) (sqrt PI)))))) 1539342816.296 * [enter]simplify: Simplifying (/ (pow (* n 2) (/ k 2)) (sqrt PI)) 1539342816.296 * * [misc]simplify: iters left: 5 (9 enodes) 1539342816.298 * * [misc]simplify: iters left: 4 (10 enodes) 1539342816.301 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ k 2)) (sqrt PI)) 1539342816.301 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (pow PI (/ k 2)) (sqrt (* 2 n))) (/ (pow (* n 2) (/ k 2)) (sqrt PI)))))) 1539342816.301 * * * * [misc]progress: [ 71 / 107 ] simplifiying candidate # 1539342816.301 * [enter]simplify: Simplifying (/ (pow PI (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.301 * * [misc]simplify: iters left: 6 (11 enodes) 1539342816.304 * * [misc]simplify: iters left: 5 (15 enodes) 1539342816.308 * * [misc]simplify: iters left: 4 (21 enodes) 1539342816.310 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.315 * [exit]simplify: Simplified to (/ (pow PI (/ k 2)) (sqrt (sqrt (* (* n PI) 2)))) 1539342816.315 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (pow PI (/ k 2)) (sqrt (sqrt (* (* n PI) 2)))) (/ (pow (* n 2) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))))))) 1539342816.315 * [enter]simplify: Simplifying (/ (pow (* n 2) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.315 * * [misc]simplify: iters left: 6 (12 enodes) 1539342816.319 * * [misc]simplify: iters left: 5 (15 enodes) 1539342816.323 * * [misc]simplify: iters left: 4 (21 enodes) 1539342816.329 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.333 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ k 2)) (sqrt (sqrt (* n (* 2 PI))))) 1539342816.333 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (pow PI (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))) (/ (pow (* n 2) (/ k 2)) (sqrt (sqrt (* n (* 2 PI))))))))) 1539342816.333 * * * * [misc]progress: [ 72 / 107 ] simplifiying candidate # 1539342816.333 * [enter]simplify: Simplifying (/ (pow PI (/ k 2)) 1) 1539342816.333 * * [misc]simplify: iters left: 5 (7 enodes) 1539342816.334 * * [misc]simplify: iters left: 4 (9 enodes) 1539342816.336 * * [misc]simplify: iters left: 3 (11 enodes) 1539342816.337 * [exit]simplify: Simplified to (pow PI (/ k 2)) 1539342816.337 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (pow PI (/ k 2)) (/ (pow (* n 2) (/ k 2)) (sqrt (* (* 2 n) PI))))))) 1539342816.337 * [enter]simplify: Simplifying (/ (pow (* n 2) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342816.337 * * [misc]simplify: iters left: 6 (11 enodes) 1539342816.339 * * [misc]simplify: iters left: 5 (14 enodes) 1539342816.341 * * [misc]simplify: iters left: 4 (20 enodes) 1539342816.343 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.346 * [exit]simplify: Simplified to (/ (pow (* n 2) (/ k 2)) (sqrt (* (* PI n) 2))) 1539342816.346 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (pow PI (/ k 2)) (/ (pow (* n 2) (/ k 2)) (sqrt (* (* PI n) 2))))))) 1539342816.346 * * * * [misc]progress: [ 73 / 107 ] simplifiying candidate # 1539342816.346 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) 1539342816.346 * * [misc]simplify: iters left: 6 (16 enodes) 1539342816.350 * * [misc]simplify: iters left: 5 (27 enodes) 1539342816.358 * * [misc]simplify: iters left: 4 (40 enodes) 1539342816.370 * * [misc]simplify: iters left: 3 (44 enodes) 1539342816.380 * * [misc]simplify: iters left: 2 (47 enodes) 1539342816.392 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (sqrt (* PI (* 2 n))))) (/ (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (sqrt (* PI (* 2 n)))))) 1539342816.392 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (* (/ (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (sqrt (* PI (* 2 n))))) (/ (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (sqrt (* PI (* 2 n)))))) (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))))))) 1539342816.393 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342816.393 * * [misc]simplify: iters left: 6 (14 enodes) 1539342816.397 * * [misc]simplify: iters left: 5 (20 enodes) 1539342816.402 * * [misc]simplify: iters left: 4 (24 enodes) 1539342816.408 * * [misc]simplify: iters left: 3 (25 enodes) 1539342816.414 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342816.414 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))))))) 1539342816.415 * * * * [misc]progress: [ 74 / 107 ] simplifiying candidate # 1539342816.415 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (* 2 n))) 1539342816.415 * * [misc]simplify: iters left: 6 (13 enodes) 1539342816.419 * * [misc]simplify: iters left: 5 (18 enodes) 1539342816.425 * * [misc]simplify: iters left: 4 (26 enodes) 1539342816.431 * * [misc]simplify: iters left: 3 (28 enodes) 1539342816.438 * [exit]simplify: Simplified to (/ (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (sqrt (* 2 n))) 1539342816.438 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (sqrt (* 2 n))) (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt PI)))))) 1539342816.439 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt PI)) 1539342816.439 * * [misc]simplify: iters left: 6 (11 enodes) 1539342816.442 * * [misc]simplify: iters left: 5 (15 enodes) 1539342816.446 * * [misc]simplify: iters left: 4 (21 enodes) 1539342816.452 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.456 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt PI)) 1539342816.456 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (* 2 n))) (/ (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt PI)))))) 1539342816.456 * * * * [misc]progress: [ 75 / 107 ] simplifiying candidate # 1539342816.456 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.456 * * [misc]simplify: iters left: 6 (15 enodes) 1539342816.458 * * [misc]simplify: iters left: 5 (22 enodes) 1539342816.461 * * [misc]simplify: iters left: 4 (28 enodes) 1539342816.464 * * [misc]simplify: iters left: 3 (30 enodes) 1539342816.468 * [exit]simplify: Simplified to (/ (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (sqrt (sqrt (* PI (* 2 n))))) 1539342816.468 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (sqrt (sqrt (* PI (* 2 n))))) (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))))))) 1539342816.468 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.468 * * [misc]simplify: iters left: 6 (14 enodes) 1539342816.470 * * [misc]simplify: iters left: 5 (20 enodes) 1539342816.473 * * [misc]simplify: iters left: 4 (24 enodes) 1539342816.475 * * [misc]simplify: iters left: 3 (25 enodes) 1539342816.478 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.478 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt (* (* 2 n) PI)))) (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))))))) 1539342816.478 * * * * [misc]progress: [ 76 / 107 ] simplifiying candidate # 1539342816.478 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) 1) 1539342816.478 * * [misc]simplify: iters left: 6 (12 enodes) 1539342816.481 * * [misc]simplify: iters left: 5 (20 enodes) 1539342816.484 * * [misc]simplify: iters left: 4 (32 enodes) 1539342816.491 * * [misc]simplify: iters left: 3 (36 enodes) 1539342816.498 * * [misc]simplify: iters left: 2 (41 enodes) 1539342816.503 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) 1539342816.503 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* 2 n) PI))))))) 1539342816.503 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* 2 n) PI))) 1539342816.503 * * [misc]simplify: iters left: 6 (13 enodes) 1539342816.505 * * [misc]simplify: iters left: 5 (19 enodes) 1539342816.507 * * [misc]simplify: iters left: 4 (23 enodes) 1539342816.510 * * [misc]simplify: iters left: 3 (24 enodes) 1539342816.513 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* (* 2 n) PI))) 1539342816.513 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* (* 2 n) PI))))))) 1539342816.513 * * * * [misc]progress: [ 77 / 107 ] simplifiying candidate # 1539342816.513 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) 1539342816.513 * * [misc]simplify: iters left: 6 (15 enodes) 1539342816.515 * * [misc]simplify: iters left: 5 (23 enodes) 1539342816.518 * * [misc]simplify: iters left: 4 (27 enodes) 1539342816.521 * * [misc]simplify: iters left: 3 (28 enodes) 1539342816.524 * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342816.524 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) (cbrt (sqrt (* (* 2 n) PI)))) (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))))))) 1539342816.525 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342816.525 * * [misc]simplify: iters left: 6 (14 enodes) 1539342816.527 * * [misc]simplify: iters left: 5 (20 enodes) 1539342816.532 * * [misc]simplify: iters left: 4 (24 enodes) 1539342816.538 * * [misc]simplify: iters left: 3 (25 enodes) 1539342816.543 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))) 1539342816.543 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI)))))))) 1539342816.543 * * * * [misc]progress: [ 78 / 107 ] simplifiying candidate # 1539342816.544 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* 2 n))) 1539342816.544 * * [misc]simplify: iters left: 6 (12 enodes) 1539342816.545 * * [misc]simplify: iters left: 5 (15 enodes) 1539342816.547 * * [misc]simplify: iters left: 4 (21 enodes) 1539342816.550 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.553 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* 2 n))) 1539342816.553 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* 2 n))) (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt PI)))))) 1539342816.553 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt PI)) 1539342816.553 * * [misc]simplify: iters left: 6 (11 enodes) 1539342816.555 * * [misc]simplify: iters left: 5 (15 enodes) 1539342816.557 * * [misc]simplify: iters left: 4 (21 enodes) 1539342816.559 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.562 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt PI)) 1539342816.562 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* 2 n))) (/ (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt PI)))))) 1539342816.562 * * * * [misc]progress: [ 79 / 107 ] simplifiying candidate # 1539342816.562 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.562 * * [misc]simplify: iters left: 6 (14 enodes) 1539342816.564 * * [misc]simplify: iters left: 5 (20 enodes) 1539342816.568 * * [misc]simplify: iters left: 4 (24 enodes) 1539342816.570 * * [misc]simplify: iters left: 3 (25 enodes) 1539342816.575 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.576 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))))))) 1539342816.576 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.576 * * [misc]simplify: iters left: 6 (14 enodes) 1539342816.580 * * [misc]simplify: iters left: 5 (20 enodes) 1539342816.586 * * [misc]simplify: iters left: 4 (24 enodes) 1539342816.590 * * [misc]simplify: iters left: 3 (25 enodes) 1539342816.592 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.592 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt (* (* 2 n) PI)))))))) 1539342816.593 * * * * [misc]progress: [ 80 / 107 ] simplifiying candidate # 1539342816.593 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) 1) 1539342816.593 * * [misc]simplify: iters left: 6 (11 enodes) 1539342816.594 * * [misc]simplify: iters left: 5 (17 enodes) 1539342816.597 * * [misc]simplify: iters left: 4 (25 enodes) 1539342816.600 * * [misc]simplify: iters left: 3 (26 enodes) 1539342816.602 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (/ k 2))) 1539342816.602 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* 2 n) PI))))))) 1539342816.602 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (* (* 2 n) PI))) 1539342816.602 * * [misc]simplify: iters left: 6 (13 enodes) 1539342816.604 * * [misc]simplify: iters left: 5 (19 enodes) 1539342816.607 * * [misc]simplify: iters left: 4 (23 enodes) 1539342816.609 * * [misc]simplify: iters left: 3 (24 enodes) 1539342816.612 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* (* 2 n) PI))) 1539342816.612 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (* (* 2 n) PI))))))) 1539342816.612 * * * * [misc]progress: [ 81 / 107 ] simplifiying candidate # 1539342816.612 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) 1539342816.612 * * [misc]simplify: iters left: 6 (10 enodes) 1539342816.614 * * [misc]simplify: iters left: 5 (18 enodes) 1539342816.617 * * [misc]simplify: iters left: 4 (24 enodes) 1539342816.623 * * [misc]simplify: iters left: 3 (25 enodes) 1539342816.629 * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (* n (* 2 PI)))) (cbrt (sqrt (* n (* 2 PI)))))) 1539342816.629 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ 1 (* (cbrt (sqrt (* n (* 2 PI)))) (cbrt (sqrt (* n (* 2 PI)))))) (/ (pow (* PI (* n 2)) (/ k 2)) (cbrt (sqrt (* (* 2 n) PI)))))))) 1539342816.630 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (cbrt (sqrt (* (* 2 n) PI)))) 1539342816.630 * * [misc]simplify: iters left: 6 (13 enodes) 1539342816.634 * * [misc]simplify: iters left: 5 (18 enodes) 1539342816.639 * * [misc]simplify: iters left: 4 (22 enodes) 1539342816.645 * * [misc]simplify: iters left: 3 (23 enodes) 1539342816.650 * [exit]simplify: Simplified to (/ (pow (* PI (* 2 n)) (/ k 2)) (cbrt (sqrt (* PI (* 2 n))))) 1539342816.650 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ 1 (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (pow (* PI (* 2 n)) (/ k 2)) (cbrt (sqrt (* PI (* 2 n))))))))) 1539342816.650 * * * * [misc]progress: [ 82 / 107 ] simplifiying candidate # 1539342816.651 * [enter]simplify: Simplifying (/ 1 (sqrt (* 2 n))) 1539342816.651 * * [misc]simplify: iters left: 5 (6 enodes) 1539342816.653 * * [misc]simplify: iters left: 4 (9 enodes) 1539342816.655 * [exit]simplify: Simplified to (/ 1 (sqrt (* n 2))) 1539342816.655 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ 1 (sqrt (* n 2))) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt PI)))))) 1539342816.655 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt PI)) 1539342816.655 * * [misc]simplify: iters left: 6 (10 enodes) 1539342816.658 * * [misc]simplify: iters left: 5 (14 enodes) 1539342816.662 * * [misc]simplify: iters left: 4 (20 enodes) 1539342816.667 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.673 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt PI)) 1539342816.673 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ 1 (sqrt (* 2 n))) (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt PI)))))) 1539342816.673 * * * * [misc]progress: [ 83 / 107 ] simplifiying candidate # 1539342816.673 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.673 * * [misc]simplify: iters left: 6 (9 enodes) 1539342816.676 * * [misc]simplify: iters left: 5 (15 enodes) 1539342816.681 * * [misc]simplify: iters left: 4 (21 enodes) 1539342816.686 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.691 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (* (* 2 PI) n)))) 1539342816.691 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* (/ 1 (sqrt (sqrt (* (* 2 PI) n)))) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))))))) 1539342816.692 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))) 1539342816.692 * * [misc]simplify: iters left: 6 (13 enodes) 1539342816.694 * * [misc]simplify: iters left: 5 (18 enodes) 1539342816.696 * * [misc]simplify: iters left: 4 (22 enodes) 1539342816.699 * * [misc]simplify: iters left: 3 (23 enodes) 1539342816.701 * [exit]simplify: Simplified to (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (sqrt (* PI (* 2 n))))) 1539342816.701 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ 1 (sqrt (sqrt (* (* 2 n) PI)))) (/ (pow (* PI (* 2 n)) (/ k 2)) (sqrt (sqrt (* PI (* 2 n))))))))) 1539342816.701 * * * * [misc]progress: [ 84 / 107 ] simplifiying candidate # 1539342816.702 * [enter]simplify: Simplifying (/ 1 1) 1539342816.702 * * [misc]simplify: iters left: 2 (2 enodes) 1539342816.702 * * [misc]simplify: iters left: 1 (4 enodes) 1539342816.702 * [exit]simplify: Simplified to 1 1539342816.702 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (* 1 (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))))))) 1539342816.702 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342816.702 * * [misc]simplify: iters left: 6 (12 enodes) 1539342816.704 * * [misc]simplify: iters left: 5 (17 enodes) 1539342816.706 * * [misc]simplify: iters left: 4 (21 enodes) 1539342816.709 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.711 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt (* (* 2 n) PI))) 1539342816.711 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* 1 (/ (pow (* (* 2 n) PI) (/ k 2)) (sqrt (* (* 2 n) PI))))))) 1539342816.711 * * * * [misc]progress: [ 85 / 107 ] simplifiying candidate # 1539342816.711 * * * * [misc]progress: [ 86 / 107 ] simplifiying candidate # 1539342816.711 * * * * [misc]progress: [ 87 / 107 ] simplifiying candidate # 1539342816.711 * * * * [misc]progress: [ 88 / 107 ] simplifiying candidate # 1539342816.712 * [enter]simplify: Simplifying (cbrt (sqrt (* (* 2 n) PI))) 1539342816.712 * * [misc]simplify: iters left: 6 (7 enodes) 1539342816.713 * * [misc]simplify: iters left: 5 (11 enodes) 1539342816.714 * * [misc]simplify: iters left: 4 (17 enodes) 1539342816.716 * * [misc]simplify: iters left: 3 (19 enodes) 1539342816.718 * [exit]simplify: Simplified to (cbrt (sqrt (* (* 2 n) PI))) 1539342816.718 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ (pow (* PI (* n 2)) (/ k 2)) (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI))))) (cbrt (sqrt (* (* 2 n) PI))))))) 1539342816.718 * * * * [misc]progress: [ 89 / 107 ] simplifiying candidate # 1539342816.718 * [enter]simplify: Simplifying (sqrt PI) 1539342816.718 * * [misc]simplify: iters left: 1 (2 enodes) 1539342816.719 * [exit]simplify: Simplified to (sqrt PI) 1539342816.719 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* 2 n))) (sqrt PI))))) 1539342816.719 * * * * [misc]progress: [ 90 / 107 ] simplifiying candidate # 1539342816.719 * [enter]simplify: Simplifying (sqrt (sqrt (* (* 2 n) PI))) 1539342816.719 * * [misc]simplify: iters left: 6 (7 enodes) 1539342816.721 * * [misc]simplify: iters left: 5 (11 enodes) 1539342816.724 * * [misc]simplify: iters left: 4 (17 enodes) 1539342816.728 * * [misc]simplify: iters left: 3 (19 enodes) 1539342816.732 * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) 1539342816.732 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (sqrt (* (* 2 n) PI)))) (sqrt (sqrt (* (* 2 n) PI))))))) 1539342816.732 * * * * [misc]progress: [ 91 / 107 ] simplifiying candidate # 1539342816.733 * [enter]simplify: Simplifying (sqrt (* (* 2 n) PI)) 1539342816.733 * * [misc]simplify: iters left: 5 (6 enodes) 1539342816.735 * * [misc]simplify: iters left: 4 (10 enodes) 1539342816.737 * * [misc]simplify: iters left: 3 (16 enodes) 1539342816.741 * * [misc]simplify: iters left: 2 (18 enodes) 1539342816.746 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1539342816.746 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ (pow (* PI (* n 2)) (/ k 2)) 1) (sqrt (* (* 2 n) PI)))))) 1539342816.746 * * * * [misc]progress: [ 92 / 107 ] simplifiying candidate # 1539342816.746 * [enter]simplify: Simplifying (pow PI (/ k 2)) 1539342816.746 * * [misc]simplify: iters left: 3 (5 enodes) 1539342816.748 * [exit]simplify: Simplified to (pow PI (/ k 2)) 1539342816.748 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow PI (/ k 2)) (/ (sqrt (* (* 2 n) PI)) (pow (* n 2) (/ k 2))))))) 1539342816.748 * * * * [misc]progress: [ 93 / 107 ] simplifiying candidate # 1539342816.748 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) 1539342816.748 * * [misc]simplify: iters left: 6 (10 enodes) 1539342816.751 * * [misc]simplify: iters left: 5 (14 enodes) 1539342816.755 * * [misc]simplify: iters left: 4 (20 enodes) 1539342816.761 * * [misc]simplify: iters left: 3 (22 enodes) 1539342816.765 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) 1539342816.765 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (* (* 2 n) PI)) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) 1539342816.766 * * * * [misc]progress: [ 94 / 107 ] simplifiying candidate # 1539342816.766 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (/ k 2))) 1539342816.766 * * [misc]simplify: iters left: 6 (9 enodes) 1539342816.768 * * [misc]simplify: iters left: 5 (13 enodes) 1539342816.772 * * [misc]simplify: iters left: 4 (19 enodes) 1539342816.776 * * [misc]simplify: iters left: 3 (20 enodes) 1539342816.781 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (/ k 2))) 1539342816.781 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (/ (sqrt (* (* 2 n) PI)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) 1539342816.781 * * * * [misc]progress: [ 95 / 107 ] simplifiying candidate # 1539342816.781 * * * * [misc]progress: [ 96 / 107 ] simplifiying candidate # 1539342816.782 * [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))))))))))))))) 1539342816.782 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539342816.782 * * * * [misc]progress: [ 97 / 107 ] simplifiying candidate # 1539342816.782 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 2) (* (pow PI 2) k))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 3) (* (pow PI 3) (pow k 2))))))))))) 1539342816.782 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539342816.782 * * * * [misc]progress: [ 98 / 107 ] simplifiying candidate # 1539342816.783 * [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))) n))))))) 1539342816.783 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1539342816.783 * * * * [misc]progress: [ 99 / 107 ] simplifiying candidate # 1539342816.783 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342816.783 * * [misc]simplify: iters left: 4 (5 enodes) 1539342816.785 * * [misc]simplify: iters left: 3 (9 enodes) 1539342816.787 * * [misc]simplify: iters left: 2 (15 enodes) 1539342816.790 * * [misc]simplify: iters left: 1 (17 enodes) 1539342816.792 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342816.792 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow (* (* PI n) 2) (/ k 2)) (sqrt (* (* 2 n) PI)))))) 1539342816.792 * * * * [misc]progress: [ 100 / 107 ] simplifiying candidate # 1539342816.792 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342816.792 * * [misc]simplify: iters left: 4 (5 enodes) 1539342816.793 * * [misc]simplify: iters left: 3 (9 enodes) 1539342816.794 * * [misc]simplify: iters left: 2 (15 enodes) 1539342816.796 * * [misc]simplify: iters left: 1 (17 enodes) 1539342816.798 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342816.798 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow (* (* PI n) 2) (/ k 2)) (sqrt (* (* 2 n) PI)))))) 1539342816.798 * * * * [misc]progress: [ 101 / 107 ] simplifiying candidate # 1539342816.798 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342816.798 * * [misc]simplify: iters left: 4 (5 enodes) 1539342816.799 * * [misc]simplify: iters left: 3 (9 enodes) 1539342816.800 * * [misc]simplify: iters left: 2 (15 enodes) 1539342816.802 * * [misc]simplify: iters left: 1 (17 enodes) 1539342816.804 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342816.804 * [misc]simplify: Simplified (2 2 2 1 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow (* (* PI n) 2) (/ k 2)) (sqrt (* (* 2 n) PI)))))) 1539342816.804 * * * * [misc]progress: [ 102 / 107 ] simplifiying candidate # 1539342816.804 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342816.804 * * [misc]simplify: iters left: 4 (5 enodes) 1539342816.805 * * [misc]simplify: iters left: 3 (9 enodes) 1539342816.806 * * [misc]simplify: iters left: 2 (15 enodes) 1539342816.808 * * [misc]simplify: iters left: 1 (17 enodes) 1539342816.810 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342816.810 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* PI n) 2)))))) 1539342816.810 * * * * [misc]progress: [ 103 / 107 ] simplifiying candidate # 1539342816.810 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342816.810 * * [misc]simplify: iters left: 4 (5 enodes) 1539342816.811 * * [misc]simplify: iters left: 3 (9 enodes) 1539342816.812 * * [misc]simplify: iters left: 2 (15 enodes) 1539342816.814 * * [misc]simplify: iters left: 1 (17 enodes) 1539342816.816 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342816.816 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* PI n) 2)))))) 1539342816.816 * * * * [misc]progress: [ 104 / 107 ] simplifiying candidate # 1539342816.817 * [enter]simplify: Simplifying (* 2 (* n PI)) 1539342816.817 * * [misc]simplify: iters left: 4 (5 enodes) 1539342816.819 * * [misc]simplify: iters left: 3 (9 enodes) 1539342816.821 * * [misc]simplify: iters left: 2 (15 enodes) 1539342816.826 * * [misc]simplify: iters left: 1 (17 enodes) 1539342816.830 * [exit]simplify: Simplified to (* (* PI n) 2) 1539342816.830 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ (pow (* PI (* n 2)) (/ k 2)) (sqrt (* (* PI n) 2)))))) 1539342816.830 * * * * [misc]progress: [ 105 / 107 ] simplifiying candidate # 1539342816.830 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (log n) k) (* (sqrt 2) PI))) (- (+ (* +nan.0 (/ n (* (sqrt 2) (pow PI 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt 2) PI))) (- (* +nan.0 (/ (* k (log (* 2 PI))) (* (sqrt 2) PI)))))))))) 1539342816.830 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) +nan.0))) 1539342816.830 * * * * [misc]progress: [ 106 / 107 ] simplifiying candidate # 1539342816.831 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* (pow n 3) (pow PI 3)))))))))) 1539342816.831 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) +nan.0))) 1539342816.831 * * * * [misc]progress: [ 107 / 107 ] simplifiying candidate # 1539342816.831 * [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) (pow n 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) n))))))) 1539342816.831 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) +nan.0))) 1539342816.831 * * * [misc]progress: adding candidates to table 1539342818.231 * [misc]progress: [Phase 3 of 3] Extracting. 1539342818.231 * * [misc]regime: Finding splitpoints for: (# # # # # # # #) 1539342818.234 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1539342818.234 * * * * [misc]regimes: Trying to branch on n from (# # # # # # # #) 1539342818.303 * * * * [misc]regimes: Trying to branch on k from (# # # # # # # #) 1539342818.387 * * * [misc]regime: Found split indices: #