1546852753.079 * [misc]progress: [Phase 1 of 3] Setting up. 1546852753.079 * * * [misc]progress: [1/2] Preparing points 1546852753.079 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1546852753.144 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.144 * * * * [misc]points: Sampling 192 additional inputs, on iter 1 have 64 / 256 1546852753.193 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.193 * * * * [misc]points: Sampling 147 additional inputs, on iter 2 have 109 / 256 1546852753.235 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.235 * * * * [misc]points: Sampling 113 additional inputs, on iter 3 have 143 / 256 1546852753.298 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.298 * * * * [misc]points: Sampling 84 additional inputs, on iter 4 have 172 / 256 1546852753.324 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.324 * * * * [misc]points: Sampling 61 additional inputs, on iter 5 have 195 / 256 1546852753.344 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.344 * * * * [misc]points: Sampling 46 additional inputs, on iter 6 have 210 / 256 1546852753.361 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.361 * * * * [misc]points: Sampling 32 additional inputs, on iter 7 have 224 / 256 1546852753.375 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.375 * * * * [misc]points: Sampling 26 additional inputs, on iter 8 have 230 / 256 1546852753.388 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.388 * * * * [misc]points: Sampling 17 additional inputs, on iter 9 have 239 / 256 1546852753.393 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.393 * * * * [misc]points: Sampling 10 additional inputs, on iter 10 have 246 / 256 1546852753.397 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.397 * * * * [misc]points: Sampling 8 additional inputs, on iter 11 have 248 / 256 1546852753.402 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.402 * * * * [misc]points: Sampling 7 additional inputs, on iter 12 have 249 / 256 1546852753.406 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.406 * * * * [misc]points: Sampling 5 additional inputs, on iter 13 have 251 / 256 1546852753.409 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.410 * * * * [misc]points: Sampling 4 additional inputs, on iter 14 have 252 / 256 1546852753.414 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.414 * * * * [misc]points: Sampling 4 additional inputs, on iter 15 have 253 / 256 1546852753.417 * * * * [misc]points: Filtering points with unrepresentable outputs 1546852753.418 * * * * [exit]points: Sampled 256 points with exact outputs 1546852753.418 * * * [misc]progress: [2/2] Setting up program. 1546852753.441 * [misc]progress: [Phase 2 of 3] Improving. 1546852753.441 * * * * [misc]progress: [ 1 / 1 ] simplifiying candidate # 1546852753.441 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1546852753.441 * * [misc]simplify: iters left: 6 (13 enodes) 1546852753.444 * * [misc]simplify: iters left: 5 (28 enodes) 1546852753.450 * * [misc]simplify: iters left: 4 (44 enodes) 1546852753.466 * * [misc]simplify: iters left: 3 (54 enodes) 1546852753.478 * * [misc]simplify: iters left: 2 (57 enodes) 1546852753.490 * * [misc]simplify: iters left: 1 (65 enodes) 1546852753.505 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546852753.505 * [misc]simplify: Simplified (2) to (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) 1546852753.518 * * [misc]progress: iteration 1 / 4 1546852753.518 * * * [misc]progress: picking best candidate 1546852753.524 * * * * [misc]pick: Picked # 1546852753.524 * * * [misc]progress: localizing error 1546852753.545 * * * [misc]progress: generating rewritten candidates 1546852753.545 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1546852753.546 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1546852753.547 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1546852753.557 * * * [misc]progress: generating series expansions 1546852753.557 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1546852753.557 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546852753.557 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546852753.557 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852753.557 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852753.557 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852753.557 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852753.557 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.557 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.557 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852753.557 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.558 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.558 * [misc]taylor: Taking taylor expansion of k in k 1546852753.558 * [misc]backup-simplify: Simplify 0 into 0 1546852753.558 * [misc]backup-simplify: Simplify 1 into 1 1546852753.558 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852753.558 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852753.558 * [misc]taylor: Taking taylor expansion of 2 in k 1546852753.558 * [misc]backup-simplify: Simplify 2 into 2 1546852753.558 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852753.558 * [misc]taylor: Taking taylor expansion of n in k 1546852753.558 * [misc]backup-simplify: Simplify n into n 1546852753.558 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.558 * [misc]backup-simplify: Simplify PI into PI 1546852753.558 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852753.558 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852753.558 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852753.558 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852753.558 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.558 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852753.558 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852753.558 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852753.558 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852753.558 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852753.559 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852753.559 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852753.559 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.559 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.559 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852753.559 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.559 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.559 * [misc]taylor: Taking taylor expansion of k in n 1546852753.559 * [misc]backup-simplify: Simplify k into k 1546852753.559 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852753.559 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852753.559 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.559 * [misc]backup-simplify: Simplify 2 into 2 1546852753.559 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852753.559 * [misc]taylor: Taking taylor expansion of n in n 1546852753.559 * [misc]backup-simplify: Simplify 0 into 0 1546852753.559 * [misc]backup-simplify: Simplify 1 into 1 1546852753.559 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.559 * [misc]backup-simplify: Simplify PI into PI 1546852753.559 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852753.559 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852753.560 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852753.560 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852753.560 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.560 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852753.560 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852753.561 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852753.561 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.561 * [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)))) 1546852753.562 * [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))))) 1546852753.562 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852753.562 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852753.562 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852753.562 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852753.562 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.562 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.562 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852753.562 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.562 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.562 * [misc]taylor: Taking taylor expansion of k in n 1546852753.562 * [misc]backup-simplify: Simplify k into k 1546852753.562 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852753.562 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852753.562 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.562 * [misc]backup-simplify: Simplify 2 into 2 1546852753.562 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852753.562 * [misc]taylor: Taking taylor expansion of n in n 1546852753.562 * [misc]backup-simplify: Simplify 0 into 0 1546852753.562 * [misc]backup-simplify: Simplify 1 into 1 1546852753.562 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.562 * [misc]backup-simplify: Simplify PI into PI 1546852753.562 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852753.562 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852753.563 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852753.563 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852753.563 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.563 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852753.563 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852753.564 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852753.564 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.564 * [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)))) 1546852753.565 * [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))))) 1546852753.565 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546852753.565 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546852753.565 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852753.565 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.565 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.565 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852753.565 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.565 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.565 * [misc]taylor: Taking taylor expansion of k in k 1546852753.565 * [misc]backup-simplify: Simplify 0 into 0 1546852753.565 * [misc]backup-simplify: Simplify 1 into 1 1546852753.565 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546852753.565 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852753.565 * [misc]taylor: Taking taylor expansion of n in k 1546852753.565 * [misc]backup-simplify: Simplify n into n 1546852753.565 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852753.565 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852753.565 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852753.565 * [misc]taylor: Taking taylor expansion of 2 in k 1546852753.565 * [misc]backup-simplify: Simplify 2 into 2 1546852753.565 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.565 * [misc]backup-simplify: Simplify PI into PI 1546852753.565 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.566 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.566 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852753.566 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.566 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852753.566 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.567 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546852753.567 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852753.567 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852753.568 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852753.569 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852753.570 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852753.570 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546852753.570 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.571 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.571 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.571 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546852753.572 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852753.572 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.572 * [misc]backup-simplify: Simplify 0 into 0 1546852753.572 * [misc]backup-simplify: Simplify 0 into 0 1546852753.573 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546852753.573 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852753.575 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852753.575 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.576 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852753.576 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852753.576 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852753.576 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546852753.577 * [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))))))) 1546852753.578 * [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))))))) 1546852753.579 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.580 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852753.583 * [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 1546852753.583 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546852753.583 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.583 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.584 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.584 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852753.585 * [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 1546852753.586 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.586 * [misc]backup-simplify: Simplify 0 into 0 1546852753.586 * [misc]backup-simplify: Simplify 0 into 0 1546852753.586 * [misc]backup-simplify: Simplify 0 into 0 1546852753.586 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546852753.587 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852753.590 * [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 1546852753.590 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.591 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852753.591 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.591 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.591 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852753.594 * [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))))) 1546852753.596 * [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))))) 1546852753.602 * [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))))) 1546852753.602 * [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)))) 1546852753.602 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546852753.602 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852753.602 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852753.602 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852753.602 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852753.602 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.602 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.602 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852753.602 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.602 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.602 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.602 * [misc]taylor: Taking taylor expansion of k in k 1546852753.603 * [misc]backup-simplify: Simplify 0 into 0 1546852753.603 * [misc]backup-simplify: Simplify 1 into 1 1546852753.603 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.603 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852753.603 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852753.603 * [misc]taylor: Taking taylor expansion of 2 in k 1546852753.603 * [misc]backup-simplify: Simplify 2 into 2 1546852753.603 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852753.603 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.603 * [misc]backup-simplify: Simplify PI into PI 1546852753.603 * [misc]taylor: Taking taylor expansion of n in k 1546852753.603 * [misc]backup-simplify: Simplify n into n 1546852753.603 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852753.603 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852753.603 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852753.603 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852753.603 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852753.604 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852753.604 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852753.604 * [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)))) 1546852753.604 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852753.604 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852753.604 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852753.604 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852753.604 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.604 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.604 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852753.604 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.604 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.604 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.604 * [misc]taylor: Taking taylor expansion of k in n 1546852753.604 * [misc]backup-simplify: Simplify k into k 1546852753.604 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.604 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852753.604 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852753.604 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.605 * [misc]backup-simplify: Simplify 2 into 2 1546852753.605 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.605 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.605 * [misc]backup-simplify: Simplify PI into PI 1546852753.605 * [misc]taylor: Taking taylor expansion of n in n 1546852753.605 * [misc]backup-simplify: Simplify 0 into 0 1546852753.605 * [misc]backup-simplify: Simplify 1 into 1 1546852753.605 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.605 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.606 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.606 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852753.606 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852753.606 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852753.607 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.607 * [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))) 1546852753.608 * [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)))) 1546852753.608 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852753.608 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852753.608 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852753.608 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852753.608 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.608 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.608 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852753.608 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.608 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.608 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.608 * [misc]taylor: Taking taylor expansion of k in n 1546852753.608 * [misc]backup-simplify: Simplify k into k 1546852753.608 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.608 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852753.608 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852753.609 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.609 * [misc]backup-simplify: Simplify 2 into 2 1546852753.609 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.609 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.609 * [misc]backup-simplify: Simplify PI into PI 1546852753.609 * [misc]taylor: Taking taylor expansion of n in n 1546852753.609 * [misc]backup-simplify: Simplify 0 into 0 1546852753.609 * [misc]backup-simplify: Simplify 1 into 1 1546852753.609 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.609 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.610 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.610 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852753.610 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852753.610 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852753.611 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.611 * [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))) 1546852753.612 * [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)))) 1546852753.612 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546852753.612 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546852753.612 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852753.612 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.612 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.612 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852753.612 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.612 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.612 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.612 * [misc]taylor: Taking taylor expansion of k in k 1546852753.612 * [misc]backup-simplify: Simplify 0 into 0 1546852753.612 * [misc]backup-simplify: Simplify 1 into 1 1546852753.613 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.613 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546852753.613 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852753.613 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852753.613 * [misc]taylor: Taking taylor expansion of 2 in k 1546852753.613 * [misc]backup-simplify: Simplify 2 into 2 1546852753.613 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.613 * [misc]backup-simplify: Simplify PI into PI 1546852753.613 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.613 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.613 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852753.614 * [misc]taylor: Taking taylor expansion of n in k 1546852753.614 * [misc]backup-simplify: Simplify n into n 1546852753.614 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852753.614 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852753.614 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852753.614 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852753.614 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852753.615 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546852753.615 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546852753.616 * [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)))) 1546852753.617 * [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)))) 1546852753.618 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852753.618 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852753.621 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852753.621 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852753.621 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852753.622 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.622 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.623 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.623 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852753.625 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852753.625 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.625 * [misc]backup-simplify: Simplify 0 into 0 1546852753.625 * [misc]backup-simplify: Simplify 0 into 0 1546852753.625 * [misc]backup-simplify: Simplify 0 into 0 1546852753.626 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.627 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852753.632 * [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 1546852753.633 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.633 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852753.633 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.633 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.634 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.635 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546852753.637 * [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 1546852753.637 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.637 * [misc]backup-simplify: Simplify 0 into 0 1546852753.637 * [misc]backup-simplify: Simplify 0 into 0 1546852753.637 * [misc]backup-simplify: Simplify 0 into 0 1546852753.637 * [misc]backup-simplify: Simplify 0 into 0 1546852753.639 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.641 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.649 * [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 1546852753.649 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.650 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852753.650 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.650 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.651 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.652 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546852753.656 * [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 1546852753.656 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.656 * [misc]backup-simplify: Simplify 0 into 0 1546852753.656 * [misc]backup-simplify: Simplify 0 into 0 1546852753.657 * [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))))) 1546852753.657 * [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)) 1546852753.657 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546852753.657 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852753.657 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852753.657 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852753.657 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852753.657 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852753.657 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.657 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.657 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.657 * [misc]taylor: Taking taylor expansion of k in k 1546852753.657 * [misc]backup-simplify: Simplify 0 into 0 1546852753.657 * [misc]backup-simplify: Simplify 1 into 1 1546852753.658 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.658 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.658 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.658 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852753.658 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852753.658 * [misc]taylor: Taking taylor expansion of -2 in k 1546852753.658 * [misc]backup-simplify: Simplify -2 into -2 1546852753.658 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852753.658 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.658 * [misc]backup-simplify: Simplify PI into PI 1546852753.658 * [misc]taylor: Taking taylor expansion of n in k 1546852753.658 * [misc]backup-simplify: Simplify n into n 1546852753.658 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852753.658 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852753.658 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852753.658 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852753.658 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852753.659 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852753.659 * [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))) 1546852753.659 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852753.659 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852753.659 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852753.659 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852753.659 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852753.659 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.659 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.659 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.659 * [misc]taylor: Taking taylor expansion of k in n 1546852753.659 * [misc]backup-simplify: Simplify k into k 1546852753.659 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.659 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.659 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.659 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852753.659 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852753.659 * [misc]taylor: Taking taylor expansion of -2 in n 1546852753.659 * [misc]backup-simplify: Simplify -2 into -2 1546852753.660 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.660 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.660 * [misc]backup-simplify: Simplify PI into PI 1546852753.660 * [misc]taylor: Taking taylor expansion of n in n 1546852753.660 * [misc]backup-simplify: Simplify 0 into 0 1546852753.660 * [misc]backup-simplify: Simplify 1 into 1 1546852753.660 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.660 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852753.661 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852753.661 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852753.661 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852753.662 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.662 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852753.663 * [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)))) 1546852753.663 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852753.663 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852753.663 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852753.663 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852753.663 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852753.663 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.663 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.663 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.663 * [misc]taylor: Taking taylor expansion of k in n 1546852753.663 * [misc]backup-simplify: Simplify k into k 1546852753.663 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.663 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.663 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.663 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852753.663 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852753.663 * [misc]taylor: Taking taylor expansion of -2 in n 1546852753.663 * [misc]backup-simplify: Simplify -2 into -2 1546852753.663 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.664 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.664 * [misc]backup-simplify: Simplify PI into PI 1546852753.664 * [misc]taylor: Taking taylor expansion of n in n 1546852753.664 * [misc]backup-simplify: Simplify 0 into 0 1546852753.664 * [misc]backup-simplify: Simplify 1 into 1 1546852753.664 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.664 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852753.665 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852753.665 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852753.665 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852753.665 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.666 * [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))) 1546852753.667 * [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)))) 1546852753.667 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546852753.667 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546852753.667 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852753.667 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852753.667 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.667 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.667 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.667 * [misc]taylor: Taking taylor expansion of k in k 1546852753.667 * [misc]backup-simplify: Simplify 0 into 0 1546852753.667 * [misc]backup-simplify: Simplify 1 into 1 1546852753.667 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.667 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.667 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.667 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546852753.667 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546852753.667 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546852753.667 * [misc]taylor: Taking taylor expansion of -2 in k 1546852753.667 * [misc]backup-simplify: Simplify -2 into -2 1546852753.667 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.668 * [misc]backup-simplify: Simplify PI into PI 1546852753.668 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852753.668 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852753.668 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852753.668 * [misc]taylor: Taking taylor expansion of n in k 1546852753.668 * [misc]backup-simplify: Simplify n into n 1546852753.668 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852753.669 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852753.669 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852753.669 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852753.669 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546852753.670 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546852753.671 * [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)))) 1546852753.671 * [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)))) 1546852753.672 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852753.673 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852753.676 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852753.676 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852753.676 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852753.676 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.677 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.678 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546852753.679 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852753.679 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.679 * [misc]backup-simplify: Simplify 0 into 0 1546852753.679 * [misc]backup-simplify: Simplify 0 into 0 1546852753.679 * [misc]backup-simplify: Simplify 0 into 0 1546852753.681 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.682 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852753.687 * [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 1546852753.687 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.688 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852753.688 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.688 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.689 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546852753.694 * [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 1546852753.695 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.695 * [misc]backup-simplify: Simplify 0 into 0 1546852753.695 * [misc]backup-simplify: Simplify 0 into 0 1546852753.695 * [misc]backup-simplify: Simplify 0 into 0 1546852753.695 * [misc]backup-simplify: Simplify 0 into 0 1546852753.697 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.698 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.706 * [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 1546852753.706 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.707 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852753.707 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.708 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.709 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546852753.712 * [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 1546852753.713 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.713 * [misc]backup-simplify: Simplify 0 into 0 1546852753.713 * [misc]backup-simplify: Simplify 0 into 0 1546852753.713 * [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))))) 1546852753.713 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1546852753.714 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546852753.714 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546852753.714 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852753.714 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.714 * [misc]backup-simplify: Simplify 2 into 2 1546852753.714 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852753.714 * [misc]taylor: Taking taylor expansion of n in n 1546852753.714 * [misc]backup-simplify: Simplify 0 into 0 1546852753.714 * [misc]backup-simplify: Simplify 1 into 1 1546852753.714 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.714 * [misc]backup-simplify: Simplify PI into PI 1546852753.714 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852753.714 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.714 * [misc]backup-simplify: Simplify 2 into 2 1546852753.714 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852753.714 * [misc]taylor: Taking taylor expansion of n in n 1546852753.714 * [misc]backup-simplify: Simplify 0 into 0 1546852753.714 * [misc]backup-simplify: Simplify 1 into 1 1546852753.714 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.714 * [misc]backup-simplify: Simplify PI into PI 1546852753.715 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852753.715 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852753.715 * [misc]backup-simplify: Simplify 0 into 0 1546852753.715 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852753.716 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852753.716 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.717 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852753.718 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852753.719 * [misc]backup-simplify: Simplify 0 into 0 1546852753.720 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.722 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852753.722 * [misc]backup-simplify: Simplify 0 into 0 1546852753.724 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852753.726 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546852753.726 * [misc]backup-simplify: Simplify 0 into 0 1546852753.729 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852753.731 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546852753.732 * [misc]backup-simplify: Simplify 0 into 0 1546852753.735 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852753.738 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546852753.739 * [misc]backup-simplify: Simplify 0 into 0 1546852753.743 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546852753.747 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546852753.747 * [misc]backup-simplify: Simplify 0 into 0 1546852753.748 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546852753.748 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546852753.748 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546852753.748 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852753.748 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.748 * [misc]backup-simplify: Simplify 2 into 2 1546852753.748 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.748 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.748 * [misc]backup-simplify: Simplify PI into PI 1546852753.748 * [misc]taylor: Taking taylor expansion of n in n 1546852753.748 * [misc]backup-simplify: Simplify 0 into 0 1546852753.748 * [misc]backup-simplify: Simplify 1 into 1 1546852753.748 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.748 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852753.748 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.749 * [misc]backup-simplify: Simplify 2 into 2 1546852753.749 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.749 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.749 * [misc]backup-simplify: Simplify PI into PI 1546852753.749 * [misc]taylor: Taking taylor expansion of n in n 1546852753.749 * [misc]backup-simplify: Simplify 0 into 0 1546852753.749 * [misc]backup-simplify: Simplify 1 into 1 1546852753.749 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.749 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.749 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.751 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852753.751 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852753.751 * [misc]backup-simplify: Simplify 0 into 0 1546852753.753 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.754 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852753.754 * [misc]backup-simplify: Simplify 0 into 0 1546852753.755 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.757 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.757 * [misc]backup-simplify: Simplify 0 into 0 1546852753.759 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.760 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852753.760 * [misc]backup-simplify: Simplify 0 into 0 1546852753.761 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.763 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852753.763 * [misc]backup-simplify: Simplify 0 into 0 1546852753.765 * [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 1546852753.766 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852753.767 * [misc]backup-simplify: Simplify 0 into 0 1546852753.767 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546852753.767 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546852753.767 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546852753.767 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852753.767 * [misc]taylor: Taking taylor expansion of -2 in n 1546852753.767 * [misc]backup-simplify: Simplify -2 into -2 1546852753.767 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.767 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.767 * [misc]backup-simplify: Simplify PI into PI 1546852753.767 * [misc]taylor: Taking taylor expansion of n in n 1546852753.767 * [misc]backup-simplify: Simplify 0 into 0 1546852753.767 * [misc]backup-simplify: Simplify 1 into 1 1546852753.767 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.767 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852753.767 * [misc]taylor: Taking taylor expansion of -2 in n 1546852753.767 * [misc]backup-simplify: Simplify -2 into -2 1546852753.767 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.767 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.767 * [misc]backup-simplify: Simplify PI into PI 1546852753.767 * [misc]taylor: Taking taylor expansion of n in n 1546852753.767 * [misc]backup-simplify: Simplify 0 into 0 1546852753.767 * [misc]backup-simplify: Simplify 1 into 1 1546852753.767 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.768 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852753.768 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852753.769 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852753.769 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852753.769 * [misc]backup-simplify: Simplify 0 into 0 1546852753.770 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.770 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852753.770 * [misc]backup-simplify: Simplify 0 into 0 1546852753.771 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.772 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.772 * [misc]backup-simplify: Simplify 0 into 0 1546852753.773 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.775 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852753.775 * [misc]backup-simplify: Simplify 0 into 0 1546852753.776 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.777 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852753.778 * [misc]backup-simplify: Simplify 0 into 0 1546852753.779 * [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 1546852753.781 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852753.781 * [misc]backup-simplify: Simplify 0 into 0 1546852753.781 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546852753.781 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1546852753.782 * [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)))) 1546852753.782 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1546852753.782 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546852753.782 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546852753.782 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.782 * [misc]taylor: Taking taylor expansion of k in k 1546852753.782 * [misc]backup-simplify: Simplify 0 into 0 1546852753.782 * [misc]backup-simplify: Simplify 1 into 1 1546852753.782 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.782 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852753.782 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852753.782 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852753.782 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852753.783 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852753.783 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852753.783 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.783 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.783 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852753.783 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.783 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.783 * [misc]taylor: Taking taylor expansion of k in k 1546852753.783 * [misc]backup-simplify: Simplify 0 into 0 1546852753.783 * [misc]backup-simplify: Simplify 1 into 1 1546852753.783 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852753.783 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852753.783 * [misc]taylor: Taking taylor expansion of 2 in k 1546852753.783 * [misc]backup-simplify: Simplify 2 into 2 1546852753.783 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852753.783 * [misc]taylor: Taking taylor expansion of n in k 1546852753.783 * [misc]backup-simplify: Simplify n into n 1546852753.783 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.783 * [misc]backup-simplify: Simplify PI into PI 1546852753.783 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852753.783 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852753.783 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852753.783 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852753.783 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.783 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852753.783 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852753.783 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852753.783 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546852753.783 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546852753.783 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.783 * [misc]taylor: Taking taylor expansion of k in n 1546852753.783 * [misc]backup-simplify: Simplify k into k 1546852753.784 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.784 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546852753.784 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852753.784 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546852753.784 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852753.784 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852753.784 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852753.784 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852753.784 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.784 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.784 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852753.784 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.784 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.784 * [misc]taylor: Taking taylor expansion of k in n 1546852753.784 * [misc]backup-simplify: Simplify k into k 1546852753.784 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852753.784 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852753.784 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.784 * [misc]backup-simplify: Simplify 2 into 2 1546852753.784 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852753.784 * [misc]taylor: Taking taylor expansion of n in n 1546852753.784 * [misc]backup-simplify: Simplify 0 into 0 1546852753.784 * [misc]backup-simplify: Simplify 1 into 1 1546852753.784 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.784 * [misc]backup-simplify: Simplify PI into PI 1546852753.784 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852753.784 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852753.785 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852753.785 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852753.785 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.785 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852753.785 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852753.786 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852753.786 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.786 * [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)))) 1546852753.787 * [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))))) 1546852753.787 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of k in n 1546852753.787 * [misc]backup-simplify: Simplify k into k 1546852753.787 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.787 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546852753.787 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852753.787 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546852753.787 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.787 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.787 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.787 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.787 * [misc]taylor: Taking taylor expansion of k in n 1546852753.787 * [misc]backup-simplify: Simplify k into k 1546852753.787 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852753.787 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852753.788 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.788 * [misc]backup-simplify: Simplify 2 into 2 1546852753.788 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852753.788 * [misc]taylor: Taking taylor expansion of n in n 1546852753.788 * [misc]backup-simplify: Simplify 0 into 0 1546852753.788 * [misc]backup-simplify: Simplify 1 into 1 1546852753.788 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.788 * [misc]backup-simplify: Simplify PI into PI 1546852753.788 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852753.788 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852753.789 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852753.789 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852753.790 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.790 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852753.790 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852753.790 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852753.791 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.791 * [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)))) 1546852753.792 * [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))))) 1546852753.793 * [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))) 1546852753.793 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.793 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.793 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.793 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.793 * [misc]taylor: Taking taylor expansion of k in k 1546852753.793 * [misc]backup-simplify: Simplify 0 into 0 1546852753.793 * [misc]backup-simplify: Simplify 1 into 1 1546852753.793 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of n in k 1546852753.793 * [misc]backup-simplify: Simplify n into n 1546852753.793 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852753.793 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852753.793 * [misc]taylor: Taking taylor expansion of 2 in k 1546852753.793 * [misc]backup-simplify: Simplify 2 into 2 1546852753.793 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.793 * [misc]backup-simplify: Simplify PI into PI 1546852753.794 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.794 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.794 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852753.794 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.795 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852753.795 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.795 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546852753.796 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852753.796 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546852753.796 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.796 * [misc]taylor: Taking taylor expansion of k in k 1546852753.796 * [misc]backup-simplify: Simplify 0 into 0 1546852753.796 * [misc]backup-simplify: Simplify 1 into 1 1546852753.796 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.796 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852753.797 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852753.797 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1546852753.797 * [misc]backup-simplify: Simplify 0 into 0 1546852753.798 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852753.798 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852753.800 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852753.800 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546852753.800 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.800 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.801 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.801 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546852753.802 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852753.803 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1546852753.803 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.803 * [misc]backup-simplify: Simplify 0 into 0 1546852753.803 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546852753.804 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852753.805 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852753.805 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.806 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852753.806 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852753.806 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852753.806 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546852753.807 * [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))))))) 1546852753.809 * [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))))))) 1546852753.809 * [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))))))) 1546852753.810 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.811 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852753.814 * [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 1546852753.814 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546852753.814 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.814 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.815 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.815 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852753.817 * [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 1546852753.817 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.817 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1546852753.818 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1546852753.818 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.818 * [misc]backup-simplify: Simplify 0 into 0 1546852753.818 * [misc]backup-simplify: Simplify 0 into 0 1546852753.818 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546852753.819 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852753.820 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546852753.821 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852753.825 * [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 1546852753.825 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.825 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852753.825 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.826 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.826 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852753.829 * [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))))) 1546852753.833 * [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)))))))) 1546852753.836 * [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)))))))) 1546852753.838 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852753.840 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546852753.848 * [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 1546852753.849 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1546852753.849 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.849 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.849 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852753.850 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546852753.852 * [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 1546852753.852 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.852 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1546852753.853 * [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 1546852753.853 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.853 * [misc]backup-simplify: Simplify 0 into 0 1546852753.853 * [misc]backup-simplify: Simplify 0 into 0 1546852753.853 * [misc]backup-simplify: Simplify 0 into 0 1546852753.853 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.854 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852753.856 * [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 1546852753.857 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.861 * [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 1546852753.861 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.862 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546852753.862 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.862 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.862 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1546852753.865 * [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))))))) 1546852753.870 * [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)))))))))))))) 1546852753.874 * [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)))))))))))))) 1546852753.884 * [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)))))))))))))))))))))) 1546852753.884 * [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))))) 1546852753.884 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1546852753.884 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546852753.884 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546852753.884 * [misc]taylor: Taking taylor expansion of k in k 1546852753.884 * [misc]backup-simplify: Simplify 0 into 0 1546852753.884 * [misc]backup-simplify: Simplify 1 into 1 1546852753.885 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852753.885 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852753.885 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852753.885 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852753.885 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852753.885 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852753.885 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.885 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.886 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852753.886 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.886 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.886 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.886 * [misc]taylor: Taking taylor expansion of k in k 1546852753.886 * [misc]backup-simplify: Simplify 0 into 0 1546852753.886 * [misc]backup-simplify: Simplify 1 into 1 1546852753.886 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.886 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852753.886 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852753.886 * [misc]taylor: Taking taylor expansion of 2 in k 1546852753.886 * [misc]backup-simplify: Simplify 2 into 2 1546852753.886 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852753.886 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.886 * [misc]backup-simplify: Simplify PI into PI 1546852753.886 * [misc]taylor: Taking taylor expansion of n in k 1546852753.886 * [misc]backup-simplify: Simplify n into n 1546852753.886 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852753.886 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852753.886 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852753.886 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852753.887 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852753.887 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852753.887 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852753.887 * [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)))) 1546852753.887 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852753.887 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546852753.887 * [misc]taylor: Taking taylor expansion of k in n 1546852753.887 * [misc]backup-simplify: Simplify k into k 1546852753.887 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546852753.887 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546852753.887 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852753.887 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852753.887 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852753.887 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852753.887 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.887 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.887 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852753.887 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.888 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.888 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.888 * [misc]taylor: Taking taylor expansion of k in n 1546852753.888 * [misc]backup-simplify: Simplify k into k 1546852753.888 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.888 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852753.888 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852753.888 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.888 * [misc]backup-simplify: Simplify 2 into 2 1546852753.888 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.888 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.888 * [misc]backup-simplify: Simplify PI into PI 1546852753.888 * [misc]taylor: Taking taylor expansion of n in n 1546852753.888 * [misc]backup-simplify: Simplify 0 into 0 1546852753.888 * [misc]backup-simplify: Simplify 1 into 1 1546852753.888 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.888 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.889 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.889 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852753.889 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852753.889 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852753.890 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.890 * [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))) 1546852753.891 * [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)))) 1546852753.891 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852753.891 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546852753.891 * [misc]taylor: Taking taylor expansion of k in n 1546852753.891 * [misc]backup-simplify: Simplify k into k 1546852753.891 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546852753.891 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546852753.891 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852753.891 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852753.891 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852753.892 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852753.892 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.892 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.892 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852753.892 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.892 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.892 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.892 * [misc]taylor: Taking taylor expansion of k in n 1546852753.892 * [misc]backup-simplify: Simplify k into k 1546852753.892 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.892 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852753.892 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852753.892 * [misc]taylor: Taking taylor expansion of 2 in n 1546852753.892 * [misc]backup-simplify: Simplify 2 into 2 1546852753.892 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.892 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.892 * [misc]backup-simplify: Simplify PI into PI 1546852753.892 * [misc]taylor: Taking taylor expansion of n in n 1546852753.892 * [misc]backup-simplify: Simplify 0 into 0 1546852753.892 * [misc]backup-simplify: Simplify 1 into 1 1546852753.892 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.893 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.893 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.893 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852753.893 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852753.893 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852753.894 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.895 * [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))) 1546852753.895 * [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)))) 1546852753.896 * [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)) 1546852753.896 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1546852753.896 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546852753.896 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546852753.896 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852753.896 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.896 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.896 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852753.896 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.896 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.896 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.896 * [misc]taylor: Taking taylor expansion of k in k 1546852753.896 * [misc]backup-simplify: Simplify 0 into 0 1546852753.896 * [misc]backup-simplify: Simplify 1 into 1 1546852753.897 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.897 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546852753.897 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852753.897 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852753.897 * [misc]taylor: Taking taylor expansion of 2 in k 1546852753.897 * [misc]backup-simplify: Simplify 2 into 2 1546852753.897 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.897 * [misc]backup-simplify: Simplify PI into PI 1546852753.897 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852753.898 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852753.898 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852753.898 * [misc]taylor: Taking taylor expansion of n in k 1546852753.898 * [misc]backup-simplify: Simplify n into n 1546852753.898 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852753.898 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852753.898 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852753.898 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852753.898 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852753.899 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546852753.899 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546852753.900 * [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)))) 1546852753.900 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546852753.900 * [misc]taylor: Taking taylor expansion of k in k 1546852753.900 * [misc]backup-simplify: Simplify 0 into 0 1546852753.900 * [misc]backup-simplify: Simplify 1 into 1 1546852753.900 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852753.901 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852753.901 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1546852753.901 * [misc]backup-simplify: Simplify 0 into 0 1546852753.903 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852753.903 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852753.906 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852753.906 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852753.906 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852753.907 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.907 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.908 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.908 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852753.910 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852753.911 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546852753.911 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.911 * [misc]backup-simplify: Simplify 0 into 0 1546852753.911 * [misc]backup-simplify: Simplify 0 into 0 1546852753.912 * [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)))))) 1546852753.912 * [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)))))) 1546852753.914 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.915 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852753.920 * [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 1546852753.920 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.921 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852753.921 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.921 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.922 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.922 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546852753.925 * [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 1546852753.925 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1546852753.926 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546852753.926 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.926 * [misc]backup-simplify: Simplify 0 into 0 1546852753.926 * [misc]backup-simplify: Simplify 0 into 0 1546852753.926 * [misc]backup-simplify: Simplify 0 into 0 1546852753.928 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852753.928 * [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)))))) 1546852753.929 * [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)))))) 1546852753.931 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.932 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852753.940 * [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 1546852753.940 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.941 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852753.941 * [misc]backup-simplify: Simplify (- 0) into 0 1546852753.941 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.942 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852753.943 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546852753.947 * [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 1546852753.947 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1546852753.948 * [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 1546852753.948 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.948 * [misc]backup-simplify: Simplify 0 into 0 1546852753.948 * [misc]backup-simplify: Simplify 0 into 0 1546852753.948 * [misc]backup-simplify: Simplify 0 into 0 1546852753.948 * [misc]backup-simplify: Simplify 0 into 0 1546852753.949 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852753.950 * [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)))))) 1546852753.951 * [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)))))) 1546852753.954 * [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)))))))) 1546852753.954 * [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))) 1546852753.954 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1546852753.954 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546852753.954 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852753.954 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852753.954 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852753.954 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852753.954 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852753.954 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.954 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.954 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.954 * [misc]taylor: Taking taylor expansion of k in k 1546852753.955 * [misc]backup-simplify: Simplify 0 into 0 1546852753.955 * [misc]backup-simplify: Simplify 1 into 1 1546852753.955 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.955 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.955 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.955 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852753.955 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852753.955 * [misc]taylor: Taking taylor expansion of -2 in k 1546852753.955 * [misc]backup-simplify: Simplify -2 into -2 1546852753.955 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852753.955 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.955 * [misc]backup-simplify: Simplify PI into PI 1546852753.955 * [misc]taylor: Taking taylor expansion of n in k 1546852753.955 * [misc]backup-simplify: Simplify n into n 1546852753.955 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852753.955 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852753.955 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852753.955 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852753.956 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852753.956 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852753.956 * [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))) 1546852753.956 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546852753.956 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546852753.956 * [misc]taylor: Taking taylor expansion of -1 in k 1546852753.956 * [misc]backup-simplify: Simplify -1 into -1 1546852753.956 * [misc]taylor: Taking taylor expansion of k in k 1546852753.956 * [misc]backup-simplify: Simplify 0 into 0 1546852753.956 * [misc]backup-simplify: Simplify 1 into 1 1546852753.956 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546852753.956 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852753.957 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546852753.958 * [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)))) 1546852753.958 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.958 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.958 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of k in n 1546852753.958 * [misc]backup-simplify: Simplify k into k 1546852753.958 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.958 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.958 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.958 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of -2 in n 1546852753.958 * [misc]backup-simplify: Simplify -2 into -2 1546852753.958 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.958 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.958 * [misc]backup-simplify: Simplify PI into PI 1546852753.958 * [misc]taylor: Taking taylor expansion of n in n 1546852753.958 * [misc]backup-simplify: Simplify 0 into 0 1546852753.958 * [misc]backup-simplify: Simplify 1 into 1 1546852753.959 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.959 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852753.960 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852753.960 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852753.960 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852753.962 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.963 * [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))) 1546852753.963 * [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)))) 1546852753.963 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546852753.963 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546852753.963 * [misc]taylor: Taking taylor expansion of -1 in n 1546852753.963 * [misc]backup-simplify: Simplify -1 into -1 1546852753.963 * [misc]taylor: Taking taylor expansion of k in n 1546852753.964 * [misc]backup-simplify: Simplify k into k 1546852753.964 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546852753.964 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546852753.964 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546852753.964 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546852753.965 * [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))) 1546852753.965 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.965 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.965 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of k in n 1546852753.965 * [misc]backup-simplify: Simplify k into k 1546852753.965 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852753.965 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852753.965 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.965 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of -2 in n 1546852753.965 * [misc]backup-simplify: Simplify -2 into -2 1546852753.965 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852753.965 * [misc]taylor: Taking taylor expansion of PI in n 1546852753.965 * [misc]backup-simplify: Simplify PI into PI 1546852753.965 * [misc]taylor: Taking taylor expansion of n in n 1546852753.965 * [misc]backup-simplify: Simplify 0 into 0 1546852753.965 * [misc]backup-simplify: Simplify 1 into 1 1546852753.966 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852753.966 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852753.967 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852753.967 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852753.967 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852753.967 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.968 * [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))) 1546852753.969 * [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)))) 1546852753.969 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546852753.969 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546852753.969 * [misc]taylor: Taking taylor expansion of -1 in n 1546852753.969 * [misc]backup-simplify: Simplify -1 into -1 1546852753.969 * [misc]taylor: Taking taylor expansion of k in n 1546852753.969 * [misc]backup-simplify: Simplify k into k 1546852753.969 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546852753.969 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546852753.969 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546852753.969 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546852753.970 * [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))) 1546852753.970 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1546852753.970 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546852753.970 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546852753.970 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852753.970 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852753.970 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.970 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.970 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852753.970 * [misc]taylor: Taking taylor expansion of k in k 1546852753.970 * [misc]backup-simplify: Simplify 0 into 0 1546852753.971 * [misc]backup-simplify: Simplify 1 into 1 1546852753.971 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852753.971 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852753.971 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852753.971 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546852753.971 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546852753.971 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546852753.971 * [misc]taylor: Taking taylor expansion of -2 in k 1546852753.971 * [misc]backup-simplify: Simplify -2 into -2 1546852753.971 * [misc]taylor: Taking taylor expansion of PI in k 1546852753.971 * [misc]backup-simplify: Simplify PI into PI 1546852753.971 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852753.972 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852753.972 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852753.972 * [misc]taylor: Taking taylor expansion of n in k 1546852753.972 * [misc]backup-simplify: Simplify n into n 1546852753.972 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852753.972 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852753.972 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852753.972 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852753.973 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546852753.973 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546852753.974 * [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)))) 1546852753.974 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546852753.974 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546852753.974 * [misc]taylor: Taking taylor expansion of -1 in k 1546852753.974 * [misc]backup-simplify: Simplify -1 into -1 1546852753.974 * [misc]taylor: Taking taylor expansion of k in k 1546852753.974 * [misc]backup-simplify: Simplify 0 into 0 1546852753.974 * [misc]backup-simplify: Simplify 1 into 1 1546852753.974 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546852753.975 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852753.975 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546852753.976 * [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))))) 1546852753.977 * [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))))) 1546852753.978 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852753.978 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852753.981 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852753.981 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852753.982 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852753.982 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.982 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.983 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546852753.985 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852753.986 * [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 1546852753.986 * [misc]taylor: Taking taylor expansion of 0 in k 1546852753.986 * [misc]backup-simplify: Simplify 0 into 0 1546852753.986 * [misc]backup-simplify: Simplify 0 into 0 1546852753.986 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546852753.987 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852753.988 * [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)))))) 1546852753.989 * [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)))))) 1546852753.990 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852753.991 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852753.996 * [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 1546852753.997 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852753.997 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852753.997 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852753.998 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852753.999 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546852754.001 * [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 1546852754.001 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852754.002 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1546852754.003 * [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 1546852754.003 * [misc]taylor: Taking taylor expansion of 0 in k 1546852754.003 * [misc]backup-simplify: Simplify 0 into 0 1546852754.003 * [misc]backup-simplify: Simplify 0 into 0 1546852754.003 * [misc]backup-simplify: Simplify 0 into 0 1546852754.003 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852754.005 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852754.006 * [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)))))) 1546852754.007 * [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)))))) 1546852754.010 * [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))))))))))) 1546852754.010 * * * [misc]progress: simplifying candidates 1546852754.010 * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # 1546852754.011 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546852754.011 * * [misc]simplify: iters left: 6 (11 enodes) 1546852754.013 * * [misc]simplify: iters left: 5 (21 enodes) 1546852754.017 * * [misc]simplify: iters left: 4 (47 enodes) 1546852754.025 * * [misc]simplify: iters left: 3 (109 enodes) 1546852754.061 * * [misc]simplify: iters left: 2 (300 enodes) 1546852754.252 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546852754.252 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1546852754.252 * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # 1546852754.253 * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # 1546852754.253 * [enter]simplify: Simplifying (* PI (* n 2)) 1546852754.253 * * [misc]simplify: iters left: 4 (5 enodes) 1546852754.254 * * [misc]simplify: iters left: 3 (9 enodes) 1546852754.255 * * [misc]simplify: iters left: 2 (15 enodes) 1546852754.257 * * [misc]simplify: iters left: 1 (17 enodes) 1546852754.259 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546852754.259 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1546852754.259 * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # 1546852754.259 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852754.259 * * [misc]simplify: iters left: 5 (8 enodes) 1546852754.261 * * [misc]simplify: iters left: 4 (12 enodes) 1546852754.263 * * [misc]simplify: iters left: 3 (18 enodes) 1546852754.265 * * [misc]simplify: iters left: 2 (20 enodes) 1546852754.267 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852754.268 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1546852754.268 * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # 1546852754.268 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546852754.268 * * [misc]simplify: iters left: 5 (6 enodes) 1546852754.269 * * [misc]simplify: iters left: 4 (8 enodes) 1546852754.270 * * [misc]simplify: iters left: 3 (11 enodes) 1546852754.272 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546852754.272 * [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))) 1546852754.272 * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # 1546852754.272 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546852754.272 * * [misc]simplify: iters left: 5 (6 enodes) 1546852754.273 * * [misc]simplify: iters left: 4 (8 enodes) 1546852754.274 * * [misc]simplify: iters left: 3 (11 enodes) 1546852754.276 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546852754.276 * [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))) 1546852754.276 * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # 1546852754.276 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546852754.276 * * [misc]simplify: iters left: 4 (5 enodes) 1546852754.278 * * [misc]simplify: iters left: 3 (7 enodes) 1546852754.280 * * [misc]simplify: iters left: 2 (10 enodes) 1546852754.283 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546852754.283 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1546852754.283 * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # 1546852754.283 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852754.283 * * [misc]simplify: iters left: 5 (9 enodes) 1546852754.286 * * [misc]simplify: iters left: 4 (15 enodes) 1546852754.291 * * [misc]simplify: iters left: 3 (21 enodes) 1546852754.296 * * [misc]simplify: iters left: 2 (22 enodes) 1546852754.302 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852754.302 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1546852754.302 * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # 1546852754.302 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852754.302 * * [misc]simplify: iters left: 5 (9 enodes) 1546852754.305 * * [misc]simplify: iters left: 4 (15 enodes) 1546852754.310 * * [misc]simplify: iters left: 3 (21 enodes) 1546852754.316 * * [misc]simplify: iters left: 2 (22 enodes) 1546852754.321 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852754.321 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1546852754.321 * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # 1546852754.322 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546852754.322 * * [misc]simplify: iters left: 5 (7 enodes) 1546852754.324 * * [misc]simplify: iters left: 4 (9 enodes) 1546852754.327 * * [misc]simplify: iters left: 3 (12 enodes) 1546852754.330 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546852754.330 * [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))) 1546852754.330 * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # 1546852754.330 * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # 1546852754.331 * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # 1546852754.332 * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # 1546852754.332 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546852754.332 * * [misc]simplify: iters left: 6 (14 enodes) 1546852754.337 * * [misc]simplify: iters left: 5 (26 enodes) 1546852754.345 * * [misc]simplify: iters left: 4 (53 enodes) 1546852754.358 * * [misc]simplify: iters left: 3 (137 enodes) 1546852754.411 * * [misc]simplify: iters left: 2 (487 enodes) 1546852754.946 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1546852754.946 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1546852754.946 * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # 1546852754.946 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1546852754.946 * * [misc]simplify: iters left: 6 (14 enodes) 1546852754.949 * * [misc]simplify: iters left: 5 (26 enodes) 1546852754.953 * * [misc]simplify: iters left: 4 (53 enodes) 1546852754.964 * * [misc]simplify: iters left: 3 (137 enodes) 1546852755.009 * * [misc]simplify: iters left: 2 (487 enodes) 1546852755.566 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1546852755.566 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1546852755.566 * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # 1546852755.567 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1546852755.567 * * [misc]simplify: iters left: 6 (14 enodes) 1546852755.569 * * [misc]simplify: iters left: 5 (24 enodes) 1546852755.573 * * [misc]simplify: iters left: 4 (42 enodes) 1546852755.580 * * [misc]simplify: iters left: 3 (71 enodes) 1546852755.596 * * [misc]simplify: iters left: 2 (208 enodes) 1546852755.771 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1546852755.771 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1546852755.771 * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # 1546852755.771 * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # 1546852755.771 * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # 1546852755.771 * [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))) 1546852755.771 * * [misc]simplify: iters left: 6 (16 enodes) 1546852755.774 * * [misc]simplify: iters left: 5 (31 enodes) 1546852755.780 * * [misc]simplify: iters left: 4 (67 enodes) 1546852755.791 * * [misc]simplify: iters left: 3 (124 enodes) 1546852755.829 * * [misc]simplify: iters left: 2 (195 enodes) 1546852755.889 * * [misc]simplify: iters left: 1 (309 enodes) 1546852756.064 * [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)))) 1546852756.064 * [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)))))) 1546852756.064 * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # 1546852756.064 * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # 1546852756.064 * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # 1546852756.064 * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # 1546852756.064 * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # 1546852756.064 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.064 * * [misc]simplify: iters left: 6 (12 enodes) 1546852756.066 * * [misc]simplify: iters left: 5 (19 enodes) 1546852756.069 * * [misc]simplify: iters left: 4 (25 enodes) 1546852756.072 * * [misc]simplify: iters left: 3 (26 enodes) 1546852756.076 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.076 * [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))))) 1546852756.076 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1546852756.076 * * [misc]simplify: iters left: 6 (12 enodes) 1546852756.078 * * [misc]simplify: iters left: 5 (18 enodes) 1546852756.081 * * [misc]simplify: iters left: 4 (24 enodes) 1546852756.084 * * [misc]simplify: iters left: 3 (25 enodes) 1546852756.088 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1546852756.088 * [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))))) 1546852756.088 * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # 1546852756.088 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1546852756.088 * * [misc]simplify: iters left: 6 (11 enodes) 1546852756.090 * * [misc]simplify: iters left: 5 (16 enodes) 1546852756.092 * * [misc]simplify: iters left: 4 (22 enodes) 1546852756.095 * * [misc]simplify: iters left: 3 (24 enodes) 1546852756.098 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1546852756.098 * [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))))) 1546852756.098 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546852756.098 * * [misc]simplify: iters left: 6 (12 enodes) 1546852756.100 * * [misc]simplify: iters left: 5 (18 enodes) 1546852756.103 * * [misc]simplify: iters left: 4 (24 enodes) 1546852756.106 * * [misc]simplify: iters left: 3 (25 enodes) 1546852756.109 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546852756.109 * [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))))) 1546852756.109 * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # 1546852756.109 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546852756.109 * * [misc]simplify: iters left: 6 (9 enodes) 1546852756.111 * * [misc]simplify: iters left: 5 (16 enodes) 1546852756.114 * * [misc]simplify: iters left: 4 (24 enodes) 1546852756.118 * * [misc]simplify: iters left: 3 (26 enodes) 1546852756.123 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546852756.123 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1546852756.124 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1546852756.124 * * [misc]simplify: iters left: 6 (11 enodes) 1546852756.127 * * [misc]simplify: iters left: 5 (17 enodes) 1546852756.132 * * [misc]simplify: iters left: 4 (23 enodes) 1546852756.140 * * [misc]simplify: iters left: 3 (24 enodes) 1546852756.146 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1546852756.146 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1546852756.146 * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # 1546852756.147 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.147 * * [misc]simplify: iters left: 6 (12 enodes) 1546852756.151 * * [misc]simplify: iters left: 5 (19 enodes) 1546852756.156 * * [misc]simplify: iters left: 4 (25 enodes) 1546852756.163 * * [misc]simplify: iters left: 3 (26 enodes) 1546852756.169 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.169 * [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))))) 1546852756.169 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1546852756.169 * * [misc]simplify: iters left: 6 (12 enodes) 1546852756.173 * * [misc]simplify: iters left: 5 (18 enodes) 1546852756.178 * * [misc]simplify: iters left: 4 (24 enodes) 1546852756.185 * * [misc]simplify: iters left: 3 (25 enodes) 1546852756.191 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1546852756.191 * [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))))) 1546852756.191 * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # 1546852756.192 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1546852756.192 * * [misc]simplify: iters left: 6 (11 enodes) 1546852756.195 * * [misc]simplify: iters left: 5 (16 enodes) 1546852756.200 * * [misc]simplify: iters left: 4 (22 enodes) 1546852756.206 * * [misc]simplify: iters left: 3 (24 enodes) 1546852756.212 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1546852756.212 * [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))))) 1546852756.212 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1546852756.212 * * [misc]simplify: iters left: 6 (12 enodes) 1546852756.216 * * [misc]simplify: iters left: 5 (18 enodes) 1546852756.221 * * [misc]simplify: iters left: 4 (24 enodes) 1546852756.228 * * [misc]simplify: iters left: 3 (25 enodes) 1546852756.234 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1546852756.234 * [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))))) 1546852756.234 * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # 1546852756.235 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1546852756.235 * * [misc]simplify: iters left: 6 (9 enodes) 1546852756.238 * * [misc]simplify: iters left: 5 (16 enodes) 1546852756.242 * * [misc]simplify: iters left: 4 (24 enodes) 1546852756.248 * * [misc]simplify: iters left: 3 (26 enodes) 1546852756.250 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1546852756.250 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1546852756.251 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1546852756.251 * * [misc]simplify: iters left: 6 (11 enodes) 1546852756.252 * * [misc]simplify: iters left: 5 (17 enodes) 1546852756.255 * * [misc]simplify: iters left: 4 (23 enodes) 1546852756.258 * * [misc]simplify: iters left: 3 (24 enodes) 1546852756.261 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1546852756.261 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1546852756.261 * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # 1546852756.261 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.261 * * [misc]simplify: iters left: 6 (11 enodes) 1546852756.263 * * [misc]simplify: iters left: 5 (15 enodes) 1546852756.265 * * [misc]simplify: iters left: 4 (18 enodes) 1546852756.268 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.268 * [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))))) 1546852756.268 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546852756.268 * * [misc]simplify: iters left: 6 (11 enodes) 1546852756.270 * * [misc]simplify: iters left: 5 (14 enodes) 1546852756.273 * * [misc]simplify: iters left: 4 (17 enodes) 1546852756.275 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546852756.275 * [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))))) 1546852756.275 * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # 1546852756.276 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546852756.276 * * [misc]simplify: iters left: 6 (10 enodes) 1546852756.277 * * [misc]simplify: iters left: 5 (12 enodes) 1546852756.279 * * [misc]simplify: iters left: 4 (15 enodes) 1546852756.281 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546852756.281 * [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))))) 1546852756.282 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546852756.282 * * [misc]simplify: iters left: 6 (11 enodes) 1546852756.283 * * [misc]simplify: iters left: 5 (14 enodes) 1546852756.285 * * [misc]simplify: iters left: 4 (17 enodes) 1546852756.288 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546852756.288 * [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))))) 1546852756.288 * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # 1546852756.288 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1546852756.288 * * [misc]simplify: iters left: 6 (9 enodes) 1546852756.290 * * [misc]simplify: iters left: 5 (13 enodes) 1546852756.292 * * [misc]simplify: iters left: 4 (18 enodes) 1546852756.294 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546852756.294 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546852756.294 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546852756.294 * * [misc]simplify: iters left: 6 (10 enodes) 1546852756.296 * * [misc]simplify: iters left: 5 (13 enodes) 1546852756.298 * * [misc]simplify: iters left: 4 (16 enodes) 1546852756.301 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1546852756.301 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1546852756.301 * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # 1546852756.302 * [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)))) 1546852756.302 * * [misc]simplify: iters left: 6 (16 enodes) 1546852756.307 * * [misc]simplify: iters left: 5 (28 enodes) 1546852756.316 * * [misc]simplify: iters left: 4 (46 enodes) 1546852756.329 * * [misc]simplify: iters left: 3 (50 enodes) 1546852756.342 * * [misc]simplify: iters left: 2 (53 enodes) 1546852756.356 * [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)))) 1546852756.356 * [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))))) 1546852756.356 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546852756.356 * * [misc]simplify: iters left: 6 (14 enodes) 1546852756.361 * * [misc]simplify: iters left: 5 (20 enodes) 1546852756.367 * * [misc]simplify: iters left: 4 (29 enodes) 1546852756.373 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.377 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546852756.377 * [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))))) 1546852756.377 * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # 1546852756.377 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1546852756.377 * * [misc]simplify: iters left: 6 (15 enodes) 1546852756.380 * * [misc]simplify: iters left: 5 (23 enodes) 1546852756.383 * * [misc]simplify: iters left: 4 (34 enodes) 1546852756.389 * * [misc]simplify: iters left: 3 (37 enodes) 1546852756.394 * [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)))))) 1546852756.394 * [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))))) 1546852756.394 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546852756.394 * * [misc]simplify: iters left: 6 (14 enodes) 1546852756.397 * * [misc]simplify: iters left: 5 (20 enodes) 1546852756.400 * * [misc]simplify: iters left: 4 (29 enodes) 1546852756.404 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.408 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546852756.408 * [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))))) 1546852756.408 * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # 1546852756.409 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1546852756.409 * * [misc]simplify: iters left: 6 (14 enodes) 1546852756.413 * * [misc]simplify: iters left: 5 (24 enodes) 1546852756.418 * * [misc]simplify: iters left: 4 (39 enodes) 1546852756.424 * * [misc]simplify: iters left: 3 (54 enodes) 1546852756.431 * * [misc]simplify: iters left: 2 (80 enodes) 1546852756.441 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1546852756.442 * [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)))) 1546852756.442 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1546852756.442 * * [misc]simplify: iters left: 6 (13 enodes) 1546852756.444 * * [misc]simplify: iters left: 5 (19 enodes) 1546852756.447 * * [misc]simplify: iters left: 4 (28 enodes) 1546852756.451 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.458 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1546852756.458 * [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)))) 1546852756.459 * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # 1546852756.459 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.459 * * [misc]simplify: iters left: 6 (15 enodes) 1546852756.464 * * [misc]simplify: iters left: 5 (23 enodes) 1546852756.471 * * [misc]simplify: iters left: 4 (32 enodes) 1546852756.479 * * [misc]simplify: iters left: 3 (34 enodes) 1546852756.490 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.490 * [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))))) 1546852756.490 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546852756.490 * * [misc]simplify: iters left: 6 (14 enodes) 1546852756.495 * * [misc]simplify: iters left: 5 (20 enodes) 1546852756.500 * * [misc]simplify: iters left: 4 (29 enodes) 1546852756.508 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.516 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1546852756.516 * [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))))) 1546852756.516 * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # 1546852756.516 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546852756.516 * * [misc]simplify: iters left: 6 (14 enodes) 1546852756.521 * * [misc]simplify: iters left: 5 (20 enodes) 1546852756.527 * * [misc]simplify: iters left: 4 (29 enodes) 1546852756.535 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.542 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546852756.542 * [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))))) 1546852756.543 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546852756.543 * * [misc]simplify: iters left: 6 (14 enodes) 1546852756.547 * * [misc]simplify: iters left: 5 (20 enodes) 1546852756.553 * * [misc]simplify: iters left: 4 (29 enodes) 1546852756.561 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.569 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1546852756.569 * [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))))) 1546852756.569 * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # 1546852756.570 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1546852756.570 * * [misc]simplify: iters left: 6 (13 enodes) 1546852756.574 * * [misc]simplify: iters left: 5 (21 enodes) 1546852756.581 * * [misc]simplify: iters left: 4 (32 enodes) 1546852756.589 * * [misc]simplify: iters left: 3 (33 enodes) 1546852756.597 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1546852756.597 * [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)))) 1546852756.597 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1546852756.598 * * [misc]simplify: iters left: 6 (13 enodes) 1546852756.602 * * [misc]simplify: iters left: 5 (19 enodes) 1546852756.607 * * [misc]simplify: iters left: 4 (28 enodes) 1546852756.615 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.622 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1546852756.622 * [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)))) 1546852756.623 * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # 1546852756.623 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1546852756.623 * * [misc]simplify: iters left: 6 (6 enodes) 1546852756.625 * * [misc]simplify: iters left: 5 (10 enodes) 1546852756.628 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1546852756.628 * [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))))) 1546852756.628 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546852756.628 * * [misc]simplify: iters left: 6 (13 enodes) 1546852756.632 * * [misc]simplify: iters left: 5 (19 enodes) 1546852756.638 * * [misc]simplify: iters left: 4 (28 enodes) 1546852756.647 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.653 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1546852756.653 * [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))))) 1546852756.653 * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # 1546852756.653 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1546852756.653 * * [misc]simplify: iters left: 4 (5 enodes) 1546852756.654 * * [misc]simplify: iters left: 3 (7 enodes) 1546852756.655 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1546852756.655 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546852756.655 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546852756.655 * * [misc]simplify: iters left: 6 (13 enodes) 1546852756.657 * * [misc]simplify: iters left: 5 (19 enodes) 1546852756.660 * * [misc]simplify: iters left: 4 (28 enodes) 1546852756.664 * * [misc]simplify: iters left: 3 (30 enodes) 1546852756.668 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1546852756.668 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1546852756.668 * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # 1546852756.668 * [enter]simplify: Simplifying (/ 1 1) 1546852756.668 * * [misc]simplify: iters left: 2 (2 enodes) 1546852756.669 * * [misc]simplify: iters left: 1 (4 enodes) 1546852756.669 * [exit]simplify: Simplified to 1 1546852756.669 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1546852756.669 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1546852756.669 * * [misc]simplify: iters left: 6 (12 enodes) 1546852756.671 * * [misc]simplify: iters left: 5 (18 enodes) 1546852756.674 * * [misc]simplify: iters left: 4 (27 enodes) 1546852756.678 * * [misc]simplify: iters left: 3 (29 enodes) 1546852756.683 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1546852756.683 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1546852756.684 * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # 1546852756.684 * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # 1546852756.684 * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # 1546852756.684 * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # 1546852756.684 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1546852756.684 * * [misc]simplify: iters left: 2 (3 enodes) 1546852756.685 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1546852756.685 * [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)))) 1546852756.685 * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # 1546852756.685 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546852756.685 * * [misc]simplify: iters left: 2 (3 enodes) 1546852756.686 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546852756.686 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1546852756.686 * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # 1546852756.687 * [enter]simplify: Simplifying (sqrt k) 1546852756.687 * * [misc]simplify: iters left: 1 (2 enodes) 1546852756.687 * [exit]simplify: Simplified to (sqrt k) 1546852756.687 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1546852756.687 * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # 1546852756.688 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546852756.688 * * [misc]simplify: iters left: 5 (7 enodes) 1546852756.690 * * [misc]simplify: iters left: 4 (12 enodes) 1546852756.693 * * [misc]simplify: iters left: 3 (18 enodes) 1546852756.698 * * [misc]simplify: iters left: 2 (20 enodes) 1546852756.703 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546852756.703 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1546852756.703 * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # 1546852756.704 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546852756.704 * * [misc]simplify: iters left: 5 (7 enodes) 1546852756.707 * * [misc]simplify: iters left: 4 (12 enodes) 1546852756.710 * * [misc]simplify: iters left: 3 (18 enodes) 1546852756.713 * * [misc]simplify: iters left: 2 (20 enodes) 1546852756.715 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546852756.716 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1546852756.716 * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # 1546852756.716 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546852756.716 * * [misc]simplify: iters left: 5 (7 enodes) 1546852756.717 * * [misc]simplify: iters left: 4 (9 enodes) 1546852756.718 * * [misc]simplify: iters left: 3 (12 enodes) 1546852756.720 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546852756.720 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546852756.720 * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # 1546852756.720 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852756.720 * * [misc]simplify: iters left: 6 (12 enodes) 1546852756.723 * * [misc]simplify: iters left: 5 (18 enodes) 1546852756.725 * * [misc]simplify: iters left: 4 (27 enodes) 1546852756.729 * * [misc]simplify: iters left: 3 (29 enodes) 1546852756.734 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546852756.734 * [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))))))) 1546852756.734 * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # 1546852756.734 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852756.734 * * [misc]simplify: iters left: 6 (11 enodes) 1546852756.736 * * [misc]simplify: iters left: 5 (17 enodes) 1546852756.738 * * [misc]simplify: iters left: 4 (26 enodes) 1546852756.744 * * [misc]simplify: iters left: 3 (27 enodes) 1546852756.752 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546852756.752 * [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))))))) 1546852756.753 * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # 1546852756.753 * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # 1546852756.753 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1546852756.753 * * [misc]simplify: iters left: 5 (7 enodes) 1546852756.755 * * [misc]simplify: iters left: 4 (12 enodes) 1546852756.759 * * [misc]simplify: iters left: 3 (18 enodes) 1546852756.764 * * [misc]simplify: iters left: 2 (20 enodes) 1546852756.769 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1546852756.769 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1546852756.769 * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # 1546852756.769 * [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))))) 1546852756.770 * * [misc]simplify: iters left: 6 (37 enodes) 1546852756.786 * * [misc]simplify: iters left: 5 (105 enodes) 1546852756.829 * * [misc]simplify: iters left: 4 (339 enodes) 1546852757.098 * [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))))) 1546852757.098 * [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))) 1546852757.098 * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # 1546852757.098 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546852757.099 * * [misc]simplify: iters left: 6 (15 enodes) 1546852757.105 * * [misc]simplify: iters left: 5 (33 enodes) 1546852757.116 * * [misc]simplify: iters left: 4 (64 enodes) 1546852757.140 * * [misc]simplify: iters left: 3 (171 enodes) 1546852757.244 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546852757.244 * [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))) 1546852757.244 * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # 1546852757.244 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546852757.244 * * [misc]simplify: iters left: 6 (15 enodes) 1546852757.248 * * [misc]simplify: iters left: 5 (30 enodes) 1546852757.253 * * [misc]simplify: iters left: 4 (65 enodes) 1546852757.268 * * [misc]simplify: iters left: 3 (200 enodes) 1546852757.350 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546852757.350 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1546852757.350 * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # 1546852757.350 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852757.350 * * [misc]simplify: iters left: 4 (5 enodes) 1546852757.351 * * [misc]simplify: iters left: 3 (9 enodes) 1546852757.353 * * [misc]simplify: iters left: 2 (15 enodes) 1546852757.355 * * [misc]simplify: iters left: 1 (17 enodes) 1546852757.357 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852757.357 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546852757.357 * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # 1546852757.357 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852757.357 * * [misc]simplify: iters left: 4 (5 enodes) 1546852757.358 * * [misc]simplify: iters left: 3 (9 enodes) 1546852757.360 * * [misc]simplify: iters left: 2 (15 enodes) 1546852757.364 * * [misc]simplify: iters left: 1 (17 enodes) 1546852757.367 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852757.368 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546852757.368 * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # 1546852757.368 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852757.368 * * [misc]simplify: iters left: 4 (5 enodes) 1546852757.370 * * [misc]simplify: iters left: 3 (9 enodes) 1546852757.372 * * [misc]simplify: iters left: 2 (15 enodes) 1546852757.377 * * [misc]simplify: iters left: 1 (17 enodes) 1546852757.381 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852757.381 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1546852757.381 * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # 1546852757.381 * [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)))))))))))))))))))))) 1546852757.381 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546852757.381 * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # 1546852757.382 * [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)))))))) 1546852757.382 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546852757.382 * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # 1546852757.382 * [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))))))))))) 1546852757.382 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546852757.382 * * * [misc]progress: adding candidates to table 1546852758.261 * * [misc]progress: iteration 2 / 4 1546852758.261 * * * [misc]progress: picking best candidate 1546852758.309 * * * * [misc]pick: Picked # 1546852758.309 * * * [misc]progress: localizing error 1546852758.315 * * * [misc]progress: generating rewritten candidates 1546852758.315 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2) 1546852758.317 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1) 1546852758.318 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1546852758.322 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) 1546852758.326 * * * [misc]progress: generating series expansions 1546852758.326 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2) 1546852758.326 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546852758.326 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546852758.326 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852758.326 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852758.326 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852758.326 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852758.326 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.326 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.326 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852758.326 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.326 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.326 * [misc]taylor: Taking taylor expansion of k in k 1546852758.326 * [misc]backup-simplify: Simplify 0 into 0 1546852758.326 * [misc]backup-simplify: Simplify 1 into 1 1546852758.326 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852758.326 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852758.326 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.326 * [misc]backup-simplify: Simplify 2 into 2 1546852758.326 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852758.326 * [misc]taylor: Taking taylor expansion of n in k 1546852758.326 * [misc]backup-simplify: Simplify n into n 1546852758.326 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.326 * [misc]backup-simplify: Simplify PI into PI 1546852758.326 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852758.326 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852758.326 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852758.327 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852758.327 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.327 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.327 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852758.327 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852758.327 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852758.327 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852758.327 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852758.327 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852758.327 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.327 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.327 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852758.327 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.327 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.327 * [misc]taylor: Taking taylor expansion of k in n 1546852758.327 * [misc]backup-simplify: Simplify k into k 1546852758.327 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852758.327 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.327 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.327 * [misc]backup-simplify: Simplify 2 into 2 1546852758.327 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.327 * [misc]taylor: Taking taylor expansion of n in n 1546852758.327 * [misc]backup-simplify: Simplify 0 into 0 1546852758.327 * [misc]backup-simplify: Simplify 1 into 1 1546852758.327 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.327 * [misc]backup-simplify: Simplify PI into PI 1546852758.328 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.328 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.328 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.329 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.329 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.329 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852758.329 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852758.329 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852758.329 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.330 * [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)))) 1546852758.330 * [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))))) 1546852758.330 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852758.330 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852758.330 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852758.330 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852758.330 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.330 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.330 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852758.330 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.330 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.330 * [misc]taylor: Taking taylor expansion of k in n 1546852758.330 * [misc]backup-simplify: Simplify k into k 1546852758.330 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852758.330 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.330 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.331 * [misc]backup-simplify: Simplify 2 into 2 1546852758.331 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.331 * [misc]taylor: Taking taylor expansion of n in n 1546852758.331 * [misc]backup-simplify: Simplify 0 into 0 1546852758.331 * [misc]backup-simplify: Simplify 1 into 1 1546852758.331 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.331 * [misc]backup-simplify: Simplify PI into PI 1546852758.331 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.331 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.331 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.332 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.332 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.332 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852758.332 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852758.332 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852758.332 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.333 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1546852758.333 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1546852758.333 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546852758.333 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546852758.333 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852758.333 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.333 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.333 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852758.333 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.333 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.333 * [misc]taylor: Taking taylor expansion of k in k 1546852758.334 * [misc]backup-simplify: Simplify 0 into 0 1546852758.334 * [misc]backup-simplify: Simplify 1 into 1 1546852758.334 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546852758.334 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852758.334 * [misc]taylor: Taking taylor expansion of n in k 1546852758.334 * [misc]backup-simplify: Simplify n into n 1546852758.334 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852758.334 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852758.334 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852758.334 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.334 * [misc]backup-simplify: Simplify 2 into 2 1546852758.334 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.334 * [misc]backup-simplify: Simplify PI into PI 1546852758.334 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.334 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.334 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852758.334 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.335 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.335 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.335 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546852758.336 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852758.336 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852758.338 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852758.339 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852758.342 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852758.342 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546852758.342 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.342 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.343 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.344 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546852758.345 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852758.345 * [misc]taylor: Taking taylor expansion of 0 in k 1546852758.345 * [misc]backup-simplify: Simplify 0 into 0 1546852758.345 * [misc]backup-simplify: Simplify 0 into 0 1546852758.346 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546852758.347 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852758.350 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852758.350 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.350 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852758.350 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.350 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.351 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546852758.353 * [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))))))) 1546852758.354 * [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))))))) 1546852758.356 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852758.357 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852758.362 * [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 1546852758.363 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546852758.363 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.363 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.364 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.365 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852758.367 * [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 1546852758.367 * [misc]taylor: Taking taylor expansion of 0 in k 1546852758.367 * [misc]backup-simplify: Simplify 0 into 0 1546852758.367 * [misc]backup-simplify: Simplify 0 into 0 1546852758.367 * [misc]backup-simplify: Simplify 0 into 0 1546852758.369 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546852758.370 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852758.375 * [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 1546852758.375 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.375 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852758.375 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.375 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.376 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852758.379 * [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))))) 1546852758.381 * [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))))) 1546852758.386 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (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))))) 1546852758.386 * [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)))) 1546852758.386 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546852758.386 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852758.386 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852758.387 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852758.387 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852758.387 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.387 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.387 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.387 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.387 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.387 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.387 * [misc]taylor: Taking taylor expansion of k in k 1546852758.387 * [misc]backup-simplify: Simplify 0 into 0 1546852758.387 * [misc]backup-simplify: Simplify 1 into 1 1546852758.387 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.387 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852758.387 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852758.387 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.387 * [misc]backup-simplify: Simplify 2 into 2 1546852758.387 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.387 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.387 * [misc]backup-simplify: Simplify PI into PI 1546852758.387 * [misc]taylor: Taking taylor expansion of n in k 1546852758.387 * [misc]backup-simplify: Simplify n into n 1546852758.387 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.387 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852758.388 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852758.388 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.388 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.388 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.388 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852758.389 * [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)))) 1546852758.389 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.389 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.389 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.389 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.389 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of k in n 1546852758.389 * [misc]backup-simplify: Simplify k into k 1546852758.389 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.389 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.389 * [misc]backup-simplify: Simplify 2 into 2 1546852758.389 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.389 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.389 * [misc]backup-simplify: Simplify PI into PI 1546852758.389 * [misc]taylor: Taking taylor expansion of n in n 1546852758.389 * [misc]backup-simplify: Simplify 0 into 0 1546852758.389 * [misc]backup-simplify: Simplify 1 into 1 1546852758.390 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.390 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.391 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.391 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.391 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.391 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.392 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.392 * [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))) 1546852758.393 * [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)))) 1546852758.393 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.393 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.393 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.393 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.393 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of k in n 1546852758.393 * [misc]backup-simplify: Simplify k into k 1546852758.393 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.393 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.393 * [misc]backup-simplify: Simplify 2 into 2 1546852758.393 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.393 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.393 * [misc]backup-simplify: Simplify PI into PI 1546852758.393 * [misc]taylor: Taking taylor expansion of n in n 1546852758.394 * [misc]backup-simplify: Simplify 0 into 0 1546852758.394 * [misc]backup-simplify: Simplify 1 into 1 1546852758.394 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.394 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.395 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.395 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.395 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.395 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.395 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.396 * [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))) 1546852758.397 * [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)))) 1546852758.397 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546852758.397 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546852758.397 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852758.397 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.397 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.397 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.397 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.397 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.397 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.397 * [misc]taylor: Taking taylor expansion of k in k 1546852758.397 * [misc]backup-simplify: Simplify 0 into 0 1546852758.397 * [misc]backup-simplify: Simplify 1 into 1 1546852758.397 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.397 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546852758.397 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852758.397 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852758.397 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.398 * [misc]backup-simplify: Simplify 2 into 2 1546852758.398 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.398 * [misc]backup-simplify: Simplify PI into PI 1546852758.398 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.398 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.398 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852758.398 * [misc]taylor: Taking taylor expansion of n in k 1546852758.398 * [misc]backup-simplify: Simplify n into n 1546852758.398 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852758.399 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.399 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.399 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.399 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852758.400 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546852758.400 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546852758.401 * [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)))) 1546852758.401 * [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)))) 1546852758.403 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852758.403 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852758.406 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852758.406 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852758.407 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852758.407 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.407 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.408 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.408 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852758.410 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852758.410 * [misc]taylor: Taking taylor expansion of 0 in k 1546852758.410 * [misc]backup-simplify: Simplify 0 into 0 1546852758.410 * [misc]backup-simplify: Simplify 0 into 0 1546852758.410 * [misc]backup-simplify: Simplify 0 into 0 1546852758.411 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.413 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852758.417 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1546852758.418 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852758.418 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852758.418 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.418 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.419 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.420 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546852758.422 * [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 1546852758.422 * [misc]taylor: Taking taylor expansion of 0 in k 1546852758.422 * [misc]backup-simplify: Simplify 0 into 0 1546852758.422 * [misc]backup-simplify: Simplify 0 into 0 1546852758.422 * [misc]backup-simplify: Simplify 0 into 0 1546852758.422 * [misc]backup-simplify: Simplify 0 into 0 1546852758.424 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.426 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852758.437 * [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 1546852758.437 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852758.438 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852758.438 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.438 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.439 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.440 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546852758.444 * [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 1546852758.444 * [misc]taylor: Taking taylor expansion of 0 in k 1546852758.444 * [misc]backup-simplify: Simplify 0 into 0 1546852758.444 * [misc]backup-simplify: Simplify 0 into 0 1546852758.445 * [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))))) 1546852758.445 * [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)) 1546852758.445 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546852758.445 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852758.445 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852758.446 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852758.446 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852758.446 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.446 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.446 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.446 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.446 * [misc]taylor: Taking taylor expansion of k in k 1546852758.446 * [misc]backup-simplify: Simplify 0 into 0 1546852758.446 * [misc]backup-simplify: Simplify 1 into 1 1546852758.446 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.446 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.446 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.446 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852758.446 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852758.446 * [misc]taylor: Taking taylor expansion of -2 in k 1546852758.446 * [misc]backup-simplify: Simplify -2 into -2 1546852758.446 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.446 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.446 * [misc]backup-simplify: Simplify PI into PI 1546852758.446 * [misc]taylor: Taking taylor expansion of n in k 1546852758.446 * [misc]backup-simplify: Simplify n into n 1546852758.446 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.446 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852758.446 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852758.447 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.447 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.447 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852758.447 * [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))) 1546852758.447 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.447 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852758.447 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852758.447 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.447 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.447 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.447 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.447 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.447 * [misc]taylor: Taking taylor expansion of k in n 1546852758.447 * [misc]backup-simplify: Simplify k into k 1546852758.448 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.448 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.448 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.448 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.448 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.448 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.448 * [misc]backup-simplify: Simplify -2 into -2 1546852758.448 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.448 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.448 * [misc]backup-simplify: Simplify PI into PI 1546852758.448 * [misc]taylor: Taking taylor expansion of n in n 1546852758.448 * [misc]backup-simplify: Simplify 0 into 0 1546852758.448 * [misc]backup-simplify: Simplify 1 into 1 1546852758.448 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.449 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.449 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.449 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.449 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.450 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.450 * [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))) 1546852758.451 * [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)))) 1546852758.451 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.451 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852758.451 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852758.451 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.451 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.451 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.451 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.451 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.451 * [misc]taylor: Taking taylor expansion of k in n 1546852758.451 * [misc]backup-simplify: Simplify k into k 1546852758.451 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.451 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.451 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.451 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.451 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.451 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.451 * [misc]backup-simplify: Simplify -2 into -2 1546852758.451 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.452 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.452 * [misc]backup-simplify: Simplify PI into PI 1546852758.452 * [misc]taylor: Taking taylor expansion of n in n 1546852758.452 * [misc]backup-simplify: Simplify 0 into 0 1546852758.452 * [misc]backup-simplify: Simplify 1 into 1 1546852758.452 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.452 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.452 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.452 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.452 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.453 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.453 * [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))) 1546852758.453 * [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)))) 1546852758.454 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546852758.454 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546852758.454 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852758.454 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.454 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.454 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.454 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.454 * [misc]taylor: Taking taylor expansion of k in k 1546852758.454 * [misc]backup-simplify: Simplify 0 into 0 1546852758.454 * [misc]backup-simplify: Simplify 1 into 1 1546852758.454 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.454 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.454 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.454 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546852758.454 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546852758.454 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546852758.454 * [misc]taylor: Taking taylor expansion of -2 in k 1546852758.454 * [misc]backup-simplify: Simplify -2 into -2 1546852758.454 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.454 * [misc]backup-simplify: Simplify PI into PI 1546852758.454 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.454 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.455 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852758.455 * [misc]taylor: Taking taylor expansion of n in k 1546852758.455 * [misc]backup-simplify: Simplify n into n 1546852758.455 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852758.455 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.455 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.455 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852758.455 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546852758.456 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546852758.456 * [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)))) 1546852758.456 * [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)))) 1546852758.457 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852758.457 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852758.459 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852758.459 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852758.459 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852758.460 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.460 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.460 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546852758.461 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852758.461 * [misc]taylor: Taking taylor expansion of 0 in k 1546852758.461 * [misc]backup-simplify: Simplify 0 into 0 1546852758.461 * [misc]backup-simplify: Simplify 0 into 0 1546852758.461 * [misc]backup-simplify: Simplify 0 into 0 1546852758.462 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.463 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852758.466 * [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 1546852758.466 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852758.466 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852758.466 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.467 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.467 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546852758.469 * [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 1546852758.469 * [misc]taylor: Taking taylor expansion of 0 in k 1546852758.469 * [misc]backup-simplify: Simplify 0 into 0 1546852758.469 * [misc]backup-simplify: Simplify 0 into 0 1546852758.469 * [misc]backup-simplify: Simplify 0 into 0 1546852758.469 * [misc]backup-simplify: Simplify 0 into 0 1546852758.470 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.471 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852758.475 * [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 1546852758.476 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852758.476 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852758.476 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.476 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.477 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546852758.479 * [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 1546852758.479 * [misc]taylor: Taking taylor expansion of 0 in k 1546852758.479 * [misc]backup-simplify: Simplify 0 into 0 1546852758.479 * [misc]backup-simplify: Simplify 0 into 0 1546852758.480 * [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))))) 1546852758.480 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1) 1546852758.480 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546852758.480 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546852758.480 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.480 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.480 * [misc]backup-simplify: Simplify 2 into 2 1546852758.480 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.480 * [misc]taylor: Taking taylor expansion of n in n 1546852758.480 * [misc]backup-simplify: Simplify 0 into 0 1546852758.480 * [misc]backup-simplify: Simplify 1 into 1 1546852758.480 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.480 * [misc]backup-simplify: Simplify PI into PI 1546852758.480 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.480 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.480 * [misc]backup-simplify: Simplify 2 into 2 1546852758.480 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.480 * [misc]taylor: Taking taylor expansion of n in n 1546852758.480 * [misc]backup-simplify: Simplify 0 into 0 1546852758.480 * [misc]backup-simplify: Simplify 1 into 1 1546852758.480 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.480 * [misc]backup-simplify: Simplify PI into PI 1546852758.481 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.481 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.481 * [misc]backup-simplify: Simplify 0 into 0 1546852758.481 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.481 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.482 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.482 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852758.483 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852758.483 * [misc]backup-simplify: Simplify 0 into 0 1546852758.484 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852758.486 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852758.486 * [misc]backup-simplify: Simplify 0 into 0 1546852758.488 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852758.490 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546852758.490 * [misc]backup-simplify: Simplify 0 into 0 1546852758.493 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852758.496 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546852758.496 * [misc]backup-simplify: Simplify 0 into 0 1546852758.499 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852758.502 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546852758.502 * [misc]backup-simplify: Simplify 0 into 0 1546852758.506 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546852758.510 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546852758.510 * [misc]backup-simplify: Simplify 0 into 0 1546852758.510 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546852758.510 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546852758.510 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546852758.510 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.510 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.510 * [misc]backup-simplify: Simplify 2 into 2 1546852758.510 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.511 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.511 * [misc]backup-simplify: Simplify PI into PI 1546852758.511 * [misc]taylor: Taking taylor expansion of n in n 1546852758.511 * [misc]backup-simplify: Simplify 0 into 0 1546852758.511 * [misc]backup-simplify: Simplify 1 into 1 1546852758.511 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.511 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.511 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.511 * [misc]backup-simplify: Simplify 2 into 2 1546852758.511 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.511 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.511 * [misc]backup-simplify: Simplify PI into PI 1546852758.511 * [misc]taylor: Taking taylor expansion of n in n 1546852758.511 * [misc]backup-simplify: Simplify 0 into 0 1546852758.511 * [misc]backup-simplify: Simplify 1 into 1 1546852758.512 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.512 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.512 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.513 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852758.514 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852758.514 * [misc]backup-simplify: Simplify 0 into 0 1546852758.515 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.516 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852758.516 * [misc]backup-simplify: Simplify 0 into 0 1546852758.518 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.519 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852758.519 * [misc]backup-simplify: Simplify 0 into 0 1546852758.521 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.523 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852758.523 * [misc]backup-simplify: Simplify 0 into 0 1546852758.526 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.528 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852758.529 * [misc]backup-simplify: Simplify 0 into 0 1546852758.531 * [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 1546852758.534 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852758.534 * [misc]backup-simplify: Simplify 0 into 0 1546852758.534 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546852758.535 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546852758.535 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546852758.535 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.535 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.535 * [misc]backup-simplify: Simplify -2 into -2 1546852758.535 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.535 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.535 * [misc]backup-simplify: Simplify PI into PI 1546852758.535 * [misc]taylor: Taking taylor expansion of n in n 1546852758.535 * [misc]backup-simplify: Simplify 0 into 0 1546852758.535 * [misc]backup-simplify: Simplify 1 into 1 1546852758.535 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.535 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.535 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.535 * [misc]backup-simplify: Simplify -2 into -2 1546852758.535 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.535 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.535 * [misc]backup-simplify: Simplify PI into PI 1546852758.535 * [misc]taylor: Taking taylor expansion of n in n 1546852758.535 * [misc]backup-simplify: Simplify 0 into 0 1546852758.535 * [misc]backup-simplify: Simplify 1 into 1 1546852758.536 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.536 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.536 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.537 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852758.538 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852758.538 * [misc]backup-simplify: Simplify 0 into 0 1546852758.539 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.541 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852758.541 * [misc]backup-simplify: Simplify 0 into 0 1546852758.542 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.544 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852758.544 * [misc]backup-simplify: Simplify 0 into 0 1546852758.546 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.548 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852758.548 * [misc]backup-simplify: Simplify 0 into 0 1546852758.550 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.553 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852758.553 * [misc]backup-simplify: Simplify 0 into 0 1546852758.555 * [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 1546852758.558 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852758.559 * [misc]backup-simplify: Simplify 0 into 0 1546852758.559 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546852758.559 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1546852758.559 * [misc]backup-simplify: Simplify (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 1546852758.559 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 1546852758.559 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 1546852758.559 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.560 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.560 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.560 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.560 * [misc]taylor: Taking taylor expansion of k in n 1546852758.560 * [misc]backup-simplify: Simplify k into k 1546852758.560 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.560 * [misc]backup-simplify: Simplify 2 into 2 1546852758.560 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.560 * [misc]taylor: Taking taylor expansion of n in n 1546852758.560 * [misc]backup-simplify: Simplify 0 into 0 1546852758.560 * [misc]backup-simplify: Simplify 1 into 1 1546852758.560 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.560 * [misc]backup-simplify: Simplify PI into PI 1546852758.561 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.561 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.561 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.562 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.563 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.563 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852758.563 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852758.563 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852758.563 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.564 * [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)))) 1546852758.565 * [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))))) 1546852758.565 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546852758.565 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546852758.565 * [misc]taylor: Taking taylor expansion of k in n 1546852758.565 * [misc]backup-simplify: Simplify k into k 1546852758.566 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546852758.566 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546852758.566 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.566 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.566 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.566 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.566 * [misc]taylor: Taking taylor expansion of k in k 1546852758.566 * [misc]backup-simplify: Simplify 0 into 0 1546852758.566 * [misc]backup-simplify: Simplify 1 into 1 1546852758.566 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.566 * [misc]backup-simplify: Simplify 2 into 2 1546852758.566 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852758.566 * [misc]taylor: Taking taylor expansion of n in k 1546852758.566 * [misc]backup-simplify: Simplify n into n 1546852758.566 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.566 * [misc]backup-simplify: Simplify PI into PI 1546852758.566 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852758.566 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852758.567 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852758.567 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852758.567 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.567 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.567 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852758.567 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852758.567 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546852758.568 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546852758.568 * [misc]taylor: Taking taylor expansion of k in k 1546852758.568 * [misc]backup-simplify: Simplify 0 into 0 1546852758.568 * [misc]backup-simplify: Simplify 1 into 1 1546852758.568 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.568 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852758.568 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546852758.568 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546852758.568 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852758.568 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852758.568 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852758.568 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852758.568 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.568 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.568 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852758.569 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.569 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.569 * [misc]taylor: Taking taylor expansion of k in k 1546852758.569 * [misc]backup-simplify: Simplify 0 into 0 1546852758.569 * [misc]backup-simplify: Simplify 1 into 1 1546852758.569 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852758.569 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852758.569 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.569 * [misc]backup-simplify: Simplify 2 into 2 1546852758.569 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852758.569 * [misc]taylor: Taking taylor expansion of n in k 1546852758.569 * [misc]backup-simplify: Simplify n into n 1546852758.569 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.569 * [misc]backup-simplify: Simplify PI into PI 1546852758.569 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852758.569 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852758.569 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852758.569 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852758.569 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.570 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.570 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852758.570 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852758.570 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546852758.570 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546852758.570 * [misc]taylor: Taking taylor expansion of k in k 1546852758.570 * [misc]backup-simplify: Simplify 0 into 0 1546852758.570 * [misc]backup-simplify: Simplify 1 into 1 1546852758.570 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.572 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852758.572 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 1546852758.572 * [misc]taylor: Taking taylor expansion of 0 in n 1546852758.572 * [misc]backup-simplify: Simplify 0 into 0 1546852758.572 * [misc]backup-simplify: Simplify 0 into 0 1546852758.572 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546852758.573 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546852758.574 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546852758.574 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852758.574 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.574 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.574 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546852758.575 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546852758.575 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 1546852758.577 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 1546852758.577 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546852758.577 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546852758.577 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.577 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.577 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546852758.577 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546852758.577 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546852758.577 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.577 * [misc]taylor: Taking taylor expansion of n in n 1546852758.577 * [misc]backup-simplify: Simplify 0 into 0 1546852758.577 * [misc]backup-simplify: Simplify 1 into 1 1546852758.577 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.577 * [misc]backup-simplify: Simplify PI into PI 1546852758.577 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.578 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.578 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546852758.578 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.579 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546852758.579 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546852758.579 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.579 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.579 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546852758.579 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546852758.581 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852758.581 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546852758.583 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852758.584 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852758.585 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852758.585 * [misc]backup-simplify: Simplify 0 into 0 1546852758.586 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852758.587 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546852758.587 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546852758.589 * [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 1546852758.589 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852758.589 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.589 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.590 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546852758.591 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546852758.594 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 1546852758.597 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 1546852758.597 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 1546852758.597 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 1546852758.597 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 1546852758.598 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.598 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.598 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 1546852758.598 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 1546852758.598 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546852758.598 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.598 * [misc]backup-simplify: Simplify 2 into 2 1546852758.598 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546852758.598 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546852758.598 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 1546852758.598 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852758.598 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.598 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.598 * [misc]backup-simplify: Simplify 2 into 2 1546852758.598 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.598 * [misc]taylor: Taking taylor expansion of n in n 1546852758.598 * [misc]backup-simplify: Simplify 0 into 0 1546852758.598 * [misc]backup-simplify: Simplify 1 into 1 1546852758.598 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.598 * [misc]backup-simplify: Simplify PI into PI 1546852758.599 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.599 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.599 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.600 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.601 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.601 * [misc]taylor: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 1546852758.601 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546852758.601 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.601 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.601 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546852758.601 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546852758.601 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546852758.601 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546852758.601 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.601 * [misc]taylor: Taking taylor expansion of n in n 1546852758.601 * [misc]backup-simplify: Simplify 0 into 0 1546852758.601 * [misc]backup-simplify: Simplify 1 into 1 1546852758.601 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.602 * [misc]backup-simplify: Simplify PI into PI 1546852758.602 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.602 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.603 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546852758.603 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.603 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546852758.603 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546852758.604 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546852758.604 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.604 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.604 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546852758.604 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546852758.604 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546852758.604 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.604 * [misc]taylor: Taking taylor expansion of n in n 1546852758.604 * [misc]backup-simplify: Simplify 0 into 0 1546852758.604 * [misc]backup-simplify: Simplify 1 into 1 1546852758.604 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.604 * [misc]backup-simplify: Simplify PI into PI 1546852758.604 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.605 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.605 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546852758.605 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.606 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546852758.606 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546852758.606 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.606 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.606 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546852758.606 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546852758.607 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.608 * [misc]backup-simplify: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 1546852758.609 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 1546852758.610 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 1546852758.610 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.611 * [misc]backup-simplify: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 1546852758.612 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852758.613 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852758.615 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852758.617 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 1546852758.618 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 1546852758.619 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546852758.621 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 1546852758.626 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546852758.627 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852758.627 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546852758.629 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852758.631 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852758.636 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546852758.644 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546852758.651 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546852758.652 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 1546852758.652 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852758.653 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1546852758.654 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1546852758.656 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546852758.658 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546852758.659 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546852758.660 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546852758.666 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546852758.666 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 1546852758.666 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 1546852758.666 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 1546852758.666 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852758.666 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.666 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.666 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.666 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.666 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.666 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.666 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.666 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.666 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.667 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.667 * [misc]taylor: Taking taylor expansion of k in n 1546852758.667 * [misc]backup-simplify: Simplify k into k 1546852758.667 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.667 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.667 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.667 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.667 * [misc]backup-simplify: Simplify 2 into 2 1546852758.667 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.667 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.667 * [misc]backup-simplify: Simplify PI into PI 1546852758.667 * [misc]taylor: Taking taylor expansion of n in n 1546852758.667 * [misc]backup-simplify: Simplify 0 into 0 1546852758.667 * [misc]backup-simplify: Simplify 1 into 1 1546852758.667 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.667 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.668 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.668 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.668 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.668 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.668 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.669 * [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))) 1546852758.669 * [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)))) 1546852758.669 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852758.669 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546852758.669 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.669 * [misc]taylor: Taking taylor expansion of k in n 1546852758.669 * [misc]backup-simplify: Simplify k into k 1546852758.669 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.669 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546852758.670 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852758.670 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546852758.670 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.670 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.670 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.670 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.670 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of k in k 1546852758.670 * [misc]backup-simplify: Simplify 0 into 0 1546852758.670 * [misc]backup-simplify: Simplify 1 into 1 1546852758.670 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.670 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.670 * [misc]backup-simplify: Simplify 2 into 2 1546852758.670 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.670 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.670 * [misc]backup-simplify: Simplify PI into PI 1546852758.670 * [misc]taylor: Taking taylor expansion of n in k 1546852758.670 * [misc]backup-simplify: Simplify n into n 1546852758.670 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.670 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852758.670 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852758.670 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.671 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.671 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.671 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852758.671 * [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)))) 1546852758.671 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546852758.671 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546852758.671 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.671 * [misc]taylor: Taking taylor expansion of k in k 1546852758.671 * [misc]backup-simplify: Simplify 0 into 0 1546852758.671 * [misc]backup-simplify: Simplify 1 into 1 1546852758.671 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.671 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.671 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852758.672 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.672 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.672 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.672 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.672 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of k in k 1546852758.672 * [misc]backup-simplify: Simplify 0 into 0 1546852758.672 * [misc]backup-simplify: Simplify 1 into 1 1546852758.672 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.672 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.672 * [misc]backup-simplify: Simplify 2 into 2 1546852758.672 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.672 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.672 * [misc]backup-simplify: Simplify PI into PI 1546852758.672 * [misc]taylor: Taking taylor expansion of n in k 1546852758.672 * [misc]backup-simplify: Simplify n into n 1546852758.672 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.672 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852758.672 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852758.672 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.672 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.672 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.673 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852758.673 * [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)))) 1546852758.673 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546852758.673 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546852758.673 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.673 * [misc]taylor: Taking taylor expansion of k in k 1546852758.673 * [misc]backup-simplify: Simplify 0 into 0 1546852758.673 * [misc]backup-simplify: Simplify 1 into 1 1546852758.673 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.673 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.673 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852758.674 * [misc]backup-simplify: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1546852758.674 * [misc]taylor: Taking taylor expansion of 0 in n 1546852758.674 * [misc]backup-simplify: Simplify 0 into 0 1546852758.674 * [misc]backup-simplify: Simplify 0 into 0 1546852758.674 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546852758.674 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546852758.674 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.674 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.674 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.674 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.674 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.674 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.674 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of k in n 1546852758.674 * [misc]backup-simplify: Simplify k into k 1546852758.674 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.674 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.674 * [misc]backup-simplify: Simplify 2 into 2 1546852758.674 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.674 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.674 * [misc]backup-simplify: Simplify PI into PI 1546852758.675 * [misc]taylor: Taking taylor expansion of n in n 1546852758.675 * [misc]backup-simplify: Simplify 0 into 0 1546852758.675 * [misc]backup-simplify: Simplify 1 into 1 1546852758.675 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.675 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.675 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.675 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.675 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.675 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.676 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.676 * [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))) 1546852758.677 * [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)))) 1546852758.677 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852758.677 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852758.678 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852758.678 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852758.678 * [misc]backup-simplify: Simplify 0 into 0 1546852758.678 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546852758.679 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852758.680 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546852758.680 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546852758.680 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546852758.680 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852758.680 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.680 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.680 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852758.680 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.680 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.680 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.680 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.680 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.681 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.681 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.681 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.681 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.681 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.681 * [misc]taylor: Taking taylor expansion of k in n 1546852758.681 * [misc]backup-simplify: Simplify k into k 1546852758.681 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.681 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.681 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.681 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.681 * [misc]backup-simplify: Simplify 2 into 2 1546852758.681 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.681 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.681 * [misc]backup-simplify: Simplify PI into PI 1546852758.681 * [misc]taylor: Taking taylor expansion of n in n 1546852758.681 * [misc]backup-simplify: Simplify 0 into 0 1546852758.681 * [misc]backup-simplify: Simplify 1 into 1 1546852758.681 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.682 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.682 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.682 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.682 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.682 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.683 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.684 * [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))) 1546852758.684 * [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)))) 1546852758.685 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852758.686 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852758.686 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852758.687 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852758.688 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852758.689 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852758.692 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852758.692 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852758.693 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852758.693 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.693 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.694 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.694 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852758.696 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852758.697 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546852758.698 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546852758.698 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.698 * [misc]backup-simplify: Simplify 0 into 0 1546852758.698 * [misc]backup-simplify: Simplify 0 into 0 1546852758.698 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.700 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852758.701 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546852758.701 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546852758.701 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546852758.701 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852758.701 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.701 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.701 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852758.701 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.701 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.701 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.702 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.702 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.702 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.702 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.702 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.702 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.702 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.702 * [misc]taylor: Taking taylor expansion of k in n 1546852758.702 * [misc]backup-simplify: Simplify k into k 1546852758.702 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.702 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.702 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.702 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.702 * [misc]backup-simplify: Simplify 2 into 2 1546852758.702 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.702 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.702 * [misc]backup-simplify: Simplify PI into PI 1546852758.702 * [misc]taylor: Taking taylor expansion of n in n 1546852758.702 * [misc]backup-simplify: Simplify 0 into 0 1546852758.702 * [misc]backup-simplify: Simplify 1 into 1 1546852758.702 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.703 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.703 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.703 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.703 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.703 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.704 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.705 * [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))) 1546852758.705 * [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)))) 1546852758.706 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852758.707 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852758.707 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852758.708 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852758.711 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546852758.711 * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1546852758.711 * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 1546852758.711 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852758.711 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546852758.711 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546852758.711 * [misc]taylor: Taking taylor expansion of -1 in n 1546852758.711 * [misc]backup-simplify: Simplify -1 into -1 1546852758.711 * [misc]taylor: Taking taylor expansion of k in n 1546852758.711 * [misc]backup-simplify: Simplify k into k 1546852758.711 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546852758.711 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546852758.711 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546852758.711 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546852758.711 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.712 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of k in n 1546852758.712 * [misc]backup-simplify: Simplify k into k 1546852758.712 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.712 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.712 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.712 * [misc]backup-simplify: Simplify -2 into -2 1546852758.712 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.712 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.712 * [misc]backup-simplify: Simplify PI into PI 1546852758.712 * [misc]taylor: Taking taylor expansion of n in n 1546852758.712 * [misc]backup-simplify: Simplify 0 into 0 1546852758.712 * [misc]backup-simplify: Simplify 1 into 1 1546852758.712 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.712 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.713 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.713 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.713 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.713 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.714 * [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))) 1546852758.714 * [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)))) 1546852758.715 * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852758.715 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546852758.715 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546852758.715 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546852758.715 * [misc]taylor: Taking taylor expansion of -1 in k 1546852758.715 * [misc]backup-simplify: Simplify -1 into -1 1546852758.715 * [misc]taylor: Taking taylor expansion of k in k 1546852758.715 * [misc]backup-simplify: Simplify 0 into 0 1546852758.715 * [misc]backup-simplify: Simplify 1 into 1 1546852758.715 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546852758.716 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.716 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546852758.716 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.716 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.716 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of k in k 1546852758.716 * [misc]backup-simplify: Simplify 0 into 0 1546852758.716 * [misc]backup-simplify: Simplify 1 into 1 1546852758.716 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.716 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.716 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.716 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of -2 in k 1546852758.716 * [misc]backup-simplify: Simplify -2 into -2 1546852758.716 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.716 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.716 * [misc]backup-simplify: Simplify PI into PI 1546852758.716 * [misc]taylor: Taking taylor expansion of n in k 1546852758.716 * [misc]backup-simplify: Simplify n into n 1546852758.716 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.717 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852758.717 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852758.717 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.717 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.717 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852758.717 * [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))) 1546852758.717 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546852758.717 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546852758.717 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546852758.717 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546852758.717 * [misc]taylor: Taking taylor expansion of -1 in k 1546852758.717 * [misc]backup-simplify: Simplify -1 into -1 1546852758.717 * [misc]taylor: Taking taylor expansion of k in k 1546852758.717 * [misc]backup-simplify: Simplify 0 into 0 1546852758.717 * [misc]backup-simplify: Simplify 1 into 1 1546852758.717 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546852758.717 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.718 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546852758.718 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.718 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.718 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of k in k 1546852758.718 * [misc]backup-simplify: Simplify 0 into 0 1546852758.718 * [misc]backup-simplify: Simplify 1 into 1 1546852758.718 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.718 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.718 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.718 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of -2 in k 1546852758.718 * [misc]backup-simplify: Simplify -2 into -2 1546852758.718 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.718 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.718 * [misc]backup-simplify: Simplify PI into PI 1546852758.718 * [misc]taylor: Taking taylor expansion of n in k 1546852758.718 * [misc]backup-simplify: Simplify n into n 1546852758.718 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.718 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852758.718 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852758.718 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.719 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.719 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852758.719 * [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))) 1546852758.719 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546852758.719 * [misc]taylor: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852758.719 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.719 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.719 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852758.719 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.719 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.719 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.719 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.719 * [misc]backup-simplify: Simplify -2 into -2 1546852758.719 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.719 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.719 * [misc]backup-simplify: Simplify PI into PI 1546852758.719 * [misc]taylor: Taking taylor expansion of n in n 1546852758.719 * [misc]backup-simplify: Simplify 0 into 0 1546852758.719 * [misc]backup-simplify: Simplify 1 into 1 1546852758.719 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.720 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.720 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.720 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.720 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.720 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.720 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.720 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.720 * [misc]taylor: Taking taylor expansion of k in n 1546852758.720 * [misc]backup-simplify: Simplify k into k 1546852758.720 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.720 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.720 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.721 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.721 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.721 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.721 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852758.721 * [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)))) 1546852758.722 * [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))))) 1546852758.722 * [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))))) 1546852758.722 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546852758.723 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852758.723 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546852758.723 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.724 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.724 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.724 * [misc]backup-simplify: Simplify -2 into -2 1546852758.724 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.724 * [misc]backup-simplify: Simplify PI into PI 1546852758.724 * [misc]taylor: Taking taylor expansion of n in n 1546852758.724 * [misc]backup-simplify: Simplify 0 into 0 1546852758.724 * [misc]backup-simplify: Simplify 1 into 1 1546852758.724 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.724 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.724 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.724 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.724 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.724 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.725 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.725 * [misc]taylor: Taking taylor expansion of k in n 1546852758.725 * [misc]backup-simplify: Simplify k into k 1546852758.725 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.725 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.725 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.725 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.725 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.725 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.725 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852758.726 * [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)))) 1546852758.726 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852758.727 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852758.727 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546852758.728 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546852758.728 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.728 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852758.728 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852758.728 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.729 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852758.729 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852758.731 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852758.731 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546852758.732 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852758.734 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546852758.734 * [misc]backup-simplify: Simplify 0 into 0 1546852758.734 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.735 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852758.735 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546852758.735 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546852758.735 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546852758.735 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.735 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.735 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852758.735 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852758.735 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.735 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.735 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.735 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.735 * [misc]backup-simplify: Simplify -2 into -2 1546852758.735 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.735 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.735 * [misc]backup-simplify: Simplify PI into PI 1546852758.735 * [misc]taylor: Taking taylor expansion of n in n 1546852758.735 * [misc]backup-simplify: Simplify 0 into 0 1546852758.735 * [misc]backup-simplify: Simplify 1 into 1 1546852758.736 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.736 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.736 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.736 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.736 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.736 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.736 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.736 * [misc]taylor: Taking taylor expansion of k in n 1546852758.736 * [misc]backup-simplify: Simplify k into k 1546852758.736 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.736 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.737 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.737 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.737 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.737 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852758.738 * [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)))) 1546852758.738 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852758.738 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852758.739 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546852758.739 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546852758.742 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546852758.743 * * * * [misc]progress: [ 4 / 4 ] generating series at (2) 1546852758.743 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1546852758.743 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 1546852758.743 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546852758.743 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546852758.743 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.743 * [misc]taylor: Taking taylor expansion of k in n 1546852758.743 * [misc]backup-simplify: Simplify k into k 1546852758.743 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.743 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546852758.743 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852758.743 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546852758.743 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852758.743 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852758.744 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852758.744 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852758.744 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.744 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.744 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852758.744 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.744 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.744 * [misc]taylor: Taking taylor expansion of k in n 1546852758.744 * [misc]backup-simplify: Simplify k into k 1546852758.744 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852758.744 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.744 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.744 * [misc]backup-simplify: Simplify 2 into 2 1546852758.744 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.744 * [misc]taylor: Taking taylor expansion of n in n 1546852758.744 * [misc]backup-simplify: Simplify 0 into 0 1546852758.744 * [misc]backup-simplify: Simplify 1 into 1 1546852758.744 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.744 * [misc]backup-simplify: Simplify PI into PI 1546852758.744 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.745 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.745 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.746 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.747 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.747 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852758.747 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852758.747 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852758.747 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.748 * [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)))) 1546852758.749 * [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))))) 1546852758.749 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546852758.749 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546852758.749 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.749 * [misc]taylor: Taking taylor expansion of k in k 1546852758.749 * [misc]backup-simplify: Simplify 0 into 0 1546852758.749 * [misc]backup-simplify: Simplify 1 into 1 1546852758.749 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.749 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.750 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852758.750 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852758.750 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852758.750 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852758.750 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852758.750 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.750 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.750 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852758.750 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.750 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.750 * [misc]taylor: Taking taylor expansion of k in k 1546852758.750 * [misc]backup-simplify: Simplify 0 into 0 1546852758.750 * [misc]backup-simplify: Simplify 1 into 1 1546852758.750 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852758.750 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852758.750 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.750 * [misc]backup-simplify: Simplify 2 into 2 1546852758.750 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852758.750 * [misc]taylor: Taking taylor expansion of n in k 1546852758.750 * [misc]backup-simplify: Simplify n into n 1546852758.750 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.750 * [misc]backup-simplify: Simplify PI into PI 1546852758.750 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852758.750 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852758.751 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852758.751 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852758.751 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.751 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.751 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852758.751 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852758.751 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546852758.751 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546852758.751 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.751 * [misc]taylor: Taking taylor expansion of k in k 1546852758.751 * [misc]backup-simplify: Simplify 0 into 0 1546852758.751 * [misc]backup-simplify: Simplify 1 into 1 1546852758.752 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.752 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.752 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852758.752 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852758.752 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852758.752 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852758.752 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852758.752 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.752 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852758.752 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.752 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.752 * [misc]taylor: Taking taylor expansion of k in k 1546852758.753 * [misc]backup-simplify: Simplify 0 into 0 1546852758.753 * [misc]backup-simplify: Simplify 1 into 1 1546852758.753 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852758.753 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852758.753 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.753 * [misc]backup-simplify: Simplify 2 into 2 1546852758.753 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852758.753 * [misc]taylor: Taking taylor expansion of n in k 1546852758.753 * [misc]backup-simplify: Simplify n into n 1546852758.753 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.753 * [misc]backup-simplify: Simplify PI into PI 1546852758.753 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852758.753 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852758.753 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852758.753 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852758.753 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.753 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.754 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852758.754 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852758.754 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 1546852758.754 * [misc]taylor: Taking taylor expansion of 0 in n 1546852758.754 * [misc]backup-simplify: Simplify 0 into 0 1546852758.754 * [misc]backup-simplify: Simplify 0 into 0 1546852758.754 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546852758.755 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546852758.755 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546852758.756 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852758.756 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.756 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.756 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546852758.757 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546852758.757 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1546852758.757 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546852758.757 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546852758.757 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.757 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.757 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546852758.757 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546852758.757 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.757 * [misc]backup-simplify: Simplify 2 into 2 1546852758.757 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546852758.758 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546852758.758 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546852758.758 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.758 * [misc]taylor: Taking taylor expansion of n in n 1546852758.758 * [misc]backup-simplify: Simplify 0 into 0 1546852758.758 * [misc]backup-simplify: Simplify 1 into 1 1546852758.758 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.758 * [misc]backup-simplify: Simplify PI into PI 1546852758.758 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.759 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.759 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.759 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546852758.760 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546852758.760 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546852758.760 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.760 * [misc]backup-simplify: Simplify 0 into 0 1546852758.760 * [misc]backup-simplify: Simplify 0 into 0 1546852758.761 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546852758.761 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546852758.763 * [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 1546852758.763 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852758.763 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.763 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.764 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546852758.765 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546852758.765 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546852758.766 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852758.767 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 1546852758.767 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1546852758.767 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1546852758.767 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1546852758.767 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.767 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.767 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1546852758.767 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1546852758.767 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546852758.767 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.767 * [misc]backup-simplify: Simplify 2 into 2 1546852758.767 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546852758.768 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546852758.768 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852758.768 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.768 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.768 * [misc]backup-simplify: Simplify 2 into 2 1546852758.768 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.768 * [misc]taylor: Taking taylor expansion of n in n 1546852758.768 * [misc]backup-simplify: Simplify 0 into 0 1546852758.768 * [misc]backup-simplify: Simplify 1 into 1 1546852758.768 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.768 * [misc]backup-simplify: Simplify PI into PI 1546852758.768 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.768 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.769 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.770 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.770 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.770 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546852758.770 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.770 * [misc]taylor: Taking taylor expansion of n in n 1546852758.770 * [misc]backup-simplify: Simplify 0 into 0 1546852758.770 * [misc]backup-simplify: Simplify 1 into 1 1546852758.770 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.770 * [misc]backup-simplify: Simplify PI into PI 1546852758.771 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.771 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.771 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.772 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546852758.772 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546852758.772 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546852758.772 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.772 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.772 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546852758.772 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546852758.772 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.772 * [misc]backup-simplify: Simplify 2 into 2 1546852758.772 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546852758.772 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546852758.772 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546852758.772 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.772 * [misc]taylor: Taking taylor expansion of n in n 1546852758.773 * [misc]backup-simplify: Simplify 0 into 0 1546852758.773 * [misc]backup-simplify: Simplify 1 into 1 1546852758.773 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.773 * [misc]backup-simplify: Simplify PI into PI 1546852758.773 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.773 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.774 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.774 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546852758.775 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.776 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1546852758.776 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1546852758.776 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546852758.777 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546852758.777 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546852758.777 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.777 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.777 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.777 * [misc]backup-simplify: Simplify 0 into 0 1546852758.778 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546852758.780 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546852758.782 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546852758.783 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546852758.783 * [misc]backup-simplify: Simplify 0 into 0 1546852758.784 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852758.784 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 1546852758.787 * [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 1546852758.787 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1546852758.788 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.788 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.788 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 1546852758.790 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 1546852758.790 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.792 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852758.793 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 1546852758.793 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 1546852758.793 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 1546852758.793 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 1546852758.793 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.793 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.793 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 1546852758.793 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 1546852758.793 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546852758.793 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.793 * [misc]backup-simplify: Simplify 2 into 2 1546852758.794 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546852758.794 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546852758.794 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852758.794 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.794 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.794 * [misc]backup-simplify: Simplify 2 into 2 1546852758.794 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.794 * [misc]taylor: Taking taylor expansion of n in n 1546852758.794 * [misc]backup-simplify: Simplify 0 into 0 1546852758.794 * [misc]backup-simplify: Simplify 1 into 1 1546852758.794 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.794 * [misc]backup-simplify: Simplify PI into PI 1546852758.795 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.795 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.795 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.796 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.796 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.796 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546852758.796 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.796 * [misc]taylor: Taking taylor expansion of n in n 1546852758.796 * [misc]backup-simplify: Simplify 0 into 0 1546852758.796 * [misc]backup-simplify: Simplify 1 into 1 1546852758.796 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.796 * [misc]backup-simplify: Simplify PI into PI 1546852758.796 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.797 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.797 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.797 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546852758.797 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1546852758.797 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1546852758.797 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 1546852758.797 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.797 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.797 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 1546852758.797 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 1546852758.797 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546852758.797 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.797 * [misc]backup-simplify: Simplify 2 into 2 1546852758.797 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546852758.797 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546852758.798 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1546852758.798 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852758.798 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852758.798 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.798 * [misc]backup-simplify: Simplify 2 into 2 1546852758.798 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.798 * [misc]taylor: Taking taylor expansion of n in n 1546852758.798 * [misc]backup-simplify: Simplify 0 into 0 1546852758.798 * [misc]backup-simplify: Simplify 1 into 1 1546852758.798 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.798 * [misc]backup-simplify: Simplify PI into PI 1546852758.798 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.798 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852758.798 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.799 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852758.799 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.799 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.799 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546852758.799 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.799 * [misc]taylor: Taking taylor expansion of n in n 1546852758.799 * [misc]backup-simplify: Simplify 0 into 0 1546852758.800 * [misc]backup-simplify: Simplify 1 into 1 1546852758.800 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.800 * [misc]backup-simplify: Simplify PI into PI 1546852758.800 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.800 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.800 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.800 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546852758.800 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1546852758.800 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1546852758.801 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.801 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.801 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1546852758.801 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546852758.801 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.801 * [misc]backup-simplify: Simplify 2 into 2 1546852758.801 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546852758.801 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546852758.801 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1546852758.801 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852758.801 * [misc]taylor: Taking taylor expansion of n in n 1546852758.801 * [misc]backup-simplify: Simplify 0 into 0 1546852758.801 * [misc]backup-simplify: Simplify 1 into 1 1546852758.801 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.801 * [misc]backup-simplify: Simplify PI into PI 1546852758.801 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852758.802 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852758.802 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.802 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1546852758.802 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.803 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 1546852758.803 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 1546852758.803 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546852758.804 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.804 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.805 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 1546852758.805 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 1546852758.806 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 1546852758.806 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546852758.806 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1546852758.806 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1546852758.806 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.806 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.806 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.807 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.807 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.807 * [misc]backup-simplify: Simplify 0 into 0 1546852758.807 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852758.808 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852758.810 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852758.810 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852758.811 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546852758.811 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1546852758.813 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 1546852758.814 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546852758.815 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1546852758.815 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1546852758.817 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 1546852758.819 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546852758.821 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1546852758.822 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852758.823 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1546852758.824 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1546852758.825 * [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)))) 1546852758.828 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546852758.829 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546852758.829 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1546852758.833 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1546852758.834 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546852758.834 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 1546852758.834 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of k in n 1546852758.834 * [misc]backup-simplify: Simplify k into k 1546852758.834 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546852758.834 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546852758.834 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.834 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.834 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.834 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.834 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of k in n 1546852758.834 * [misc]backup-simplify: Simplify k into k 1546852758.834 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.834 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.834 * [misc]backup-simplify: Simplify 2 into 2 1546852758.834 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.834 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.834 * [misc]backup-simplify: Simplify PI into PI 1546852758.834 * [misc]taylor: Taking taylor expansion of n in n 1546852758.834 * [misc]backup-simplify: Simplify 0 into 0 1546852758.834 * [misc]backup-simplify: Simplify 1 into 1 1546852758.834 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.835 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.835 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.835 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.835 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.835 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.836 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.836 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1546852758.836 * [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)))) 1546852758.836 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546852758.836 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546852758.836 * [misc]taylor: Taking taylor expansion of k in k 1546852758.836 * [misc]backup-simplify: Simplify 0 into 0 1546852758.836 * [misc]backup-simplify: Simplify 1 into 1 1546852758.836 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.837 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852758.837 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.837 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.837 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.837 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.837 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of k in k 1546852758.837 * [misc]backup-simplify: Simplify 0 into 0 1546852758.837 * [misc]backup-simplify: Simplify 1 into 1 1546852758.837 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.837 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.837 * [misc]backup-simplify: Simplify 2 into 2 1546852758.837 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.837 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.837 * [misc]backup-simplify: Simplify PI into PI 1546852758.837 * [misc]taylor: Taking taylor expansion of n in k 1546852758.837 * [misc]backup-simplify: Simplify n into n 1546852758.837 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.837 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852758.837 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852758.838 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.838 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.838 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.838 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852758.839 * [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)))) 1546852758.839 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546852758.839 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546852758.839 * [misc]taylor: Taking taylor expansion of k in k 1546852758.839 * [misc]backup-simplify: Simplify 0 into 0 1546852758.839 * [misc]backup-simplify: Simplify 1 into 1 1546852758.839 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.839 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852758.839 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852758.839 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852758.839 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852758.839 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852758.839 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.839 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.839 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.839 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.839 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.839 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.839 * [misc]taylor: Taking taylor expansion of k in k 1546852758.839 * [misc]backup-simplify: Simplify 0 into 0 1546852758.839 * [misc]backup-simplify: Simplify 1 into 1 1546852758.839 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.839 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852758.840 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852758.840 * [misc]taylor: Taking taylor expansion of 2 in k 1546852758.840 * [misc]backup-simplify: Simplify 2 into 2 1546852758.840 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.840 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.840 * [misc]backup-simplify: Simplify PI into PI 1546852758.840 * [misc]taylor: Taking taylor expansion of n in k 1546852758.840 * [misc]backup-simplify: Simplify n into n 1546852758.840 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.840 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852758.840 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852758.840 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.840 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852758.840 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852758.840 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852758.840 * [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)))) 1546852758.841 * [misc]backup-simplify: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 1546852758.841 * [misc]taylor: Taking taylor expansion of 0 in n 1546852758.841 * [misc]backup-simplify: Simplify 0 into 0 1546852758.841 * [misc]backup-simplify: Simplify 0 into 0 1546852758.841 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546852758.841 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.841 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.841 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.841 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.841 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.841 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.841 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of k in n 1546852758.841 * [misc]backup-simplify: Simplify k into k 1546852758.841 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.841 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.841 * [misc]backup-simplify: Simplify 2 into 2 1546852758.841 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.841 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.841 * [misc]backup-simplify: Simplify PI into PI 1546852758.841 * [misc]taylor: Taking taylor expansion of n in n 1546852758.841 * [misc]backup-simplify: Simplify 0 into 0 1546852758.841 * [misc]backup-simplify: Simplify 1 into 1 1546852758.842 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.842 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.842 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.842 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.842 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.842 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.843 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.843 * [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))) 1546852758.844 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1546852758.844 * [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))))) 1546852758.845 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1546852758.845 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1546852758.845 * [misc]backup-simplify: Simplify 0 into 0 1546852758.846 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852758.846 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546852758.846 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.846 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.846 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.846 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.846 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.846 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.846 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of k in n 1546852758.846 * [misc]backup-simplify: Simplify k into k 1546852758.846 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.846 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.846 * [misc]backup-simplify: Simplify 2 into 2 1546852758.846 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.846 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.846 * [misc]backup-simplify: Simplify PI into PI 1546852758.846 * [misc]taylor: Taking taylor expansion of n in n 1546852758.846 * [misc]backup-simplify: Simplify 0 into 0 1546852758.846 * [misc]backup-simplify: Simplify 1 into 1 1546852758.847 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.847 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.847 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.847 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.847 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.847 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.848 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.849 * [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))) 1546852758.849 * [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)))) 1546852758.850 * [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))))) 1546852758.850 * [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)))))) 1546852758.851 * [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)))))) 1546852758.852 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852758.853 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852758.856 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852758.856 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852758.856 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852758.856 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.856 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.857 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.858 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852758.859 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852758.860 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1546852758.860 * [misc]backup-simplify: Simplify (- 0) into 0 1546852758.860 * [misc]backup-simplify: Simplify 0 into 0 1546852758.860 * [misc]backup-simplify: Simplify 0 into 0 1546852758.861 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852758.862 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1546852758.862 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852758.862 * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852758.862 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.862 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.862 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852758.862 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852758.862 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852758.862 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852758.862 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.862 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.862 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.862 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.862 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.862 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.863 * [misc]taylor: Taking taylor expansion of k in n 1546852758.863 * [misc]backup-simplify: Simplify k into k 1546852758.863 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.863 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852758.863 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852758.863 * [misc]taylor: Taking taylor expansion of 2 in n 1546852758.863 * [misc]backup-simplify: Simplify 2 into 2 1546852758.863 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.863 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.863 * [misc]backup-simplify: Simplify PI into PI 1546852758.863 * [misc]taylor: Taking taylor expansion of n in n 1546852758.863 * [misc]backup-simplify: Simplify 0 into 0 1546852758.863 * [misc]backup-simplify: Simplify 1 into 1 1546852758.863 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.863 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852758.864 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852758.864 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.864 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852758.864 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852758.865 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852758.866 * [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))) 1546852758.866 * [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)))) 1546852758.867 * [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))))) 1546852758.868 * [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)))))) 1546852758.868 * [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)))))) 1546852758.871 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1546852758.871 * [misc]backup-simplify: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1546852758.871 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 1546852758.871 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1546852758.871 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.871 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852758.871 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852758.871 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.871 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.871 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.872 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.872 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.872 * [misc]taylor: Taking taylor expansion of k in n 1546852758.872 * [misc]backup-simplify: Simplify k into k 1546852758.872 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.872 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.872 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.872 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.872 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.872 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.872 * [misc]backup-simplify: Simplify -2 into -2 1546852758.872 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.872 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.872 * [misc]backup-simplify: Simplify PI into PI 1546852758.872 * [misc]taylor: Taking taylor expansion of n in n 1546852758.872 * [misc]backup-simplify: Simplify 0 into 0 1546852758.872 * [misc]backup-simplify: Simplify 1 into 1 1546852758.872 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.873 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.873 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.873 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.873 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.874 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.875 * [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))) 1546852758.875 * [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)))) 1546852758.875 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546852758.875 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546852758.875 * [misc]taylor: Taking taylor expansion of -1 in n 1546852758.875 * [misc]backup-simplify: Simplify -1 into -1 1546852758.875 * [misc]taylor: Taking taylor expansion of k in n 1546852758.875 * [misc]backup-simplify: Simplify k into k 1546852758.876 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546852758.876 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546852758.876 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546852758.876 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546852758.877 * [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))) 1546852758.877 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.877 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.877 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of k in k 1546852758.877 * [misc]backup-simplify: Simplify 0 into 0 1546852758.877 * [misc]backup-simplify: Simplify 1 into 1 1546852758.877 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.877 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.877 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.877 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of -2 in k 1546852758.877 * [misc]backup-simplify: Simplify -2 into -2 1546852758.877 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.877 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.877 * [misc]backup-simplify: Simplify PI into PI 1546852758.877 * [misc]taylor: Taking taylor expansion of n in k 1546852758.877 * [misc]backup-simplify: Simplify n into n 1546852758.877 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.878 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852758.878 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852758.878 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.878 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.878 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852758.878 * [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))) 1546852758.878 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546852758.878 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546852758.878 * [misc]taylor: Taking taylor expansion of -1 in k 1546852758.878 * [misc]backup-simplify: Simplify -1 into -1 1546852758.878 * [misc]taylor: Taking taylor expansion of k in k 1546852758.878 * [misc]backup-simplify: Simplify 0 into 0 1546852758.879 * [misc]backup-simplify: Simplify 1 into 1 1546852758.879 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546852758.879 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.879 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546852758.879 * [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)))) 1546852758.880 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.880 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.880 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of k in k 1546852758.880 * [misc]backup-simplify: Simplify 0 into 0 1546852758.880 * [misc]backup-simplify: Simplify 1 into 1 1546852758.880 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852758.880 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852758.880 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.880 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of -2 in k 1546852758.880 * [misc]backup-simplify: Simplify -2 into -2 1546852758.880 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852758.880 * [misc]taylor: Taking taylor expansion of PI in k 1546852758.880 * [misc]backup-simplify: Simplify PI into PI 1546852758.880 * [misc]taylor: Taking taylor expansion of n in k 1546852758.880 * [misc]backup-simplify: Simplify n into n 1546852758.880 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852758.881 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852758.881 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852758.881 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852758.881 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852758.881 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852758.881 * [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))) 1546852758.881 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546852758.881 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546852758.881 * [misc]taylor: Taking taylor expansion of -1 in k 1546852758.881 * [misc]backup-simplify: Simplify -1 into -1 1546852758.881 * [misc]taylor: Taking taylor expansion of k in k 1546852758.881 * [misc]backup-simplify: Simplify 0 into 0 1546852758.881 * [misc]backup-simplify: Simplify 1 into 1 1546852758.882 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546852758.882 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852758.882 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546852758.882 * [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)))) 1546852758.883 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852758.883 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.883 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.883 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852758.883 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.883 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.883 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.883 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.883 * [misc]backup-simplify: Simplify -2 into -2 1546852758.883 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.883 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.883 * [misc]backup-simplify: Simplify PI into PI 1546852758.883 * [misc]taylor: Taking taylor expansion of n in n 1546852758.883 * [misc]backup-simplify: Simplify 0 into 0 1546852758.883 * [misc]backup-simplify: Simplify 1 into 1 1546852758.883 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.884 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.884 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.884 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.884 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.884 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.884 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.884 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.884 * [misc]taylor: Taking taylor expansion of k in n 1546852758.884 * [misc]backup-simplify: Simplify k into k 1546852758.884 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.884 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.884 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.885 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.885 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.885 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.886 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852758.886 * [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)))) 1546852758.887 * [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))))) 1546852758.888 * [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))))) 1546852758.888 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546852758.889 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852758.890 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1546852758.890 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546852758.890 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852758.890 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.890 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.890 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852758.890 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.890 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.890 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.890 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.890 * [misc]backup-simplify: Simplify -2 into -2 1546852758.890 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.890 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.890 * [misc]backup-simplify: Simplify PI into PI 1546852758.890 * [misc]taylor: Taking taylor expansion of n in n 1546852758.890 * [misc]backup-simplify: Simplify 0 into 0 1546852758.890 * [misc]backup-simplify: Simplify 1 into 1 1546852758.891 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.891 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.891 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.891 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.891 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.891 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.891 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.891 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.891 * [misc]taylor: Taking taylor expansion of k in n 1546852758.892 * [misc]backup-simplify: Simplify k into k 1546852758.892 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.892 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.892 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.893 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.893 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.893 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.894 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852758.894 * [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)))) 1546852758.895 * [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))))) 1546852758.896 * [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)))))) 1546852758.896 * [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)))))) 1546852758.897 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.897 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852758.898 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852758.898 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852758.899 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852758.899 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852758.901 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852758.901 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546852758.902 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852758.903 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 1546852758.903 * [misc]backup-simplify: Simplify 0 into 0 1546852758.903 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852758.904 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852758.904 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 1546852758.905 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852758.905 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852758.905 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of -2 in n 1546852758.905 * [misc]backup-simplify: Simplify -2 into -2 1546852758.905 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of PI in n 1546852758.905 * [misc]backup-simplify: Simplify PI into PI 1546852758.905 * [misc]taylor: Taking taylor expansion of n in n 1546852758.905 * [misc]backup-simplify: Simplify 0 into 0 1546852758.905 * [misc]backup-simplify: Simplify 1 into 1 1546852758.905 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852758.905 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852758.905 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852758.905 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852758.905 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.905 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.905 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852758.906 * [misc]taylor: Taking taylor expansion of k in n 1546852758.906 * [misc]backup-simplify: Simplify k into k 1546852758.906 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852758.906 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852758.906 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852758.906 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852758.906 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852758.906 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852758.906 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852758.907 * [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)))) 1546852758.907 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852758.908 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1546852758.908 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1546852758.910 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1546852758.910 * * * [misc]progress: simplifying candidates 1546852758.910 * * * * [misc]progress: [ 1 / 120 ] simplifiying candidate # 1546852758.910 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546852758.910 * * [misc]simplify: iters left: 6 (11 enodes) 1546852758.912 * * [misc]simplify: iters left: 5 (21 enodes) 1546852758.916 * * [misc]simplify: iters left: 4 (47 enodes) 1546852758.924 * * [misc]simplify: iters left: 3 (109 enodes) 1546852758.972 * * [misc]simplify: iters left: 2 (300 enodes) 1546852759.161 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546852759.161 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))))))) 1546852759.161 * * * * [misc]progress: [ 2 / 120 ] simplifiying candidate # 1546852759.161 * * * * [misc]progress: [ 3 / 120 ] simplifiying candidate # 1546852759.162 * [enter]simplify: Simplifying (* PI (* n 2)) 1546852759.162 * * [misc]simplify: iters left: 4 (5 enodes) 1546852759.163 * * [misc]simplify: iters left: 3 (9 enodes) 1546852759.164 * * [misc]simplify: iters left: 2 (15 enodes) 1546852759.166 * * [misc]simplify: iters left: 1 (17 enodes) 1546852759.168 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546852759.168 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2))))))) 1546852759.168 * * * * [misc]progress: [ 4 / 120 ] simplifiying candidate # 1546852759.168 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852759.168 * * [misc]simplify: iters left: 5 (8 enodes) 1546852759.170 * * [misc]simplify: iters left: 4 (12 enodes) 1546852759.171 * * [misc]simplify: iters left: 3 (18 enodes) 1546852759.174 * * [misc]simplify: iters left: 2 (20 enodes) 1546852759.176 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852759.176 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2)))))) 1546852759.177 * * * * [misc]progress: [ 5 / 120 ] simplifiying candidate # 1546852759.177 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546852759.177 * * [misc]simplify: iters left: 5 (6 enodes) 1546852759.178 * * [misc]simplify: iters left: 4 (8 enodes) 1546852759.179 * * [misc]simplify: iters left: 3 (11 enodes) 1546852759.180 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546852759.180 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))))) 1546852759.180 * * * * [misc]progress: [ 6 / 120 ] simplifiying candidate # 1546852759.181 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546852759.181 * * [misc]simplify: iters left: 5 (6 enodes) 1546852759.182 * * [misc]simplify: iters left: 4 (8 enodes) 1546852759.183 * * [misc]simplify: iters left: 3 (11 enodes) 1546852759.184 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546852759.184 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))))) 1546852759.184 * * * * [misc]progress: [ 7 / 120 ] simplifiying candidate # 1546852759.184 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546852759.184 * * [misc]simplify: iters left: 4 (5 enodes) 1546852759.185 * * [misc]simplify: iters left: 3 (7 enodes) 1546852759.186 * * [misc]simplify: iters left: 2 (10 enodes) 1546852759.188 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546852759.188 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2)))))) 1546852759.188 * * * * [misc]progress: [ 8 / 120 ] simplifiying candidate # 1546852759.188 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852759.188 * * [misc]simplify: iters left: 5 (9 enodes) 1546852759.189 * * [misc]simplify: iters left: 4 (15 enodes) 1546852759.192 * * [misc]simplify: iters left: 3 (21 enodes) 1546852759.194 * * [misc]simplify: iters left: 2 (22 enodes) 1546852759.197 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852759.197 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546852759.197 * * * * [misc]progress: [ 9 / 120 ] simplifiying candidate # 1546852759.197 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852759.197 * * [misc]simplify: iters left: 5 (9 enodes) 1546852759.199 * * [misc]simplify: iters left: 4 (15 enodes) 1546852759.201 * * [misc]simplify: iters left: 3 (21 enodes) 1546852759.204 * * [misc]simplify: iters left: 2 (22 enodes) 1546852759.207 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852759.207 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546852759.207 * * * * [misc]progress: [ 10 / 120 ] simplifiying candidate # 1546852759.207 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546852759.207 * * [misc]simplify: iters left: 5 (7 enodes) 1546852759.209 * * [misc]simplify: iters left: 4 (9 enodes) 1546852759.214 * * [misc]simplify: iters left: 3 (12 enodes) 1546852759.218 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546852759.218 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546852759.218 * * * * [misc]progress: [ 11 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 12 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 13 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 14 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 15 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 16 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 17 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 18 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 19 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 20 / 120 ] simplifiying candidate # 1546852759.218 * * * * [misc]progress: [ 21 / 120 ] simplifiying candidate # 1546852759.219 * * * * [misc]progress: [ 22 / 120 ] simplifiying candidate # 1546852759.219 * * * * [misc]progress: [ 23 / 120 ] simplifiying candidate # 1546852759.219 * * * * [misc]progress: [ 24 / 120 ] simplifiying candidate # 1546852759.219 * * * * [misc]progress: [ 25 / 120 ] simplifiying candidate # 1546852759.219 * * * * [misc]progress: [ 26 / 120 ] simplifiying candidate # 1546852759.219 * * * * [misc]progress: [ 27 / 120 ] simplifiying candidate # 1546852759.219 * * * * [misc]progress: [ 28 / 120 ] simplifiying candidate # 1546852759.219 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1546852759.219 * * [misc]simplify: iters left: 6 (14 enodes) 1546852759.224 * * [misc]simplify: iters left: 5 (26 enodes) 1546852759.232 * * [misc]simplify: iters left: 4 (59 enodes) 1546852759.254 * * [misc]simplify: iters left: 3 (164 enodes) 1546852759.310 * * [misc]simplify: iters left: 2 (488 enodes) 1546852759.590 * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n)))) 1546852759.590 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n))))))) 1546852759.590 * * * * [misc]progress: [ 29 / 120 ] simplifiying candidate # 1546852759.590 * [enter]simplify: Simplifying (- (log (sqrt k)) (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) 1546852759.590 * * [misc]simplify: iters left: 6 (14 enodes) 1546852759.595 * * [misc]simplify: iters left: 5 (26 enodes) 1546852759.604 * * [misc]simplify: iters left: 4 (59 enodes) 1546852759.628 * * [misc]simplify: iters left: 3 (164 enodes) 1546852759.676 * * [misc]simplify: iters left: 2 (488 enodes) 1546852759.982 * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n)))) 1546852759.982 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (+ -1/2 (/ k 2)) (log (* (* PI 2) n))))))) 1546852759.982 * * * * [misc]progress: [ 30 / 120 ] simplifiying candidate # 1546852759.982 * [enter]simplify: Simplifying (- (log (sqrt k)) (log (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852759.982 * * [misc]simplify: iters left: 6 (14 enodes) 1546852759.987 * * [misc]simplify: iters left: 5 (24 enodes) 1546852759.995 * * [misc]simplify: iters left: 4 (46 enodes) 1546852760.010 * * [misc]simplify: iters left: 3 (103 enodes) 1546852760.033 * * [misc]simplify: iters left: 2 (336 enodes) 1546852760.236 * [exit]simplify: Simplified to (+ (* (log (* n (* PI 2))) (+ (/ k 2) -1/2)) (log (sqrt k))) 1546852760.236 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (* (log (* n (* PI 2))) (+ (/ k 2) -1/2)) (log (sqrt k)))))) 1546852760.236 * * * * [misc]progress: [ 31 / 120 ] simplifiying candidate # 1546852760.236 * * * * [misc]progress: [ 32 / 120 ] simplifiying candidate # 1546852760.236 * * * * [misc]progress: [ 33 / 120 ] simplifiying candidate # 1546852760.237 * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852760.237 * * [misc]simplify: iters left: 6 (16 enodes) 1546852760.243 * * [misc]simplify: iters left: 5 (31 enodes) 1546852760.252 * * [misc]simplify: iters left: 4 (70 enodes) 1546852760.277 * * [misc]simplify: iters left: 3 (130 enodes) 1546852760.308 * * [misc]simplify: iters left: 2 (206 enodes) 1546852760.360 * * [misc]simplify: iters left: 1 (288 enodes) 1546852760.457 * [exit]simplify: Simplified to (/ (/ (* k (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) 1546852760.458 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* k (sqrt k)) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))))) 1546852760.458 * * * * [misc]progress: [ 34 / 120 ] simplifiying candidate # 1546852760.458 * * * * [misc]progress: [ 35 / 120 ] simplifiying candidate # 1546852760.458 * * * * [misc]progress: [ 36 / 120 ] simplifiying candidate # 1546852760.458 * * * * [misc]progress: [ 37 / 120 ] simplifiying candidate # 1546852760.458 * * * * [misc]progress: [ 38 / 120 ] simplifiying candidate # 1546852760.458 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1546852760.458 * * [misc]simplify: iters left: 6 (12 enodes) 1546852760.460 * * [misc]simplify: iters left: 5 (19 enodes) 1546852760.463 * * [misc]simplify: iters left: 4 (27 enodes) 1546852760.466 * * [misc]simplify: iters left: 3 (29 enodes) 1546852760.470 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1546852760.470 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546852760.470 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852760.471 * * [misc]simplify: iters left: 6 (12 enodes) 1546852760.472 * * [misc]simplify: iters left: 5 (18 enodes) 1546852760.475 * * [misc]simplify: iters left: 4 (24 enodes) 1546852760.478 * * [misc]simplify: iters left: 3 (25 enodes) 1546852760.481 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546852760.481 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546852760.482 * * * * [misc]progress: [ 39 / 120 ] simplifiying candidate # 1546852760.482 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2)) 1546852760.482 * * [misc]simplify: iters left: 6 (12 enodes) 1546852760.484 * * [misc]simplify: iters left: 5 (19 enodes) 1546852760.490 * * [misc]simplify: iters left: 4 (27 enodes) 1546852760.497 * * [misc]simplify: iters left: 3 (29 enodes) 1546852760.504 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) 1546852760.504 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546852760.505 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852760.505 * * [misc]simplify: iters left: 6 (12 enodes) 1546852760.509 * * [misc]simplify: iters left: 5 (18 enodes) 1546852760.514 * * [misc]simplify: iters left: 4 (24 enodes) 1546852760.520 * * [misc]simplify: iters left: 3 (25 enodes) 1546852760.526 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546852760.527 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* (* n 2) PI))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546852760.527 * * * * [misc]progress: [ 40 / 120 ] simplifiying candidate # 1546852760.527 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) 1546852760.527 * * [misc]simplify: iters left: 6 (11 enodes) 1546852760.530 * * [misc]simplify: iters left: 5 (15 enodes) 1546852760.535 * * [misc]simplify: iters left: 4 (20 enodes) 1546852760.540 * * [misc]simplify: iters left: 3 (21 enodes) 1546852760.546 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) 1546852760.546 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546852760.546 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852760.546 * * [misc]simplify: iters left: 6 (11 enodes) 1546852760.548 * * [misc]simplify: iters left: 5 (14 enodes) 1546852760.550 * * [misc]simplify: iters left: 4 (17 enodes) 1546852760.553 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852760.553 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2)))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546852760.553 * * * * [misc]progress: [ 41 / 120 ] simplifiying candidate # 1546852760.553 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546852760.554 * * [misc]simplify: iters left: 6 (16 enodes) 1546852760.557 * * [misc]simplify: iters left: 5 (28 enodes) 1546852760.561 * * [misc]simplify: iters left: 4 (46 enodes) 1546852760.568 * * [misc]simplify: iters left: 3 (50 enodes) 1546852760.574 * * [misc]simplify: iters left: 2 (53 enodes) 1546852760.583 * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546852760.583 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546852760.583 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852760.583 * * [misc]simplify: iters left: 6 (14 enodes) 1546852760.588 * * [misc]simplify: iters left: 5 (20 enodes) 1546852760.594 * * [misc]simplify: iters left: 4 (29 enodes) 1546852760.601 * * [misc]simplify: iters left: 3 (30 enodes) 1546852760.610 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852760.610 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546852760.610 * * * * [misc]progress: [ 42 / 120 ] simplifiying candidate # 1546852760.610 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852760.610 * * [misc]simplify: iters left: 6 (15 enodes) 1546852760.615 * * [misc]simplify: iters left: 5 (23 enodes) 1546852760.622 * * [misc]simplify: iters left: 4 (34 enodes) 1546852760.631 * * [misc]simplify: iters left: 3 (36 enodes) 1546852760.640 * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852760.640 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546852760.640 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852760.641 * * [misc]simplify: iters left: 6 (14 enodes) 1546852760.645 * * [misc]simplify: iters left: 5 (20 enodes) 1546852760.651 * * [misc]simplify: iters left: 4 (29 enodes) 1546852760.659 * * [misc]simplify: iters left: 3 (30 enodes) 1546852760.666 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852760.666 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546852760.666 * * * * [misc]progress: [ 43 / 120 ] simplifiying candidate # 1546852760.667 * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) 1546852760.667 * * [misc]simplify: iters left: 6 (6 enodes) 1546852760.669 * * [misc]simplify: iters left: 5 (10 enodes) 1546852760.672 * * [misc]simplify: iters left: 4 (16 enodes) 1546852760.676 * * [misc]simplify: iters left: 3 (18 enodes) 1546852760.680 * * [misc]simplify: iters left: 2 (23 enodes) 1546852760.685 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546852760.685 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546852760.686 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852760.686 * * [misc]simplify: iters left: 6 (13 enodes) 1546852760.691 * * [misc]simplify: iters left: 5 (19 enodes) 1546852760.697 * * [misc]simplify: iters left: 4 (28 enodes) 1546852760.705 * * [misc]simplify: iters left: 3 (30 enodes) 1546852760.713 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546852760.713 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546852760.713 * * * * [misc]progress: [ 44 / 120 ] simplifiying candidate # 1546852760.713 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1546852760.713 * * [misc]simplify: iters left: 6 (11 enodes) 1546852760.717 * * [misc]simplify: iters left: 5 (16 enodes) 1546852760.720 * * [misc]simplify: iters left: 4 (22 enodes) 1546852760.723 * * [misc]simplify: iters left: 3 (23 enodes) 1546852760.726 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1546852760.726 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546852760.727 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852760.727 * * [misc]simplify: iters left: 6 (12 enodes) 1546852760.729 * * [misc]simplify: iters left: 5 (18 enodes) 1546852760.731 * * [misc]simplify: iters left: 4 (24 enodes) 1546852760.735 * * [misc]simplify: iters left: 3 (25 enodes) 1546852760.738 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546852760.738 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546852760.738 * * * * [misc]progress: [ 45 / 120 ] simplifiying candidate # 1546852760.738 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2)) 1546852760.738 * * [misc]simplify: iters left: 6 (11 enodes) 1546852760.741 * * [misc]simplify: iters left: 5 (16 enodes) 1546852760.746 * * [misc]simplify: iters left: 4 (22 enodes) 1546852760.751 * * [misc]simplify: iters left: 3 (23 enodes) 1546852760.757 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) 1546852760.757 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546852760.757 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852760.757 * * [misc]simplify: iters left: 6 (12 enodes) 1546852760.761 * * [misc]simplify: iters left: 5 (18 enodes) 1546852760.766 * * [misc]simplify: iters left: 4 (24 enodes) 1546852760.772 * * [misc]simplify: iters left: 3 (25 enodes) 1546852760.779 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546852760.779 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (* (* PI n) 2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546852760.779 * * * * [misc]progress: [ 46 / 120 ] simplifiying candidate # 1546852760.779 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) 1546852760.779 * * [misc]simplify: iters left: 6 (10 enodes) 1546852760.782 * * [misc]simplify: iters left: 5 (12 enodes) 1546852760.785 * * [misc]simplify: iters left: 4 (15 enodes) 1546852760.788 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) 1546852760.788 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546852760.788 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852760.789 * * [misc]simplify: iters left: 6 (11 enodes) 1546852760.790 * * [misc]simplify: iters left: 5 (14 enodes) 1546852760.792 * * [misc]simplify: iters left: 4 (17 enodes) 1546852760.795 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852760.795 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546852760.795 * * * * [misc]progress: [ 47 / 120 ] simplifiying candidate # 1546852760.795 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546852760.795 * * [misc]simplify: iters left: 6 (15 enodes) 1546852760.800 * * [misc]simplify: iters left: 5 (23 enodes) 1546852760.807 * * [misc]simplify: iters left: 4 (32 enodes) 1546852760.816 * * [misc]simplify: iters left: 3 (34 enodes) 1546852760.821 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546852760.821 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546852760.821 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852760.821 * * [misc]simplify: iters left: 6 (14 enodes) 1546852760.823 * * [misc]simplify: iters left: 5 (20 enodes) 1546852760.826 * * [misc]simplify: iters left: 4 (29 enodes) 1546852760.830 * * [misc]simplify: iters left: 3 (30 enodes) 1546852760.834 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852760.834 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546852760.834 * * * * [misc]progress: [ 48 / 120 ] simplifiying candidate # 1546852760.834 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852760.834 * * [misc]simplify: iters left: 6 (14 enodes) 1546852760.837 * * [misc]simplify: iters left: 5 (20 enodes) 1546852760.840 * * [misc]simplify: iters left: 4 (29 enodes) 1546852760.844 * * [misc]simplify: iters left: 3 (30 enodes) 1546852760.848 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852760.848 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546852760.848 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852760.848 * * [misc]simplify: iters left: 6 (14 enodes) 1546852760.850 * * [misc]simplify: iters left: 5 (20 enodes) 1546852760.855 * * [misc]simplify: iters left: 4 (29 enodes) 1546852760.863 * * [misc]simplify: iters left: 3 (30 enodes) 1546852760.870 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852760.870 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546852760.870 * * * * [misc]progress: [ 49 / 120 ] simplifiying candidate # 1546852760.870 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) 1) 1546852760.871 * * [misc]simplify: iters left: 4 (5 enodes) 1546852760.872 * * [misc]simplify: iters left: 3 (7 enodes) 1546852760.875 * * [misc]simplify: iters left: 2 (9 enodes) 1546852760.876 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546852760.876 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546852760.877 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852760.877 * * [misc]simplify: iters left: 6 (13 enodes) 1546852760.881 * * [misc]simplify: iters left: 5 (19 enodes) 1546852760.887 * * [misc]simplify: iters left: 4 (28 enodes) 1546852760.895 * * [misc]simplify: iters left: 3 (30 enodes) 1546852760.903 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546852760.903 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546852760.903 * * * * [misc]progress: [ 50 / 120 ] simplifiying candidate # 1546852760.903 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1546852760.904 * * [misc]simplify: iters left: 6 (9 enodes) 1546852760.907 * * [misc]simplify: iters left: 5 (16 enodes) 1546852760.911 * * [misc]simplify: iters left: 4 (22 enodes) 1546852760.916 * * [misc]simplify: iters left: 3 (23 enodes) 1546852760.919 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1546852760.919 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546852760.919 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852760.919 * * [misc]simplify: iters left: 6 (11 enodes) 1546852760.921 * * [misc]simplify: iters left: 5 (17 enodes) 1546852760.924 * * [misc]simplify: iters left: 4 (23 enodes) 1546852760.928 * * [misc]simplify: iters left: 3 (24 enodes) 1546852760.931 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546852760.931 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1546852760.931 * * * * [misc]progress: [ 51 / 120 ] simplifiying candidate # 1546852760.931 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) 1/2)) 1546852760.931 * * [misc]simplify: iters left: 6 (9 enodes) 1546852760.933 * * [misc]simplify: iters left: 5 (16 enodes) 1546852760.935 * * [misc]simplify: iters left: 4 (22 enodes) 1546852760.938 * * [misc]simplify: iters left: 3 (23 enodes) 1546852760.940 * [exit]simplify: Simplified to (/ 1 (sqrt (* n (* 2 PI)))) 1546852760.941 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))) 1546852760.941 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852760.941 * * [misc]simplify: iters left: 6 (11 enodes) 1546852760.942 * * [misc]simplify: iters left: 5 (17 enodes) 1546852760.945 * * [misc]simplify: iters left: 4 (23 enodes) 1546852760.950 * * [misc]simplify: iters left: 3 (24 enodes) 1546852760.956 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546852760.956 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (* n (* 2 PI)))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2))))))) 1546852760.956 * * * * [misc]progress: [ 52 / 120 ] simplifiying candidate # 1546852760.957 * [enter]simplify: Simplifying (/ 1 (pow PI (- 1/2 (/ k 2)))) 1546852760.957 * * [misc]simplify: iters left: 6 (9 enodes) 1546852760.959 * * [misc]simplify: iters left: 5 (13 enodes) 1546852760.963 * * [misc]simplify: iters left: 4 (16 enodes) 1546852760.967 * [exit]simplify: Simplified to (/ 1 (pow PI (- 1/2 (/ k 2)))) 1546852760.967 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546852760.968 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852760.968 * * [misc]simplify: iters left: 6 (10 enodes) 1546852760.971 * * [misc]simplify: iters left: 5 (13 enodes) 1546852760.975 * * [misc]simplify: iters left: 4 (16 enodes) 1546852760.979 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852760.979 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546852760.979 * * * * [misc]progress: [ 53 / 120 ] simplifiying candidate # 1546852760.980 * [enter]simplify: Simplifying (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546852760.980 * * [misc]simplify: iters left: 6 (14 enodes) 1546852760.984 * * [misc]simplify: iters left: 5 (24 enodes) 1546852760.991 * * [misc]simplify: iters left: 4 (33 enodes) 1546852761.000 * * [misc]simplify: iters left: 3 (34 enodes) 1546852761.008 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1546852761.008 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546852761.009 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.009 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.013 * * [misc]simplify: iters left: 5 (19 enodes) 1546852761.018 * * [misc]simplify: iters left: 4 (28 enodes) 1546852761.026 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.034 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546852761.034 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))))) 1546852761.034 * * * * [misc]progress: [ 54 / 120 ] simplifiying candidate # 1546852761.034 * [enter]simplify: Simplifying (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.034 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.038 * * [misc]simplify: iters left: 5 (21 enodes) 1546852761.044 * * [misc]simplify: iters left: 4 (30 enodes) 1546852761.052 * * [misc]simplify: iters left: 3 (31 enodes) 1546852761.060 * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1546852761.060 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546852761.060 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.061 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.065 * * [misc]simplify: iters left: 5 (19 enodes) 1546852761.071 * * [misc]simplify: iters left: 4 (28 enodes) 1546852761.079 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.086 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546852761.086 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))))) 1546852761.086 * * * * [misc]progress: [ 55 / 120 ] simplifiying candidate # 1546852761.087 * [enter]simplify: Simplifying (/ 1 1) 1546852761.087 * * [misc]simplify: iters left: 2 (2 enodes) 1546852761.088 * * [misc]simplify: iters left: 1 (4 enodes) 1546852761.088 * [exit]simplify: Simplified to 1 1546852761.088 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546852761.089 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.089 * * [misc]simplify: iters left: 6 (12 enodes) 1546852761.093 * * [misc]simplify: iters left: 5 (18 enodes) 1546852761.098 * * [misc]simplify: iters left: 4 (27 enodes) 1546852761.105 * * [misc]simplify: iters left: 3 (29 enodes) 1546852761.113 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.113 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1546852761.113 * * * * [misc]progress: [ 56 / 120 ] simplifiying candidate # 1546852761.113 * * * * [misc]progress: [ 57 / 120 ] simplifiying candidate # 1546852761.113 * * * * [misc]progress: [ 58 / 120 ] simplifiying candidate # 1546852761.113 * * * * [misc]progress: [ 59 / 120 ] simplifiying candidate # 1546852761.113 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852761.113 * * [misc]simplify: iters left: 5 (9 enodes) 1546852761.116 * * [misc]simplify: iters left: 4 (15 enodes) 1546852761.121 * * [misc]simplify: iters left: 3 (21 enodes) 1546852761.126 * * [misc]simplify: iters left: 2 (22 enodes) 1546852761.132 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852761.132 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546852761.132 * * * * [misc]progress: [ 60 / 120 ] simplifiying candidate # 1546852761.132 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852761.132 * * [misc]simplify: iters left: 5 (9 enodes) 1546852761.135 * * [misc]simplify: iters left: 4 (15 enodes) 1546852761.139 * * [misc]simplify: iters left: 3 (21 enodes) 1546852761.145 * * [misc]simplify: iters left: 2 (22 enodes) 1546852761.150 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852761.150 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546852761.150 * * * * [misc]progress: [ 61 / 120 ] simplifiying candidate # 1546852761.151 * [enter]simplify: Simplifying (pow (* n 2) (- 1/2 (/ k 2))) 1546852761.151 * * [misc]simplify: iters left: 5 (8 enodes) 1546852761.154 * * [misc]simplify: iters left: 4 (11 enodes) 1546852761.157 * * [misc]simplify: iters left: 3 (14 enodes) 1546852761.161 * [exit]simplify: Simplified to (pow (* n 2) (- 1/2 (/ k 2))) 1546852761.161 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546852761.161 * * * * [misc]progress: [ 62 / 120 ] simplifiying candidate # 1546852761.161 * [enter]simplify: Simplifying (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.162 * * [misc]simplify: iters left: 6 (11 enodes) 1546852761.165 * * [misc]simplify: iters left: 5 (17 enodes) 1546852761.170 * * [misc]simplify: iters left: 4 (26 enodes) 1546852761.177 * * [misc]simplify: iters left: 3 (27 enodes) 1546852761.181 * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546852761.181 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852761.181 * * * * [misc]progress: [ 63 / 120 ] simplifiying candidate # 1546852761.182 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.182 * * [misc]simplify: iters left: 6 (11 enodes) 1546852761.184 * * [misc]simplify: iters left: 5 (17 enodes) 1546852761.186 * * [misc]simplify: iters left: 4 (26 enodes) 1546852761.190 * * [misc]simplify: iters left: 3 (27 enodes) 1546852761.193 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546852761.193 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852761.193 * * * * [misc]progress: [ 64 / 120 ] simplifiying candidate # 1546852761.193 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546852761.193 * * [misc]simplify: iters left: 5 (10 enodes) 1546852761.195 * * [misc]simplify: iters left: 4 (16 enodes) 1546852761.197 * * [misc]simplify: iters left: 3 (25 enodes) 1546852761.201 * * [misc]simplify: iters left: 2 (26 enodes) 1546852761.205 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546852761.205 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546852761.205 * * * * [misc]progress: [ 65 / 120 ] simplifiying candidate # 1546852761.205 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546852761.205 * * [misc]simplify: iters left: 4 (4 enodes) 1546852761.206 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546852761.206 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1546852761.206 * * * * [misc]progress: [ 66 / 120 ] simplifiying candidate # 1546852761.206 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546852761.206 * * [misc]simplify: iters left: 2 (3 enodes) 1546852761.206 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546852761.206 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1546852761.207 * * * * [misc]progress: [ 67 / 120 ] simplifiying candidate # 1546852761.207 * * * * [misc]progress: [ 68 / 120 ] simplifiying candidate # 1546852761.207 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852761.207 * * [misc]simplify: iters left: 5 (8 enodes) 1546852761.208 * * [misc]simplify: iters left: 4 (12 enodes) 1546852761.210 * * [misc]simplify: iters left: 3 (18 enodes) 1546852761.213 * * [misc]simplify: iters left: 2 (20 enodes) 1546852761.215 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852761.215 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* PI (* n 2)) 1/2)) (pow (* (* 2 n) PI) (/ k 2))))) 1546852761.215 * * * * [misc]progress: [ 69 / 120 ] simplifiying candidate # 1546852761.215 * * * * [misc]progress: [ 70 / 120 ] simplifiying candidate # 1546852761.216 * [enter]simplify: Simplifying (- 1) 1546852761.216 * * [misc]simplify: iters left: 2 (2 enodes) 1546852761.217 * * [misc]simplify: iters left: 1 (5 enodes) 1546852761.217 * [exit]simplify: Simplified to -1 1546852761.217 * [misc]simplify: Simplified (2 2) to (λ (k n) (pow (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) -1)) 1546852761.217 * * * * [misc]progress: [ 71 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 72 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 73 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 74 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 75 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 76 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 77 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 78 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 79 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 80 / 120 ] simplifiying candidate # 1546852761.217 * * * * [misc]progress: [ 81 / 120 ] simplifiying candidate # 1546852761.218 * * * * [misc]progress: [ 82 / 120 ] simplifiying candidate # 1546852761.218 * * * * [misc]progress: [ 83 / 120 ] simplifiying candidate # 1546852761.218 * * * * [misc]progress: [ 84 / 120 ] simplifiying candidate # 1546852761.218 * * * * [misc]progress: [ 85 / 120 ] simplifiying candidate # 1546852761.218 * [enter]simplify: Simplifying (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.218 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.220 * * [misc]simplify: iters left: 5 (19 enodes) 1546852761.223 * * [misc]simplify: iters left: 4 (28 enodes) 1546852761.230 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.238 * [exit]simplify: Simplified to (cbrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546852761.238 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (cbrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546852761.238 * * * * [misc]progress: [ 86 / 120 ] simplifiying candidate # 1546852761.238 * [enter]simplify: Simplifying (sqrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.238 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.242 * * [misc]simplify: iters left: 5 (19 enodes) 1546852761.248 * * [misc]simplify: iters left: 4 (28 enodes) 1546852761.256 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.264 * [exit]simplify: Simplified to (sqrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546852761.264 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (/ (sqrt k) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546852761.264 * * * * [misc]progress: [ 87 / 120 ] simplifiying candidate # 1546852761.265 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852761.265 * * [misc]simplify: iters left: 6 (12 enodes) 1546852761.269 * * [misc]simplify: iters left: 5 (18 enodes) 1546852761.274 * * [misc]simplify: iters left: 4 (24 enodes) 1546852761.281 * * [misc]simplify: iters left: 3 (25 enodes) 1546852761.287 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546852761.287 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546852761.287 * * * * [misc]progress: [ 88 / 120 ] simplifiying candidate # 1546852761.288 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852761.288 * * [misc]simplify: iters left: 6 (12 enodes) 1546852761.291 * * [misc]simplify: iters left: 5 (18 enodes) 1546852761.297 * * [misc]simplify: iters left: 4 (24 enodes) 1546852761.303 * * [misc]simplify: iters left: 3 (25 enodes) 1546852761.310 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546852761.310 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* PI (* n 2)) 1/2))) (/ (cbrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546852761.310 * * * * [misc]progress: [ 89 / 120 ] simplifiying candidate # 1546852761.310 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852761.310 * * [misc]simplify: iters left: 6 (11 enodes) 1546852761.314 * * [misc]simplify: iters left: 5 (14 enodes) 1546852761.318 * * [misc]simplify: iters left: 4 (17 enodes) 1546852761.323 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852761.323 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546852761.323 * * * * [misc]progress: [ 90 / 120 ] simplifiying candidate # 1546852761.323 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.323 * * [misc]simplify: iters left: 6 (14 enodes) 1546852761.328 * * [misc]simplify: iters left: 5 (20 enodes) 1546852761.335 * * [misc]simplify: iters left: 4 (29 enodes) 1546852761.342 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.349 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852761.349 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852761.349 * * * * [misc]progress: [ 91 / 120 ] simplifiying candidate # 1546852761.349 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.349 * * [misc]simplify: iters left: 6 (14 enodes) 1546852761.352 * * [misc]simplify: iters left: 5 (20 enodes) 1546852761.355 * * [misc]simplify: iters left: 4 (29 enodes) 1546852761.359 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.363 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852761.363 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852761.363 * * * * [misc]progress: [ 92 / 120 ] simplifiying candidate # 1546852761.363 * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.363 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.365 * * [misc]simplify: iters left: 5 (19 enodes) 1546852761.371 * * [misc]simplify: iters left: 4 (28 enodes) 1546852761.375 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.379 * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546852761.379 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))) 1546852761.379 * * * * [misc]progress: [ 93 / 120 ] simplifiying candidate # 1546852761.379 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852761.379 * * [misc]simplify: iters left: 6 (12 enodes) 1546852761.381 * * [misc]simplify: iters left: 5 (18 enodes) 1546852761.384 * * [misc]simplify: iters left: 4 (24 enodes) 1546852761.387 * * [misc]simplify: iters left: 3 (25 enodes) 1546852761.391 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546852761.391 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546852761.391 * * * * [misc]progress: [ 94 / 120 ] simplifiying candidate # 1546852761.391 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852761.391 * * [misc]simplify: iters left: 6 (12 enodes) 1546852761.393 * * [misc]simplify: iters left: 5 (18 enodes) 1546852761.396 * * [misc]simplify: iters left: 4 (24 enodes) 1546852761.399 * * [misc]simplify: iters left: 3 (25 enodes) 1546852761.402 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))) 1546852761.402 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) 1/2))) (/ (sqrt (sqrt k)) (pow (* (* PI n) 2) (- (/ k 2)))))) 1546852761.402 * * * * [misc]progress: [ 95 / 120 ] simplifiying candidate # 1546852761.403 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852761.403 * * [misc]simplify: iters left: 6 (11 enodes) 1546852761.405 * * [misc]simplify: iters left: 5 (14 enodes) 1546852761.407 * * [misc]simplify: iters left: 4 (17 enodes) 1546852761.411 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852761.411 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546852761.411 * * * * [misc]progress: [ 96 / 120 ] simplifiying candidate # 1546852761.411 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.411 * * [misc]simplify: iters left: 6 (14 enodes) 1546852761.416 * * [misc]simplify: iters left: 5 (20 enodes) 1546852761.419 * * [misc]simplify: iters left: 4 (29 enodes) 1546852761.423 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.427 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852761.427 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852761.427 * * * * [misc]progress: [ 97 / 120 ] simplifiying candidate # 1546852761.427 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.427 * * [misc]simplify: iters left: 6 (14 enodes) 1546852761.430 * * [misc]simplify: iters left: 5 (20 enodes) 1546852761.433 * * [misc]simplify: iters left: 4 (29 enodes) 1546852761.437 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.441 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1546852761.441 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852761.441 * * * * [misc]progress: [ 98 / 120 ] simplifiying candidate # 1546852761.441 * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.441 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.444 * * [misc]simplify: iters left: 5 (19 enodes) 1546852761.449 * * [misc]simplify: iters left: 4 (28 enodes) 1546852761.457 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.464 * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) 1546852761.464 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))) 1546852761.464 * * * * [misc]progress: [ 99 / 120 ] simplifiying candidate # 1546852761.465 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852761.465 * * [misc]simplify: iters left: 6 (11 enodes) 1546852761.468 * * [misc]simplify: iters left: 5 (17 enodes) 1546852761.473 * * [misc]simplify: iters left: 4 (23 enodes) 1546852761.477 * * [misc]simplify: iters left: 3 (24 enodes) 1546852761.481 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546852761.481 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1546852761.481 * * * * [misc]progress: [ 100 / 120 ] simplifiying candidate # 1546852761.481 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))) 1546852761.481 * * [misc]simplify: iters left: 6 (11 enodes) 1546852761.483 * * [misc]simplify: iters left: 5 (17 enodes) 1546852761.485 * * [misc]simplify: iters left: 4 (23 enodes) 1546852761.488 * * [misc]simplify: iters left: 3 (24 enodes) 1546852761.492 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))) 1546852761.492 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* PI (* n 2)) 1/2))) (/ (sqrt k) (pow (* 2 (* PI n)) (- (/ k 2)))))) 1546852761.492 * * * * [misc]progress: [ 101 / 120 ] simplifiying candidate # 1546852761.492 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852761.492 * * [misc]simplify: iters left: 6 (10 enodes) 1546852761.494 * * [misc]simplify: iters left: 5 (13 enodes) 1546852761.496 * * [misc]simplify: iters left: 4 (16 enodes) 1546852761.498 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))) 1546852761.498 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1546852761.498 * * * * [misc]progress: [ 102 / 120 ] simplifiying candidate # 1546852761.498 * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.499 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.501 * * [misc]simplify: iters left: 5 (19 enodes) 1546852761.504 * * [misc]simplify: iters left: 4 (28 enodes) 1546852761.508 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.512 * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546852761.512 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (/ (sqrt k) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546852761.512 * * * * [misc]progress: [ 103 / 120 ] simplifiying candidate # 1546852761.512 * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852761.512 * * [misc]simplify: iters left: 6 (13 enodes) 1546852761.514 * * [misc]simplify: iters left: 5 (19 enodes) 1546852761.517 * * [misc]simplify: iters left: 4 (28 enodes) 1546852761.521 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.526 * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))) 1546852761.526 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))))) 1546852761.526 * * * * [misc]progress: [ 104 / 120 ] simplifiying candidate # 1546852761.526 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.526 * * [misc]simplify: iters left: 6 (12 enodes) 1546852761.528 * * [misc]simplify: iters left: 5 (18 enodes) 1546852761.531 * * [misc]simplify: iters left: 4 (27 enodes) 1546852761.535 * * [misc]simplify: iters left: 3 (29 enodes) 1546852761.538 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.539 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546852761.539 * * * * [misc]progress: [ 105 / 120 ] simplifiying candidate # 1546852761.539 * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.539 * * [misc]simplify: iters left: 6 (12 enodes) 1546852761.541 * * [misc]simplify: iters left: 5 (18 enodes) 1546852761.544 * * [misc]simplify: iters left: 4 (27 enodes) 1546852761.551 * * [misc]simplify: iters left: 3 (29 enodes) 1546852761.558 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.558 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546852761.558 * * * * [misc]progress: [ 106 / 120 ] simplifiying candidate # 1546852761.559 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852761.559 * * [misc]simplify: iters left: 6 (12 enodes) 1546852761.563 * * [misc]simplify: iters left: 5 (20 enodes) 1546852761.568 * * [misc]simplify: iters left: 4 (29 enodes) 1546852761.576 * * [misc]simplify: iters left: 3 (30 enodes) 1546852761.584 * [exit]simplify: Simplified to (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1546852761.584 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))) 1546852761.584 * * * * [misc]progress: [ 107 / 120 ] simplifiying candidate # 1546852761.584 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852761.585 * * [misc]simplify: iters left: 5 (8 enodes) 1546852761.587 * * [misc]simplify: iters left: 4 (12 enodes) 1546852761.590 * * [misc]simplify: iters left: 3 (18 enodes) 1546852761.595 * * [misc]simplify: iters left: 2 (20 enodes) 1546852761.600 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852761.600 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) 1/2))) (pow (* (* 2 n) PI) (/ k 2)))) 1546852761.600 * * * * [misc]progress: [ 108 / 120 ] simplifiying candidate # 1546852761.601 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546852761.601 * * [misc]simplify: iters left: 5 (10 enodes) 1546852761.604 * * [misc]simplify: iters left: 4 (16 enodes) 1546852761.609 * * [misc]simplify: iters left: 3 (25 enodes) 1546852761.616 * * [misc]simplify: iters left: 2 (26 enodes) 1546852761.622 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546852761.622 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1546852761.622 * * * * [misc]progress: [ 109 / 120 ] simplifiying candidate # 1546852761.623 * [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))))) 1546852761.623 * * [misc]simplify: iters left: 6 (37 enodes) 1546852761.639 * * [misc]simplify: iters left: 5 (105 enodes) 1546852761.683 * * [misc]simplify: iters left: 4 (339 enodes) 1546852761.887 * [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))))) 1546852761.887 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)))))))) 1546852761.887 * * * * [misc]progress: [ 110 / 120 ] simplifiying candidate # 1546852761.887 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546852761.887 * * [misc]simplify: iters left: 6 (15 enodes) 1546852761.890 * * [misc]simplify: iters left: 5 (33 enodes) 1546852761.896 * * [misc]simplify: iters left: 4 (64 enodes) 1546852761.908 * * [misc]simplify: iters left: 3 (171 enodes) 1546852761.978 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546852761.978 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))))))) 1546852761.978 * * * * [misc]progress: [ 111 / 120 ] simplifiying candidate # 1546852761.978 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546852761.978 * * [misc]simplify: iters left: 6 (15 enodes) 1546852761.981 * * [misc]simplify: iters left: 5 (30 enodes) 1546852761.990 * * [misc]simplify: iters left: 4 (65 enodes) 1546852762.016 * * [misc]simplify: iters left: 3 (200 enodes) 1546852762.117 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546852762.117 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))))) 1546852762.117 * * * * [misc]progress: [ 112 / 120 ] simplifiying candidate # 1546852762.117 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852762.118 * * [misc]simplify: iters left: 4 (5 enodes) 1546852762.118 * * [misc]simplify: iters left: 3 (9 enodes) 1546852762.120 * * [misc]simplify: iters left: 2 (15 enodes) 1546852762.122 * * [misc]simplify: iters left: 1 (17 enodes) 1546852762.124 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852762.124 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546852762.124 * * * * [misc]progress: [ 113 / 120 ] simplifiying candidate # 1546852762.124 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852762.124 * * [misc]simplify: iters left: 4 (5 enodes) 1546852762.125 * * [misc]simplify: iters left: 3 (9 enodes) 1546852762.127 * * [misc]simplify: iters left: 2 (15 enodes) 1546852762.129 * * [misc]simplify: iters left: 1 (17 enodes) 1546852762.134 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852762.134 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546852762.134 * * * * [misc]progress: [ 114 / 120 ] simplifiying candidate # 1546852762.134 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852762.134 * * [misc]simplify: iters left: 4 (5 enodes) 1546852762.135 * * [misc]simplify: iters left: 3 (9 enodes) 1546852762.136 * * [misc]simplify: iters left: 2 (15 enodes) 1546852762.138 * * [misc]simplify: iters left: 1 (17 enodes) 1546852762.141 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852762.141 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1546852762.141 * * * * [misc]progress: [ 115 / 120 ] simplifiying candidate # 1546852762.141 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546852762.141 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546852762.141 * * * * [misc]progress: [ 116 / 120 ] simplifiying candidate # 1546852762.141 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546852762.141 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546852762.141 * * * * [misc]progress: [ 117 / 120 ] simplifiying candidate # 1546852762.141 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546852762.141 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546852762.141 * * * * [misc]progress: [ 118 / 120 ] simplifiying candidate # 1546852762.142 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 1546852762.142 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546852762.142 * * * * [misc]progress: [ 119 / 120 ] simplifiying candidate # 1546852762.142 * [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)))))))) 1546852762.142 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546852762.142 * * * * [misc]progress: [ 120 / 120 ] simplifiying candidate # 1546852762.142 * [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))))))))))) 1546852762.142 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1546852762.142 * * * [misc]progress: adding candidates to table 1546852763.866 * * [misc]progress: iteration 3 / 4 1546852763.866 * * * [misc]progress: picking best candidate 1546852763.902 * * * * [misc]pick: Picked # 1546852763.902 * * * [misc]progress: localizing error 1546852763.918 * * * [misc]progress: generating rewritten candidates 1546852763.919 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 2) 1546852763.922 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 2 1) 1546852763.924 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1546852763.934 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 2) 1546852763.937 * * * [misc]progress: generating series expansions 1546852763.937 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 2) 1546852763.937 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546852763.937 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546852763.938 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852763.938 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852763.938 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852763.938 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852763.938 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852763.938 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.938 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852763.938 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852763.938 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.938 * [misc]taylor: Taking taylor expansion of k in k 1546852763.938 * [misc]backup-simplify: Simplify 0 into 0 1546852763.938 * [misc]backup-simplify: Simplify 1 into 1 1546852763.938 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852763.938 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852763.938 * [misc]taylor: Taking taylor expansion of 2 in k 1546852763.938 * [misc]backup-simplify: Simplify 2 into 2 1546852763.938 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852763.938 * [misc]taylor: Taking taylor expansion of n in k 1546852763.938 * [misc]backup-simplify: Simplify n into n 1546852763.938 * [misc]taylor: Taking taylor expansion of PI in k 1546852763.938 * [misc]backup-simplify: Simplify PI into PI 1546852763.938 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852763.938 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852763.938 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852763.938 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852763.938 * [misc]backup-simplify: Simplify (- 0) into 0 1546852763.939 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852763.939 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852763.939 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852763.939 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852763.939 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852763.939 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852763.939 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852763.939 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852763.939 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.939 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852763.939 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852763.939 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.939 * [misc]taylor: Taking taylor expansion of k in n 1546852763.939 * [misc]backup-simplify: Simplify k into k 1546852763.939 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852763.939 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852763.939 * [misc]taylor: Taking taylor expansion of 2 in n 1546852763.939 * [misc]backup-simplify: Simplify 2 into 2 1546852763.939 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852763.939 * [misc]taylor: Taking taylor expansion of n in n 1546852763.939 * [misc]backup-simplify: Simplify 0 into 0 1546852763.939 * [misc]backup-simplify: Simplify 1 into 1 1546852763.939 * [misc]taylor: Taking taylor expansion of PI in n 1546852763.939 * [misc]backup-simplify: Simplify PI into PI 1546852763.939 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852763.939 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852763.940 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852763.940 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852763.941 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852763.941 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852763.941 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852763.941 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852763.941 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852763.942 * [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)))) 1546852763.942 * [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))))) 1546852763.942 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852763.942 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852763.942 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852763.942 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852763.942 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852763.942 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.942 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852763.942 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852763.942 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.942 * [misc]taylor: Taking taylor expansion of k in n 1546852763.942 * [misc]backup-simplify: Simplify k into k 1546852763.942 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852763.942 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852763.942 * [misc]taylor: Taking taylor expansion of 2 in n 1546852763.942 * [misc]backup-simplify: Simplify 2 into 2 1546852763.942 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852763.942 * [misc]taylor: Taking taylor expansion of n in n 1546852763.942 * [misc]backup-simplify: Simplify 0 into 0 1546852763.942 * [misc]backup-simplify: Simplify 1 into 1 1546852763.942 * [misc]taylor: Taking taylor expansion of PI in n 1546852763.942 * [misc]backup-simplify: Simplify PI into PI 1546852763.943 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852763.943 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852763.943 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852763.943 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852763.944 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852763.944 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852763.944 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852763.944 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852763.944 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852763.945 * [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)))) 1546852763.945 * [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))))) 1546852763.945 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546852763.945 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546852763.945 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852763.945 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852763.945 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.945 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852763.945 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852763.945 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.945 * [misc]taylor: Taking taylor expansion of k in k 1546852763.945 * [misc]backup-simplify: Simplify 0 into 0 1546852763.945 * [misc]backup-simplify: Simplify 1 into 1 1546852763.945 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546852763.945 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852763.945 * [misc]taylor: Taking taylor expansion of n in k 1546852763.945 * [misc]backup-simplify: Simplify n into n 1546852763.946 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852763.946 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852763.946 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852763.946 * [misc]taylor: Taking taylor expansion of 2 in k 1546852763.946 * [misc]backup-simplify: Simplify 2 into 2 1546852763.946 * [misc]taylor: Taking taylor expansion of PI in k 1546852763.946 * [misc]backup-simplify: Simplify PI into PI 1546852763.946 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852763.946 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852763.946 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852763.946 * [misc]backup-simplify: Simplify (- 0) into 0 1546852763.946 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852763.947 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852763.947 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546852763.947 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852763.948 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852763.948 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852763.949 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852763.951 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852763.951 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546852763.951 * [misc]backup-simplify: Simplify (- 0) into 0 1546852763.951 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852763.952 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852763.952 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546852763.953 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852763.953 * [misc]taylor: Taking taylor expansion of 0 in k 1546852763.953 * [misc]backup-simplify: Simplify 0 into 0 1546852763.953 * [misc]backup-simplify: Simplify 0 into 0 1546852763.954 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546852763.954 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852763.956 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852763.956 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852763.956 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852763.956 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852763.956 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852763.957 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546852763.957 * [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))))))) 1546852763.958 * [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))))))) 1546852763.959 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852763.960 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852763.963 * [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 1546852763.964 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546852763.964 * [misc]backup-simplify: Simplify (- 0) into 0 1546852763.964 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852763.964 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852763.965 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852763.966 * [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 1546852763.966 * [misc]taylor: Taking taylor expansion of 0 in k 1546852763.966 * [misc]backup-simplify: Simplify 0 into 0 1546852763.966 * [misc]backup-simplify: Simplify 0 into 0 1546852763.966 * [misc]backup-simplify: Simplify 0 into 0 1546852763.968 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546852763.969 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852763.974 * [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 1546852763.974 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852763.974 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852763.975 * [misc]backup-simplify: Simplify (- 0) into 0 1546852763.975 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852763.976 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852763.978 * [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))))) 1546852763.980 * [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))))) 1546852763.988 * [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))))) 1546852763.989 * [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)))) 1546852763.989 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546852763.989 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852763.989 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852763.989 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852763.989 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852763.989 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852763.989 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.989 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852763.989 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852763.989 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.989 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852763.989 * [misc]taylor: Taking taylor expansion of k in k 1546852763.989 * [misc]backup-simplify: Simplify 0 into 0 1546852763.989 * [misc]backup-simplify: Simplify 1 into 1 1546852763.989 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852763.989 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852763.990 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852763.990 * [misc]taylor: Taking taylor expansion of 2 in k 1546852763.990 * [misc]backup-simplify: Simplify 2 into 2 1546852763.990 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852763.990 * [misc]taylor: Taking taylor expansion of PI in k 1546852763.990 * [misc]backup-simplify: Simplify PI into PI 1546852763.990 * [misc]taylor: Taking taylor expansion of n in k 1546852763.990 * [misc]backup-simplify: Simplify n into n 1546852763.990 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852763.990 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852763.990 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852763.990 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852763.990 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852763.990 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852763.991 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852763.991 * [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)))) 1546852763.991 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852763.991 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.991 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852763.991 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.991 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of k in n 1546852763.991 * [misc]backup-simplify: Simplify k into k 1546852763.991 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852763.991 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of 2 in n 1546852763.991 * [misc]backup-simplify: Simplify 2 into 2 1546852763.991 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852763.991 * [misc]taylor: Taking taylor expansion of PI in n 1546852763.991 * [misc]backup-simplify: Simplify PI into PI 1546852763.991 * [misc]taylor: Taking taylor expansion of n in n 1546852763.991 * [misc]backup-simplify: Simplify 0 into 0 1546852763.991 * [misc]backup-simplify: Simplify 1 into 1 1546852763.992 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852763.992 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852763.993 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852763.993 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852763.993 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852763.993 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852763.994 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852763.994 * [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))) 1546852763.995 * [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)))) 1546852763.995 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852763.995 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.995 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852763.995 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.995 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of k in n 1546852763.995 * [misc]backup-simplify: Simplify k into k 1546852763.995 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852763.995 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of 2 in n 1546852763.995 * [misc]backup-simplify: Simplify 2 into 2 1546852763.995 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852763.995 * [misc]taylor: Taking taylor expansion of PI in n 1546852763.995 * [misc]backup-simplify: Simplify PI into PI 1546852763.995 * [misc]taylor: Taking taylor expansion of n in n 1546852763.996 * [misc]backup-simplify: Simplify 0 into 0 1546852763.996 * [misc]backup-simplify: Simplify 1 into 1 1546852763.996 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852763.996 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852763.997 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852763.997 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852763.997 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852763.997 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852763.997 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852763.998 * [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))) 1546852763.999 * [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)))) 1546852763.999 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546852763.999 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546852763.999 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852763.999 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852763.999 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.999 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852763.999 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852763.999 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852763.999 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852763.999 * [misc]taylor: Taking taylor expansion of k in k 1546852763.999 * [misc]backup-simplify: Simplify 0 into 0 1546852763.999 * [misc]backup-simplify: Simplify 1 into 1 1546852763.999 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852763.999 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546852763.999 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852763.999 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852764.000 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.000 * [misc]backup-simplify: Simplify 2 into 2 1546852764.000 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.000 * [misc]backup-simplify: Simplify PI into PI 1546852764.000 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.000 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.000 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852764.000 * [misc]taylor: Taking taylor expansion of n in k 1546852764.000 * [misc]backup-simplify: Simplify n into n 1546852764.000 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852764.001 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.001 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852764.001 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852764.001 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852764.002 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546852764.002 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546852764.003 * [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)))) 1546852764.003 * [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)))) 1546852764.004 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852764.005 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852764.008 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852764.008 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852764.008 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852764.008 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.009 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.009 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.010 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852764.011 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852764.011 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.012 * [misc]backup-simplify: Simplify 0 into 0 1546852764.012 * [misc]backup-simplify: Simplify 0 into 0 1546852764.012 * [misc]backup-simplify: Simplify 0 into 0 1546852764.013 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.014 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852764.019 * [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 1546852764.019 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852764.019 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852764.020 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.020 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.020 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.021 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546852764.022 * [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 1546852764.022 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.022 * [misc]backup-simplify: Simplify 0 into 0 1546852764.022 * [misc]backup-simplify: Simplify 0 into 0 1546852764.022 * [misc]backup-simplify: Simplify 0 into 0 1546852764.022 * [misc]backup-simplify: Simplify 0 into 0 1546852764.023 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.024 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852764.029 * [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 1546852764.029 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852764.029 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852764.029 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.030 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.030 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.031 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546852764.033 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1546852764.033 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.033 * [misc]backup-simplify: Simplify 0 into 0 1546852764.033 * [misc]backup-simplify: Simplify 0 into 0 1546852764.033 * [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))))) 1546852764.034 * [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)) 1546852764.034 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546852764.034 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.034 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.034 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of k in k 1546852764.034 * [misc]backup-simplify: Simplify 0 into 0 1546852764.034 * [misc]backup-simplify: Simplify 1 into 1 1546852764.034 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.034 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.034 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.034 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of -2 in k 1546852764.034 * [misc]backup-simplify: Simplify -2 into -2 1546852764.034 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852764.034 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.034 * [misc]backup-simplify: Simplify PI into PI 1546852764.034 * [misc]taylor: Taking taylor expansion of n in k 1546852764.034 * [misc]backup-simplify: Simplify n into n 1546852764.034 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852764.034 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852764.034 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852764.034 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.034 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.035 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852764.035 * [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))) 1546852764.035 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.035 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.035 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of k in n 1546852764.035 * [misc]backup-simplify: Simplify k into k 1546852764.035 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.035 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.035 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.035 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.035 * [misc]backup-simplify: Simplify -2 into -2 1546852764.035 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.035 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.035 * [misc]backup-simplify: Simplify PI into PI 1546852764.035 * [misc]taylor: Taking taylor expansion of n in n 1546852764.035 * [misc]backup-simplify: Simplify 0 into 0 1546852764.035 * [misc]backup-simplify: Simplify 1 into 1 1546852764.035 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.036 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.036 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.036 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.036 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852764.037 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.037 * [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))) 1546852764.037 * [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)))) 1546852764.037 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852764.037 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852764.038 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852764.038 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852764.038 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.038 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.038 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.038 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.038 * [misc]taylor: Taking taylor expansion of k in n 1546852764.038 * [misc]backup-simplify: Simplify k into k 1546852764.038 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.038 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.038 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.038 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852764.038 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.038 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.038 * [misc]backup-simplify: Simplify -2 into -2 1546852764.038 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.038 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.038 * [misc]backup-simplify: Simplify PI into PI 1546852764.038 * [misc]taylor: Taking taylor expansion of n in n 1546852764.038 * [misc]backup-simplify: Simplify 0 into 0 1546852764.038 * [misc]backup-simplify: Simplify 1 into 1 1546852764.038 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.038 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.039 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.039 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.039 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852764.039 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.039 * [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))) 1546852764.040 * [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)))) 1546852764.040 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546852764.040 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546852764.040 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852764.040 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.040 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.040 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.040 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.040 * [misc]taylor: Taking taylor expansion of k in k 1546852764.040 * [misc]backup-simplify: Simplify 0 into 0 1546852764.040 * [misc]backup-simplify: Simplify 1 into 1 1546852764.040 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.040 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.040 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.040 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546852764.040 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546852764.040 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546852764.040 * [misc]taylor: Taking taylor expansion of -2 in k 1546852764.040 * [misc]backup-simplify: Simplify -2 into -2 1546852764.040 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.040 * [misc]backup-simplify: Simplify PI into PI 1546852764.041 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.041 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.041 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852764.041 * [misc]taylor: Taking taylor expansion of n in k 1546852764.041 * [misc]backup-simplify: Simplify n into n 1546852764.041 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852764.041 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.041 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.041 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852764.042 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546852764.042 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546852764.042 * [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)))) 1546852764.043 * [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)))) 1546852764.044 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852764.044 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852764.046 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852764.046 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852764.046 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852764.046 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.047 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.047 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546852764.048 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852764.048 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.048 * [misc]backup-simplify: Simplify 0 into 0 1546852764.048 * [misc]backup-simplify: Simplify 0 into 0 1546852764.048 * [misc]backup-simplify: Simplify 0 into 0 1546852764.049 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.050 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852764.053 * [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 1546852764.053 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852764.053 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852764.053 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.053 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.054 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546852764.055 * [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 1546852764.055 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.055 * [misc]backup-simplify: Simplify 0 into 0 1546852764.055 * [misc]backup-simplify: Simplify 0 into 0 1546852764.055 * [misc]backup-simplify: Simplify 0 into 0 1546852764.055 * [misc]backup-simplify: Simplify 0 into 0 1546852764.057 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.057 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852764.062 * [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 1546852764.062 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852764.063 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852764.063 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.063 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.064 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546852764.066 * [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 1546852764.066 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.066 * [misc]backup-simplify: Simplify 0 into 0 1546852764.066 * [misc]backup-simplify: Simplify 0 into 0 1546852764.066 * [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))))) 1546852764.066 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 2 1) 1546852764.067 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546852764.067 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546852764.067 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852764.067 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.067 * [misc]backup-simplify: Simplify 2 into 2 1546852764.067 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.067 * [misc]taylor: Taking taylor expansion of n in n 1546852764.067 * [misc]backup-simplify: Simplify 0 into 0 1546852764.067 * [misc]backup-simplify: Simplify 1 into 1 1546852764.067 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.067 * [misc]backup-simplify: Simplify PI into PI 1546852764.067 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852764.067 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.067 * [misc]backup-simplify: Simplify 2 into 2 1546852764.067 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.067 * [misc]taylor: Taking taylor expansion of n in n 1546852764.067 * [misc]backup-simplify: Simplify 0 into 0 1546852764.067 * [misc]backup-simplify: Simplify 1 into 1 1546852764.067 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.067 * [misc]backup-simplify: Simplify PI into PI 1546852764.067 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852764.067 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852764.067 * [misc]backup-simplify: Simplify 0 into 0 1546852764.068 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852764.068 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852764.068 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.069 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852764.070 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852764.070 * [misc]backup-simplify: Simplify 0 into 0 1546852764.071 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852764.072 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852764.072 * [misc]backup-simplify: Simplify 0 into 0 1546852764.073 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852764.074 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546852764.074 * [misc]backup-simplify: Simplify 0 into 0 1546852764.076 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852764.079 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546852764.079 * [misc]backup-simplify: Simplify 0 into 0 1546852764.082 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852764.085 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546852764.086 * [misc]backup-simplify: Simplify 0 into 0 1546852764.090 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546852764.094 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546852764.094 * [misc]backup-simplify: Simplify 0 into 0 1546852764.094 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546852764.094 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546852764.094 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546852764.094 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852764.094 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.094 * [misc]backup-simplify: Simplify 2 into 2 1546852764.094 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.094 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.094 * [misc]backup-simplify: Simplify PI into PI 1546852764.094 * [misc]taylor: Taking taylor expansion of n in n 1546852764.094 * [misc]backup-simplify: Simplify 0 into 0 1546852764.094 * [misc]backup-simplify: Simplify 1 into 1 1546852764.095 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.095 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852764.095 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.095 * [misc]backup-simplify: Simplify 2 into 2 1546852764.095 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.095 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.095 * [misc]backup-simplify: Simplify PI into PI 1546852764.095 * [misc]taylor: Taking taylor expansion of n in n 1546852764.095 * [misc]backup-simplify: Simplify 0 into 0 1546852764.095 * [misc]backup-simplify: Simplify 1 into 1 1546852764.095 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.096 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.096 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.097 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852764.098 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852764.098 * [misc]backup-simplify: Simplify 0 into 0 1546852764.099 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.100 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852764.101 * [misc]backup-simplify: Simplify 0 into 0 1546852764.102 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.104 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852764.104 * [misc]backup-simplify: Simplify 0 into 0 1546852764.106 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.108 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852764.108 * [misc]backup-simplify: Simplify 0 into 0 1546852764.110 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.113 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852764.113 * [misc]backup-simplify: Simplify 0 into 0 1546852764.117 * [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 1546852764.120 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852764.120 * [misc]backup-simplify: Simplify 0 into 0 1546852764.121 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546852764.121 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546852764.121 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546852764.121 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.121 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.121 * [misc]backup-simplify: Simplify -2 into -2 1546852764.121 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.121 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.121 * [misc]backup-simplify: Simplify PI into PI 1546852764.121 * [misc]taylor: Taking taylor expansion of n in n 1546852764.121 * [misc]backup-simplify: Simplify 0 into 0 1546852764.121 * [misc]backup-simplify: Simplify 1 into 1 1546852764.121 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.121 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.121 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.121 * [misc]backup-simplify: Simplify -2 into -2 1546852764.122 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.122 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.122 * [misc]backup-simplify: Simplify PI into PI 1546852764.122 * [misc]taylor: Taking taylor expansion of n in n 1546852764.122 * [misc]backup-simplify: Simplify 0 into 0 1546852764.122 * [misc]backup-simplify: Simplify 1 into 1 1546852764.122 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.122 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.122 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.124 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852764.124 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852764.124 * [misc]backup-simplify: Simplify 0 into 0 1546852764.126 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.127 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852764.127 * [misc]backup-simplify: Simplify 0 into 0 1546852764.128 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.129 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852764.129 * [misc]backup-simplify: Simplify 0 into 0 1546852764.130 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.131 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852764.131 * [misc]backup-simplify: Simplify 0 into 0 1546852764.133 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.134 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852764.134 * [misc]backup-simplify: Simplify 0 into 0 1546852764.136 * [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 1546852764.138 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852764.138 * [misc]backup-simplify: Simplify 0 into 0 1546852764.138 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546852764.138 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1546852764.138 * [misc]backup-simplify: Simplify (* (sqrt k) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 1546852764.138 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 1546852764.138 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 1546852764.138 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546852764.138 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852764.138 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852764.138 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852764.138 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852764.138 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.138 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.138 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852764.139 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.139 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.139 * [misc]taylor: Taking taylor expansion of k in n 1546852764.139 * [misc]backup-simplify: Simplify k into k 1546852764.139 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852764.139 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852764.139 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.139 * [misc]backup-simplify: Simplify 2 into 2 1546852764.139 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.139 * [misc]taylor: Taking taylor expansion of n in n 1546852764.139 * [misc]backup-simplify: Simplify 0 into 0 1546852764.139 * [misc]backup-simplify: Simplify 1 into 1 1546852764.139 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.139 * [misc]backup-simplify: Simplify PI into PI 1546852764.139 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852764.139 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852764.139 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852764.140 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852764.140 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.140 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852764.140 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852764.140 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852764.141 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852764.141 * [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)))) 1546852764.142 * [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))))) 1546852764.142 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546852764.142 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1546852764.142 * [misc]taylor: Taking taylor expansion of k in n 1546852764.142 * [misc]backup-simplify: Simplify k into k 1546852764.142 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1546852764.142 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1546852764.142 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.142 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.142 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.142 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.142 * [misc]taylor: Taking taylor expansion of k in k 1546852764.142 * [misc]backup-simplify: Simplify 0 into 0 1546852764.142 * [misc]backup-simplify: Simplify 1 into 1 1546852764.142 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.142 * [misc]backup-simplify: Simplify 2 into 2 1546852764.142 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852764.142 * [misc]taylor: Taking taylor expansion of n in k 1546852764.142 * [misc]backup-simplify: Simplify n into n 1546852764.142 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.142 * [misc]backup-simplify: Simplify PI into PI 1546852764.142 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852764.143 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852764.143 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852764.143 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852764.143 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.143 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.143 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852764.143 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852764.143 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546852764.143 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546852764.143 * [misc]taylor: Taking taylor expansion of k in k 1546852764.143 * [misc]backup-simplify: Simplify 0 into 0 1546852764.143 * [misc]backup-simplify: Simplify 1 into 1 1546852764.143 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.144 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852764.144 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.144 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.144 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.144 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.144 * [misc]taylor: Taking taylor expansion of k in k 1546852764.144 * [misc]backup-simplify: Simplify 0 into 0 1546852764.144 * [misc]backup-simplify: Simplify 1 into 1 1546852764.144 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.144 * [misc]backup-simplify: Simplify 2 into 2 1546852764.144 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852764.144 * [misc]taylor: Taking taylor expansion of n in k 1546852764.144 * [misc]backup-simplify: Simplify n into n 1546852764.144 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.144 * [misc]backup-simplify: Simplify PI into PI 1546852764.144 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852764.144 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852764.144 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852764.144 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852764.144 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.144 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.145 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852764.145 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852764.145 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546852764.145 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1546852764.145 * [misc]taylor: Taking taylor expansion of k in k 1546852764.145 * [misc]backup-simplify: Simplify 0 into 0 1546852764.145 * [misc]backup-simplify: Simplify 1 into 1 1546852764.145 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.145 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852764.145 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 1546852764.145 * [misc]taylor: Taking taylor expansion of 0 in n 1546852764.145 * [misc]backup-simplify: Simplify 0 into 0 1546852764.145 * [misc]backup-simplify: Simplify 0 into 0 1546852764.146 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1546852764.146 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 1546852764.146 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 1546852764.146 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852764.146 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852764.147 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852764.147 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 1546852764.147 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 1546852764.148 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 1546852764.148 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 1546852764.148 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546852764.148 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546852764.148 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.148 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.148 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546852764.149 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546852764.149 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546852764.149 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.149 * [misc]taylor: Taking taylor expansion of n in n 1546852764.149 * [misc]backup-simplify: Simplify 0 into 0 1546852764.149 * [misc]backup-simplify: Simplify 1 into 1 1546852764.149 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.149 * [misc]backup-simplify: Simplify PI into PI 1546852764.149 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852764.149 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852764.149 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546852764.149 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.150 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546852764.150 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546852764.150 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.150 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.150 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546852764.150 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546852764.151 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852764.151 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546852764.152 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852764.153 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852764.154 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852764.154 * [misc]backup-simplify: Simplify 0 into 0 1546852764.154 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852764.155 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1546852764.155 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1546852764.156 * [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 1546852764.156 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852764.156 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.156 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.157 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 1546852764.157 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 1546852764.159 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 1546852764.161 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 1546852764.161 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 1546852764.161 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 1546852764.161 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 1546852764.161 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.161 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.161 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 1546852764.161 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 1546852764.161 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1546852764.161 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.161 * [misc]backup-simplify: Simplify 2 into 2 1546852764.161 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1546852764.161 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1546852764.161 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 1546852764.161 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852764.161 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852764.162 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.162 * [misc]backup-simplify: Simplify 2 into 2 1546852764.162 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.162 * [misc]taylor: Taking taylor expansion of n in n 1546852764.162 * [misc]backup-simplify: Simplify 0 into 0 1546852764.162 * [misc]backup-simplify: Simplify 1 into 1 1546852764.162 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.162 * [misc]backup-simplify: Simplify PI into PI 1546852764.162 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852764.162 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852764.162 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852764.163 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852764.163 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.163 * [misc]taylor: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 1546852764.163 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546852764.163 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.163 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.163 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546852764.163 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546852764.163 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546852764.163 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546852764.163 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.163 * [misc]taylor: Taking taylor expansion of n in n 1546852764.163 * [misc]backup-simplify: Simplify 0 into 0 1546852764.163 * [misc]backup-simplify: Simplify 1 into 1 1546852764.163 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.164 * [misc]backup-simplify: Simplify PI into PI 1546852764.164 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852764.164 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852764.164 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546852764.164 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.165 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546852764.165 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 1546852764.165 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 1546852764.165 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.165 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.165 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 1546852764.165 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 1546852764.165 * [misc]taylor: Taking taylor expansion of (/ 1 (* n PI)) in n 1546852764.165 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.165 * [misc]taylor: Taking taylor expansion of n in n 1546852764.165 * [misc]backup-simplify: Simplify 0 into 0 1546852764.165 * [misc]backup-simplify: Simplify 1 into 1 1546852764.165 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.165 * [misc]backup-simplify: Simplify PI into PI 1546852764.165 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852764.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852764.166 * [misc]backup-simplify: Simplify (/ 1 PI) into (/ 1 PI) 1546852764.166 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.166 * [misc]backup-simplify: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 1546852764.166 * [misc]taylor: Taking taylor expansion of (sqrt 1/2) in n 1546852764.166 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.166 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.166 * [misc]backup-simplify: Simplify (sqrt 1/2) into (sqrt 1/2) 1546852764.167 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 1546852764.167 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852764.167 * [misc]backup-simplify: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 1546852764.168 * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 1546852764.169 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 1546852764.169 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852764.169 * [misc]backup-simplify: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 1546852764.170 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852764.171 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852764.173 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852764.174 * [misc]backup-simplify: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 1546852764.175 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 1546852764.177 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546852764.178 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 1546852764.182 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 1546852764.183 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852764.183 * [misc]backup-simplify: Simplify (* 0 (sqrt 1/2)) into 0 1546852764.185 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852764.186 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 1546852764.191 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546852764.198 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546852764.204 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 1546852764.205 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 1546852764.206 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852764.207 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 1546852764.209 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 1546852764.211 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546852764.215 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546852764.216 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546852764.217 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 1546852764.226 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546852764.226 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (/ 1 (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 1546852764.227 * [misc]approximate: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 1546852764.227 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.227 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.227 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.227 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of k in n 1546852764.227 * [misc]backup-simplify: Simplify k into k 1546852764.227 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.227 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.227 * [misc]backup-simplify: Simplify 2 into 2 1546852764.227 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.227 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.227 * [misc]backup-simplify: Simplify PI into PI 1546852764.227 * [misc]taylor: Taking taylor expansion of n in n 1546852764.227 * [misc]backup-simplify: Simplify 0 into 0 1546852764.227 * [misc]backup-simplify: Simplify 1 into 1 1546852764.228 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.228 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.228 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.229 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.229 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852764.229 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852764.229 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.230 * [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))) 1546852764.231 * [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)))) 1546852764.231 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.231 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1546852764.231 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.231 * [misc]taylor: Taking taylor expansion of k in n 1546852764.231 * [misc]backup-simplify: Simplify k into k 1546852764.231 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.231 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1546852764.232 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852764.232 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1546852764.232 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.232 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.232 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.232 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.232 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of k in k 1546852764.232 * [misc]backup-simplify: Simplify 0 into 0 1546852764.232 * [misc]backup-simplify: Simplify 1 into 1 1546852764.232 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.232 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.232 * [misc]backup-simplify: Simplify 2 into 2 1546852764.232 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852764.232 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.232 * [misc]backup-simplify: Simplify PI into PI 1546852764.232 * [misc]taylor: Taking taylor expansion of n in k 1546852764.232 * [misc]backup-simplify: Simplify n into n 1546852764.232 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852764.233 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852764.233 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852764.233 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.233 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852764.233 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852764.233 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852764.233 * [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)))) 1546852764.233 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546852764.234 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546852764.234 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.234 * [misc]taylor: Taking taylor expansion of k in k 1546852764.234 * [misc]backup-simplify: Simplify 0 into 0 1546852764.234 * [misc]backup-simplify: Simplify 1 into 1 1546852764.234 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.234 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.234 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852764.234 * [misc]taylor: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 1546852764.234 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546852764.234 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852764.234 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852764.234 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852764.234 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852764.235 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.235 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.235 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.235 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.235 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.235 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.235 * [misc]taylor: Taking taylor expansion of k in k 1546852764.235 * [misc]backup-simplify: Simplify 0 into 0 1546852764.235 * [misc]backup-simplify: Simplify 1 into 1 1546852764.235 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.235 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852764.235 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852764.235 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.235 * [misc]backup-simplify: Simplify 2 into 2 1546852764.235 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852764.235 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.235 * [misc]backup-simplify: Simplify PI into PI 1546852764.235 * [misc]taylor: Taking taylor expansion of n in k 1546852764.235 * [misc]backup-simplify: Simplify n into n 1546852764.235 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852764.235 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852764.235 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852764.235 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.236 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852764.236 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852764.236 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852764.236 * [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)))) 1546852764.236 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546852764.236 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1546852764.236 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.236 * [misc]taylor: Taking taylor expansion of k in k 1546852764.236 * [misc]backup-simplify: Simplify 0 into 0 1546852764.236 * [misc]backup-simplify: Simplify 1 into 1 1546852764.236 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.237 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.237 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1546852764.237 * [misc]backup-simplify: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1546852764.237 * [misc]taylor: Taking taylor expansion of 0 in n 1546852764.237 * [misc]backup-simplify: Simplify 0 into 0 1546852764.237 * [misc]backup-simplify: Simplify 0 into 0 1546852764.238 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546852764.238 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546852764.238 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.238 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.238 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.238 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.238 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.238 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.238 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.238 * [misc]taylor: Taking taylor expansion of k in n 1546852764.238 * [misc]backup-simplify: Simplify k into k 1546852764.239 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.239 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852764.239 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852764.239 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.239 * [misc]backup-simplify: Simplify 2 into 2 1546852764.239 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.239 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.239 * [misc]backup-simplify: Simplify PI into PI 1546852764.239 * [misc]taylor: Taking taylor expansion of n in n 1546852764.239 * [misc]backup-simplify: Simplify 0 into 0 1546852764.239 * [misc]backup-simplify: Simplify 1 into 1 1546852764.239 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.239 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.240 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.240 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.240 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852764.240 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852764.242 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.242 * [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))) 1546852764.243 * [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)))) 1546852764.243 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.244 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.245 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852764.246 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852764.246 * [misc]backup-simplify: Simplify 0 into 0 1546852764.246 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1546852764.247 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852764.248 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546852764.248 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546852764.248 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.249 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.249 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.249 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.249 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of k in n 1546852764.249 * [misc]backup-simplify: Simplify k into k 1546852764.249 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.249 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.249 * [misc]backup-simplify: Simplify 2 into 2 1546852764.249 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.249 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.249 * [misc]backup-simplify: Simplify PI into PI 1546852764.249 * [misc]taylor: Taking taylor expansion of n in n 1546852764.249 * [misc]backup-simplify: Simplify 0 into 0 1546852764.249 * [misc]backup-simplify: Simplify 1 into 1 1546852764.250 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.250 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.251 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.251 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.251 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852764.251 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852764.252 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.252 * [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))) 1546852764.253 * [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)))) 1546852764.253 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.254 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.255 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852764.256 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852764.257 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852764.257 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852764.260 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852764.260 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852764.261 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852764.261 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.261 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.262 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.262 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852764.264 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852764.264 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546852764.265 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1546852764.265 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.265 * [misc]backup-simplify: Simplify 0 into 0 1546852764.265 * [misc]backup-simplify: Simplify 0 into 0 1546852764.265 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.266 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852764.266 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1546852764.267 * [misc]backup-simplify: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1546852764.267 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.267 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.267 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.267 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.267 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.267 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.267 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of k in n 1546852764.267 * [misc]backup-simplify: Simplify k into k 1546852764.267 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.267 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.267 * [misc]backup-simplify: Simplify 2 into 2 1546852764.267 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.267 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.267 * [misc]backup-simplify: Simplify PI into PI 1546852764.267 * [misc]taylor: Taking taylor expansion of n in n 1546852764.267 * [misc]backup-simplify: Simplify 0 into 0 1546852764.267 * [misc]backup-simplify: Simplify 1 into 1 1546852764.267 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.268 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.268 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.268 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.268 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852764.268 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852764.269 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.269 * [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))) 1546852764.269 * [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)))) 1546852764.270 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.270 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.271 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852764.271 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 1546852764.273 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546852764.273 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 (- k))) (/ 1 (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1546852764.273 * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 1546852764.273 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of -1 in n 1546852764.273 * [misc]backup-simplify: Simplify -1 into -1 1546852764.273 * [misc]taylor: Taking taylor expansion of k in n 1546852764.273 * [misc]backup-simplify: Simplify k into k 1546852764.273 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1546852764.273 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1546852764.273 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1546852764.273 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1546852764.273 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.273 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.273 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of k in n 1546852764.273 * [misc]backup-simplify: Simplify k into k 1546852764.273 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.273 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.273 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.273 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.273 * [misc]backup-simplify: Simplify -2 into -2 1546852764.273 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.273 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.273 * [misc]backup-simplify: Simplify PI into PI 1546852764.274 * [misc]taylor: Taking taylor expansion of n in n 1546852764.274 * [misc]backup-simplify: Simplify 0 into 0 1546852764.274 * [misc]backup-simplify: Simplify 1 into 1 1546852764.274 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.274 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.274 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.274 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.274 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852764.275 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.275 * [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))) 1546852764.276 * [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)))) 1546852764.276 * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.276 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546852764.276 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546852764.276 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546852764.276 * [misc]taylor: Taking taylor expansion of -1 in k 1546852764.276 * [misc]backup-simplify: Simplify -1 into -1 1546852764.276 * [misc]taylor: Taking taylor expansion of k in k 1546852764.276 * [misc]backup-simplify: Simplify 0 into 0 1546852764.276 * [misc]backup-simplify: Simplify 1 into 1 1546852764.276 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546852764.276 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.277 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546852764.277 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.277 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.277 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of k in k 1546852764.277 * [misc]backup-simplify: Simplify 0 into 0 1546852764.277 * [misc]backup-simplify: Simplify 1 into 1 1546852764.277 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.277 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.277 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.277 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of -2 in k 1546852764.277 * [misc]backup-simplify: Simplify -2 into -2 1546852764.277 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852764.277 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.277 * [misc]backup-simplify: Simplify PI into PI 1546852764.277 * [misc]taylor: Taking taylor expansion of n in k 1546852764.277 * [misc]backup-simplify: Simplify n into n 1546852764.277 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852764.277 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852764.277 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852764.277 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.278 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.278 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852764.278 * [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))) 1546852764.278 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546852764.278 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546852764.278 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1546852764.278 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1546852764.278 * [misc]taylor: Taking taylor expansion of -1 in k 1546852764.278 * [misc]backup-simplify: Simplify -1 into -1 1546852764.278 * [misc]taylor: Taking taylor expansion of k in k 1546852764.278 * [misc]backup-simplify: Simplify 0 into 0 1546852764.278 * [misc]backup-simplify: Simplify 1 into 1 1546852764.278 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1546852764.278 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1546852764.278 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1546852764.279 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.279 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.279 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of k in k 1546852764.279 * [misc]backup-simplify: Simplify 0 into 0 1546852764.279 * [misc]backup-simplify: Simplify 1 into 1 1546852764.279 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.279 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.279 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.279 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of -2 in k 1546852764.279 * [misc]backup-simplify: Simplify -2 into -2 1546852764.279 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852764.279 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.279 * [misc]backup-simplify: Simplify PI into PI 1546852764.279 * [misc]taylor: Taking taylor expansion of n in k 1546852764.279 * [misc]backup-simplify: Simplify n into n 1546852764.279 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852764.279 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852764.279 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852764.279 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.279 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.279 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852764.280 * [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))) 1546852764.280 * [misc]backup-simplify: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546852764.280 * [misc]taylor: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852764.280 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.280 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.280 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852764.280 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852764.280 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852764.280 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.280 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.280 * [misc]backup-simplify: Simplify -2 into -2 1546852764.280 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.280 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.280 * [misc]backup-simplify: Simplify PI into PI 1546852764.280 * [misc]taylor: Taking taylor expansion of n in n 1546852764.280 * [misc]backup-simplify: Simplify 0 into 0 1546852764.280 * [misc]backup-simplify: Simplify 1 into 1 1546852764.280 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.280 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.281 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.281 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852764.281 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.281 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.281 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.281 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.281 * [misc]taylor: Taking taylor expansion of k in n 1546852764.281 * [misc]backup-simplify: Simplify k into k 1546852764.281 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.281 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.281 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.281 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.281 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.281 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852764.282 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852764.282 * [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)))) 1546852764.283 * [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))))) 1546852764.283 * [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))))) 1546852764.283 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1546852764.284 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1546852764.284 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546852764.284 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546852764.284 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546852764.284 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.284 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.284 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852764.284 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852764.284 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852764.284 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852764.284 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.285 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.285 * [misc]backup-simplify: Simplify -2 into -2 1546852764.285 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.285 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.285 * [misc]backup-simplify: Simplify PI into PI 1546852764.285 * [misc]taylor: Taking taylor expansion of n in n 1546852764.285 * [misc]backup-simplify: Simplify 0 into 0 1546852764.285 * [misc]backup-simplify: Simplify 1 into 1 1546852764.285 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.285 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.285 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.285 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852764.285 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.285 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.285 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.285 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.285 * [misc]taylor: Taking taylor expansion of k in n 1546852764.285 * [misc]backup-simplify: Simplify k into k 1546852764.285 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.285 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.285 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.286 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.286 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.286 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852764.286 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852764.287 * [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)))) 1546852764.287 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.288 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.288 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546852764.289 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546852764.289 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.289 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852764.289 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852764.289 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.290 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852764.290 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852764.292 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852764.293 * [misc]backup-simplify: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1546852764.294 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852764.295 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546852764.295 * [misc]backup-simplify: Simplify 0 into 0 1546852764.295 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.296 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1546852764.296 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1546852764.296 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1546852764.297 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1546852764.297 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.297 * [misc]backup-simplify: Simplify -2 into -2 1546852764.297 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.297 * [misc]backup-simplify: Simplify PI into PI 1546852764.297 * [misc]taylor: Taking taylor expansion of n in n 1546852764.297 * [misc]backup-simplify: Simplify 0 into 0 1546852764.297 * [misc]backup-simplify: Simplify 1 into 1 1546852764.297 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.297 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.297 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.297 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852764.297 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.298 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.298 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.298 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.298 * [misc]taylor: Taking taylor expansion of k in n 1546852764.298 * [misc]backup-simplify: Simplify k into k 1546852764.298 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.298 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.298 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.298 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.298 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.298 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852764.299 * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1546852764.299 * [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)))) 1546852764.299 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.300 * [misc]backup-simplify: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.300 * [misc]backup-simplify: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546852764.301 * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 1546852764.303 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546852764.303 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 2) 1546852764.304 * [misc]backup-simplify: Simplify (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1546852764.304 * [misc]approximate: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1546852764.304 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.304 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.304 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.304 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.304 * [misc]taylor: Taking taylor expansion of k in k 1546852764.304 * [misc]backup-simplify: Simplify 0 into 0 1546852764.304 * [misc]backup-simplify: Simplify 1 into 1 1546852764.304 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.304 * [misc]backup-simplify: Simplify 2 into 2 1546852764.304 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852764.304 * [misc]taylor: Taking taylor expansion of n in k 1546852764.304 * [misc]backup-simplify: Simplify n into n 1546852764.304 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.304 * [misc]backup-simplify: Simplify PI into PI 1546852764.304 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852764.305 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852764.305 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852764.305 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852764.305 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.305 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.305 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852764.305 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852764.306 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 1546852764.306 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.306 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.306 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.306 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.306 * [misc]taylor: Taking taylor expansion of k in n 1546852764.306 * [misc]backup-simplify: Simplify k into k 1546852764.306 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.306 * [misc]backup-simplify: Simplify 2 into 2 1546852764.306 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.306 * [misc]taylor: Taking taylor expansion of n in n 1546852764.306 * [misc]backup-simplify: Simplify 0 into 0 1546852764.306 * [misc]backup-simplify: Simplify 1 into 1 1546852764.306 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.306 * [misc]backup-simplify: Simplify PI into PI 1546852764.307 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852764.307 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852764.308 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852764.308 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852764.309 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.309 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852764.309 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852764.309 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852764.310 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852764.310 * [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)))) 1546852764.311 * [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))))) 1546852764.311 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546852764.311 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.312 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.312 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.312 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.312 * [misc]taylor: Taking taylor expansion of k in n 1546852764.312 * [misc]backup-simplify: Simplify k into k 1546852764.312 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.312 * [misc]backup-simplify: Simplify 2 into 2 1546852764.312 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852764.312 * [misc]taylor: Taking taylor expansion of n in n 1546852764.312 * [misc]backup-simplify: Simplify 0 into 0 1546852764.312 * [misc]backup-simplify: Simplify 1 into 1 1546852764.312 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.312 * [misc]backup-simplify: Simplify PI into PI 1546852764.312 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852764.313 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852764.313 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852764.314 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852764.314 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.315 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852764.315 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852764.315 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852764.315 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852764.316 * [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)))) 1546852764.317 * [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))))) 1546852764.317 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 1546852764.317 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 1546852764.317 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546852764.317 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546852764.317 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852764.317 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.317 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.317 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852764.318 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.318 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.318 * [misc]taylor: Taking taylor expansion of k in k 1546852764.318 * [misc]backup-simplify: Simplify 0 into 0 1546852764.318 * [misc]backup-simplify: Simplify 1 into 1 1546852764.318 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546852764.318 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852764.318 * [misc]taylor: Taking taylor expansion of n in k 1546852764.318 * [misc]backup-simplify: Simplify n into n 1546852764.318 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852764.318 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852764.318 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852764.318 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.318 * [misc]backup-simplify: Simplify 2 into 2 1546852764.318 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.318 * [misc]backup-simplify: Simplify PI into PI 1546852764.318 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.319 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.319 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852764.319 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.319 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.320 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852764.320 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546852764.321 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852764.321 * [misc]backup-simplify: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 1546852764.322 * [misc]backup-simplify: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 1546852764.323 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852764.324 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852764.327 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852764.327 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546852764.327 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.327 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.328 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852764.329 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546852764.330 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852764.332 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 1546852764.332 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.332 * [misc]backup-simplify: Simplify 0 into 0 1546852764.332 * [misc]backup-simplify: Simplify 0 into 0 1546852764.332 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546852764.333 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852764.336 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852764.336 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.336 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852764.337 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852764.337 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852764.338 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546852764.339 * [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))))))) 1546852764.342 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 1546852764.344 * [misc]backup-simplify: Simplify (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 1546852764.345 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852764.347 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852764.352 * [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 1546852764.352 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546852764.352 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.353 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.353 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852764.354 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852764.356 * [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 1546852764.359 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 1546852764.359 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.359 * [misc]backup-simplify: Simplify 0 into 0 1546852764.359 * [misc]backup-simplify: Simplify 0 into 0 1546852764.359 * [misc]backup-simplify: Simplify 0 into 0 1546852764.361 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546852764.362 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852764.367 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1546852764.367 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.367 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852764.367 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.368 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.368 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852764.371 * [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))))) 1546852764.378 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* (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))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 1546852764.382 * [misc]backup-simplify: Simplify (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 1546852764.389 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* k 1)) (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) 1546852764.390 * [misc]backup-simplify: Simplify (/ 1 (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546852764.390 * [misc]approximate: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1546852764.390 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.390 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.390 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.390 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.390 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of k in k 1546852764.390 * [misc]backup-simplify: Simplify 0 into 0 1546852764.390 * [misc]backup-simplify: Simplify 1 into 1 1546852764.390 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.390 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.390 * [misc]backup-simplify: Simplify 2 into 2 1546852764.390 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852764.390 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.390 * [misc]backup-simplify: Simplify PI into PI 1546852764.390 * [misc]taylor: Taking taylor expansion of n in k 1546852764.391 * [misc]backup-simplify: Simplify n into n 1546852764.391 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852764.391 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852764.391 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852764.391 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.391 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852764.391 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852764.391 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852764.392 * [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)))) 1546852764.392 * [misc]backup-simplify: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1546852764.392 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.392 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.392 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.392 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.392 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of k in n 1546852764.392 * [misc]backup-simplify: Simplify k into k 1546852764.392 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.392 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.392 * [misc]backup-simplify: Simplify 2 into 2 1546852764.392 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.392 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.392 * [misc]backup-simplify: Simplify PI into PI 1546852764.392 * [misc]taylor: Taking taylor expansion of n in n 1546852764.392 * [misc]backup-simplify: Simplify 0 into 0 1546852764.392 * [misc]backup-simplify: Simplify 1 into 1 1546852764.393 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.393 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.394 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.394 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.394 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852764.394 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852764.395 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.395 * [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))) 1546852764.396 * [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)))) 1546852764.397 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.397 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.397 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.397 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.397 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.397 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of k in n 1546852764.397 * [misc]backup-simplify: Simplify k into k 1546852764.397 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.397 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of 2 in n 1546852764.397 * [misc]backup-simplify: Simplify 2 into 2 1546852764.397 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.397 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.397 * [misc]backup-simplify: Simplify PI into PI 1546852764.397 * [misc]taylor: Taking taylor expansion of n in n 1546852764.397 * [misc]backup-simplify: Simplify 0 into 0 1546852764.397 * [misc]backup-simplify: Simplify 1 into 1 1546852764.398 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.398 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.398 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.398 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.398 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852764.399 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852764.399 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.400 * [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))) 1546852764.401 * [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)))) 1546852764.401 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.401 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 1546852764.401 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546852764.401 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546852764.401 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852764.401 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.401 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.402 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.402 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.402 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.402 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.402 * [misc]taylor: Taking taylor expansion of k in k 1546852764.402 * [misc]backup-simplify: Simplify 0 into 0 1546852764.402 * [misc]backup-simplify: Simplify 1 into 1 1546852764.402 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.402 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546852764.402 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852764.402 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852764.402 * [misc]taylor: Taking taylor expansion of 2 in k 1546852764.402 * [misc]backup-simplify: Simplify 2 into 2 1546852764.402 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.402 * [misc]backup-simplify: Simplify PI into PI 1546852764.402 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852764.403 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852764.403 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852764.403 * [misc]taylor: Taking taylor expansion of n in k 1546852764.403 * [misc]backup-simplify: Simplify n into n 1546852764.403 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852764.403 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.403 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852764.403 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852764.403 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852764.404 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546852764.405 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546852764.405 * [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)))) 1546852764.406 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.406 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 1546852764.408 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852764.408 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852764.411 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852764.411 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852764.412 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852764.412 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.412 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.413 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.414 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852764.415 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852764.417 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546852764.417 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.417 * [misc]backup-simplify: Simplify 0 into 0 1546852764.417 * [misc]backup-simplify: Simplify 0 into 0 1546852764.418 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546852764.418 * [misc]backup-simplify: Simplify 0 into 0 1546852764.420 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.421 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852764.426 * [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 1546852764.426 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852764.426 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852764.427 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.427 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.428 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.428 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546852764.431 * [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 1546852764.433 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546852764.433 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.433 * [misc]backup-simplify: Simplify 0 into 0 1546852764.433 * [misc]backup-simplify: Simplify 0 into 0 1546852764.433 * [misc]backup-simplify: Simplify 0 into 0 1546852764.435 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546852764.435 * [misc]backup-simplify: Simplify 0 into 0 1546852764.437 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.439 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852764.446 * [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 1546852764.447 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852764.447 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852764.447 * [misc]backup-simplify: Simplify (- 0) into 0 1546852764.448 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.448 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852764.449 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546852764.453 * [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 1546852764.455 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1546852764.455 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.455 * [misc]backup-simplify: Simplify 0 into 0 1546852764.456 * [misc]backup-simplify: Simplify 0 into 0 1546852764.456 * [misc]backup-simplify: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 1546852764.457 * [misc]backup-simplify: Simplify (/ 1 (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1546852764.457 * [misc]approximate: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 1546852764.457 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.457 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.457 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of k in k 1546852764.457 * [misc]backup-simplify: Simplify 0 into 0 1546852764.457 * [misc]backup-simplify: Simplify 1 into 1 1546852764.457 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.457 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.457 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.457 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of -2 in k 1546852764.457 * [misc]backup-simplify: Simplify -2 into -2 1546852764.457 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852764.457 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.457 * [misc]backup-simplify: Simplify PI into PI 1546852764.458 * [misc]taylor: Taking taylor expansion of n in k 1546852764.458 * [misc]backup-simplify: Simplify n into n 1546852764.458 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852764.458 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852764.458 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852764.458 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.458 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.458 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852764.458 * [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))) 1546852764.459 * [misc]backup-simplify: Simplify (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1546852764.459 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.459 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.459 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of k in n 1546852764.459 * [misc]backup-simplify: Simplify k into k 1546852764.459 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.459 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.459 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.459 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.459 * [misc]backup-simplify: Simplify -2 into -2 1546852764.459 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.459 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.459 * [misc]backup-simplify: Simplify PI into PI 1546852764.459 * [misc]taylor: Taking taylor expansion of n in n 1546852764.459 * [misc]backup-simplify: Simplify 0 into 0 1546852764.459 * [misc]backup-simplify: Simplify 1 into 1 1546852764.460 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.460 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.461 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.461 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.461 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852764.461 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.462 * [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))) 1546852764.463 * [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)))) 1546852764.463 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.463 * [misc]taylor: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1546852764.463 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852764.463 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852764.463 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852764.463 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852764.463 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852764.464 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.464 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.464 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852764.464 * [misc]taylor: Taking taylor expansion of k in n 1546852764.464 * [misc]backup-simplify: Simplify k into k 1546852764.464 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852764.464 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852764.464 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.464 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852764.464 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852764.464 * [misc]taylor: Taking taylor expansion of -2 in n 1546852764.464 * [misc]backup-simplify: Simplify -2 into -2 1546852764.464 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852764.464 * [misc]taylor: Taking taylor expansion of PI in n 1546852764.464 * [misc]backup-simplify: Simplify PI into PI 1546852764.464 * [misc]taylor: Taking taylor expansion of n in n 1546852764.464 * [misc]backup-simplify: Simplify 0 into 0 1546852764.464 * [misc]backup-simplify: Simplify 1 into 1 1546852764.464 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852764.464 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.465 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.465 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852764.465 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852764.466 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.466 * [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))) 1546852764.467 * [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)))) 1546852764.468 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.468 * [misc]taylor: Taking taylor expansion of (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 1546852764.468 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546852764.468 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546852764.468 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852764.468 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852764.468 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.468 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.469 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852764.469 * [misc]taylor: Taking taylor expansion of k in k 1546852764.469 * [misc]backup-simplify: Simplify 0 into 0 1546852764.469 * [misc]backup-simplify: Simplify 1 into 1 1546852764.469 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852764.469 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852764.469 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852764.469 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546852764.469 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546852764.469 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546852764.469 * [misc]taylor: Taking taylor expansion of -2 in k 1546852764.469 * [misc]backup-simplify: Simplify -2 into -2 1546852764.469 * [misc]taylor: Taking taylor expansion of PI in k 1546852764.469 * [misc]backup-simplify: Simplify PI into PI 1546852764.469 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852764.470 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852764.470 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852764.470 * [misc]taylor: Taking taylor expansion of n in k 1546852764.470 * [misc]backup-simplify: Simplify n into n 1546852764.470 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852764.470 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852764.470 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852764.470 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852764.471 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546852764.471 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546852764.472 * [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)))) 1546852764.473 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.473 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1546852764.475 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852764.475 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852764.478 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852764.479 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852764.479 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852764.479 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.480 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.480 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546852764.482 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852764.483 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546852764.484 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.484 * [misc]backup-simplify: Simplify 0 into 0 1546852764.484 * [misc]backup-simplify: Simplify 0 into 0 1546852764.485 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546852764.485 * [misc]backup-simplify: Simplify 0 into 0 1546852764.487 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.488 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852764.493 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1546852764.493 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852764.493 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852764.493 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.494 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.494 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546852764.495 * [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 1546852764.497 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546852764.497 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.497 * [misc]backup-simplify: Simplify 0 into 0 1546852764.497 * [misc]backup-simplify: Simplify 0 into 0 1546852764.497 * [misc]backup-simplify: Simplify 0 into 0 1546852764.498 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546852764.498 * [misc]backup-simplify: Simplify 0 into 0 1546852764.499 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852764.500 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852764.505 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1546852764.505 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852764.505 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852764.505 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852764.506 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852764.506 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546852764.509 * [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 1546852764.510 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 1546852764.510 * [misc]taylor: Taking taylor expansion of 0 in k 1546852764.510 * [misc]backup-simplify: Simplify 0 into 0 1546852764.510 * [misc]backup-simplify: Simplify 0 into 0 1546852764.511 * [misc]backup-simplify: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 1546852764.511 * * * [misc]progress: simplifying candidates 1546852764.511 * * * * [misc]progress: [ 1 / 84 ] simplifiying candidate # 1546852764.511 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546852764.511 * * [misc]simplify: iters left: 6 (11 enodes) 1546852764.513 * * [misc]simplify: iters left: 5 (21 enodes) 1546852764.517 * * [misc]simplify: iters left: 4 (47 enodes) 1546852764.526 * * [misc]simplify: iters left: 3 (109 enodes) 1546852764.565 * * [misc]simplify: iters left: 2 (300 enodes) 1546852764.770 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546852764.770 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))))))) 1546852764.771 * * * * [misc]progress: [ 2 / 84 ] simplifiying candidate # 1546852764.771 * * * * [misc]progress: [ 3 / 84 ] simplifiying candidate # 1546852764.771 * [enter]simplify: Simplifying (* PI (* n 2)) 1546852764.771 * * [misc]simplify: iters left: 4 (5 enodes) 1546852764.773 * * [misc]simplify: iters left: 3 (9 enodes) 1546852764.775 * * [misc]simplify: iters left: 2 (15 enodes) 1546852764.779 * * [misc]simplify: iters left: 1 (17 enodes) 1546852764.783 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546852764.783 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))))))) 1546852764.783 * * * * [misc]progress: [ 4 / 84 ] simplifiying candidate # 1546852764.784 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852764.784 * * [misc]simplify: iters left: 5 (8 enodes) 1546852764.786 * * [misc]simplify: iters left: 4 (12 enodes) 1546852764.790 * * [misc]simplify: iters left: 3 (18 enodes) 1546852764.795 * * [misc]simplify: iters left: 2 (20 enodes) 1546852764.798 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852764.798 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))))))) 1546852764.798 * * * * [misc]progress: [ 5 / 84 ] simplifiying candidate # 1546852764.798 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546852764.798 * * [misc]simplify: iters left: 5 (6 enodes) 1546852764.799 * * [misc]simplify: iters left: 4 (8 enodes) 1546852764.800 * * [misc]simplify: iters left: 3 (11 enodes) 1546852764.802 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546852764.802 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))) 1546852764.802 * * * * [misc]progress: [ 6 / 84 ] simplifiying candidate # 1546852764.802 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546852764.802 * * [misc]simplify: iters left: 5 (6 enodes) 1546852764.803 * * [misc]simplify: iters left: 4 (8 enodes) 1546852764.804 * * [misc]simplify: iters left: 3 (11 enodes) 1546852764.808 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546852764.808 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))))) 1546852764.808 * * * * [misc]progress: [ 7 / 84 ] simplifiying candidate # 1546852764.808 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546852764.808 * * [misc]simplify: iters left: 4 (5 enodes) 1546852764.809 * * [misc]simplify: iters left: 3 (7 enodes) 1546852764.811 * * [misc]simplify: iters left: 2 (10 enodes) 1546852764.812 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546852764.812 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))))))) 1546852764.812 * * * * [misc]progress: [ 8 / 84 ] simplifiying candidate # 1546852764.812 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852764.812 * * [misc]simplify: iters left: 5 (9 enodes) 1546852764.814 * * [misc]simplify: iters left: 4 (15 enodes) 1546852764.817 * * [misc]simplify: iters left: 3 (21 enodes) 1546852764.822 * * [misc]simplify: iters left: 2 (22 enodes) 1546852764.827 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852764.827 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))))) 1546852764.827 * * * * [misc]progress: [ 9 / 84 ] simplifiying candidate # 1546852764.828 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852764.828 * * [misc]simplify: iters left: 5 (9 enodes) 1546852764.830 * * [misc]simplify: iters left: 4 (15 enodes) 1546852764.835 * * [misc]simplify: iters left: 3 (21 enodes) 1546852764.841 * * [misc]simplify: iters left: 2 (22 enodes) 1546852764.847 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852764.847 * [misc]simplify: Simplified (2 2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))))))) 1546852764.847 * * * * [misc]progress: [ 10 / 84 ] simplifiying candidate # 1546852764.847 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546852764.847 * * [misc]simplify: iters left: 5 (7 enodes) 1546852764.849 * * [misc]simplify: iters left: 4 (9 enodes) 1546852764.852 * * [misc]simplify: iters left: 3 (12 enodes) 1546852764.856 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546852764.856 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))))))) 1546852764.856 * * * * [misc]progress: [ 11 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 12 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 13 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 14 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 15 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 16 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 17 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 18 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 19 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 20 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 21 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 22 / 84 ] simplifiying candidate # 1546852764.856 * * * * [misc]progress: [ 23 / 84 ] simplifiying candidate # 1546852764.857 * * * * [misc]progress: [ 24 / 84 ] simplifiying candidate # 1546852764.857 * * * * [misc]progress: [ 25 / 84 ] simplifiying candidate # 1546852764.857 * * * * [misc]progress: [ 26 / 84 ] simplifiying candidate # 1546852764.857 * * * * [misc]progress: [ 27 / 84 ] simplifiying candidate # 1546852764.857 * [enter]simplify: Simplifying (* (sqrt k) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852764.857 * * [misc]simplify: iters left: 6 (14 enodes) 1546852764.862 * * [misc]simplify: iters left: 5 (25 enodes) 1546852764.869 * * [misc]simplify: iters left: 4 (41 enodes) 1546852764.882 * * [misc]simplify: iters left: 3 (49 enodes) 1546852764.894 * * [misc]simplify: iters left: 2 (65 enodes) 1546852764.910 * * [misc]simplify: iters left: 1 (66 enodes) 1546852764.920 * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) 1546852764.920 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (pow (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) 1))) 1546852764.921 * * * * [misc]progress: [ 28 / 84 ] simplifiying candidate # 1546852764.921 * * * * [misc]progress: [ 29 / 84 ] simplifiying candidate # 1546852764.921 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))))) 1546852764.921 * * [misc]simplify: iters left: 6 (15 enodes) 1546852764.927 * * [misc]simplify: iters left: 5 (31 enodes) 1546852764.938 * * [misc]simplify: iters left: 4 (72 enodes) 1546852764.968 * * [misc]simplify: iters left: 3 (210 enodes) 1546852765.086 * [exit]simplify: Simplified to (+ (* (+ -1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) 1546852765.086 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (* (+ -1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k)))))) 1546852765.086 * * * * [misc]progress: [ 30 / 84 ] simplifiying candidate # 1546852765.086 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))))) 1546852765.086 * * [misc]simplify: iters left: 6 (15 enodes) 1546852765.092 * * [misc]simplify: iters left: 5 (31 enodes) 1546852765.106 * * [misc]simplify: iters left: 4 (72 enodes) 1546852765.133 * * [misc]simplify: iters left: 3 (210 enodes) 1546852765.199 * [exit]simplify: Simplified to (+ (* (+ -1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) 1546852765.199 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (* (+ -1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k)))))) 1546852765.199 * * * * [misc]progress: [ 31 / 84 ] simplifiying candidate # 1546852765.200 * [enter]simplify: Simplifying (+ (log (sqrt k)) (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546852765.200 * * [misc]simplify: iters left: 6 (15 enodes) 1546852765.205 * * [misc]simplify: iters left: 5 (25 enodes) 1546852765.213 * * [misc]simplify: iters left: 4 (46 enodes) 1546852765.227 * * [misc]simplify: iters left: 3 (104 enodes) 1546852765.266 * * [misc]simplify: iters left: 2 (337 enodes) 1546852765.456 * [exit]simplify: Simplified to (+ (* (log (* (* PI 2) n)) (+ (/ k 2) -1/2)) (log (sqrt k))) 1546852765.456 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (* (log (* (* PI 2) n)) (+ (/ k 2) -1/2)) (log (sqrt k)))))) 1546852765.456 * * * * [misc]progress: [ 32 / 84 ] simplifiying candidate # 1546852765.456 * [enter]simplify: Simplifying (+ (log (sqrt k)) (log (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546852765.456 * * [misc]simplify: iters left: 6 (16 enodes) 1546852765.459 * * [misc]simplify: iters left: 5 (29 enodes) 1546852765.464 * * [misc]simplify: iters left: 4 (41 enodes) 1546852765.470 * * [misc]simplify: iters left: 3 (65 enodes) 1546852765.481 * * [misc]simplify: iters left: 2 (163 enodes) 1546852765.581 * [exit]simplify: Simplified to (+ (* (+ (/ k 2) -1/2) (log (* (* n 2) PI))) (log (sqrt k))) 1546852765.581 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (* (+ (/ k 2) -1/2) (log (* (* n 2) PI))) (log (sqrt k)))))) 1546852765.581 * * * * [misc]progress: [ 33 / 84 ] simplifiying candidate # 1546852765.581 * * * * [misc]progress: [ 34 / 84 ] simplifiying candidate # 1546852765.581 * * * * [misc]progress: [ 35 / 84 ] simplifiying candidate # 1546852765.582 * [enter]simplify: Simplifying (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) 1546852765.582 * * [misc]simplify: iters left: 6 (18 enodes) 1546852765.588 * * [misc]simplify: iters left: 5 (39 enodes) 1546852765.602 * * [misc]simplify: iters left: 4 (88 enodes) 1546852765.627 * * [misc]simplify: iters left: 3 (159 enodes) 1546852765.667 * * [misc]simplify: iters left: 2 (281 enodes) 1546852765.802 * * [misc]simplify: iters left: 1 (424 enodes) 1546852765.998 * [exit]simplify: Simplified to (/ (/ (* (sqrt k) k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1546852765.998 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* (sqrt k) k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))) 1546852765.998 * * * * [misc]progress: [ 36 / 84 ] simplifiying candidate # 1546852765.998 * * * * [misc]progress: [ 37 / 84 ] simplifiying candidate # 1546852765.998 * * * * [misc]progress: [ 38 / 84 ] simplifiying candidate # 1546852765.998 * * * * [misc]progress: [ 39 / 84 ] simplifiying candidate # 1546852765.998 * * * * [misc]progress: [ 40 / 84 ] simplifiying candidate # 1546852765.998 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546852765.998 * * [misc]simplify: iters left: 5 (10 enodes) 1546852766.000 * * [misc]simplify: iters left: 4 (16 enodes) 1546852766.003 * * [misc]simplify: iters left: 3 (25 enodes) 1546852766.006 * * [misc]simplify: iters left: 2 (26 enodes) 1546852766.014 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546852766.014 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546852766.014 * * * * [misc]progress: [ 41 / 84 ] simplifiying candidate # 1546852766.015 * [enter]simplify: Simplifying (cbrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852766.015 * * [misc]simplify: iters left: 6 (13 enodes) 1546852766.019 * * [misc]simplify: iters left: 5 (21 enodes) 1546852766.025 * * [misc]simplify: iters left: 4 (30 enodes) 1546852766.032 * * [misc]simplify: iters left: 3 (31 enodes) 1546852766.040 * [exit]simplify: Simplified to (cbrt (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1546852766.040 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (* (cbrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) (cbrt (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))))) 1546852766.040 * * * * [misc]progress: [ 42 / 84 ] simplifiying candidate # 1546852766.040 * [enter]simplify: Simplifying (sqrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1546852766.041 * * [misc]simplify: iters left: 6 (13 enodes) 1546852766.045 * * [misc]simplify: iters left: 5 (21 enodes) 1546852766.051 * * [misc]simplify: iters left: 4 (30 enodes) 1546852766.059 * * [misc]simplify: iters left: 3 (31 enodes) 1546852766.066 * [exit]simplify: Simplified to (sqrt (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))) 1546852766.066 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (sqrt (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (sqrt (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))))))) 1546852766.066 * * * * [misc]progress: [ 43 / 84 ] simplifiying candidate # 1546852766.067 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852766.067 * * [misc]simplify: iters left: 6 (12 enodes) 1546852766.071 * * [misc]simplify: iters left: 5 (20 enodes) 1546852766.076 * * [misc]simplify: iters left: 4 (29 enodes) 1546852766.084 * * [misc]simplify: iters left: 3 (30 enodes) 1546852766.091 * [exit]simplify: Simplified to (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1546852766.092 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) 1) (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))) 1546852766.092 * * * * [misc]progress: [ 44 / 84 ] simplifiying candidate # 1546852766.092 * [enter]simplify: Simplifying (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852766.092 * * [misc]simplify: iters left: 6 (12 enodes) 1546852766.096 * * [misc]simplify: iters left: 5 (20 enodes) 1546852766.102 * * [misc]simplify: iters left: 4 (29 enodes) 1546852766.111 * * [misc]simplify: iters left: 3 (30 enodes) 1546852766.119 * [exit]simplify: Simplified to (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) 1546852766.119 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) 1) (/ 1 (pow (* (* n PI) 2) (- 1/2 (/ k 2))))))) 1546852766.119 * * * * [misc]progress: [ 45 / 84 ] simplifiying candidate # 1546852766.119 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852766.119 * * [misc]simplify: iters left: 5 (8 enodes) 1546852766.122 * * [misc]simplify: iters left: 4 (12 enodes) 1546852766.125 * * [misc]simplify: iters left: 3 (18 enodes) 1546852766.130 * * [misc]simplify: iters left: 2 (20 enodes) 1546852766.135 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852766.136 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (sqrt k) (/ 1 (pow (* PI (* n 2)) 1/2))) (pow (* (* 2 n) PI) (/ k 2))))) 1546852766.136 * * * * [misc]progress: [ 46 / 84 ] simplifiying candidate # 1546852766.136 * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546852766.136 * * [misc]simplify: iters left: 4 (4 enodes) 1546852766.137 * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1546852766.137 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (sqrt k)) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546852766.137 * * * * [misc]progress: [ 47 / 84 ] simplifiying candidate # 1546852766.138 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1546852766.138 * * [misc]simplify: iters left: 2 (3 enodes) 1546852766.139 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1546852766.139 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (* (sqrt (sqrt k)) (/ 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))) 1546852766.139 * * * * [misc]progress: [ 48 / 84 ] simplifiying candidate # 1546852766.139 * * * * [misc]progress: [ 49 / 84 ] simplifiying candidate # 1546852766.139 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546852766.139 * * [misc]simplify: iters left: 5 (10 enodes) 1546852766.142 * * [misc]simplify: iters left: 4 (16 enodes) 1546852766.147 * * [misc]simplify: iters left: 3 (25 enodes) 1546852766.154 * * [misc]simplify: iters left: 2 (26 enodes) 1546852766.161 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546852766.161 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (/ (* (sqrt k) 1) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1546852766.161 * * * * [misc]progress: [ 50 / 84 ] simplifiying candidate # 1546852766.161 * * * * [misc]progress: [ 51 / 84 ] simplifiying candidate # 1546852766.161 * * * * [misc]progress: [ 52 / 84 ] simplifiying candidate # 1546852766.161 * [enter]simplify: Simplifying (- (- 1/2 (/ k 2))) 1546852766.161 * * [misc]simplify: iters left: 6 (6 enodes) 1546852766.163 * * [misc]simplify: iters left: 5 (8 enodes) 1546852766.166 * * [misc]simplify: iters left: 4 (15 enodes) 1546852766.171 * * [misc]simplify: iters left: 3 (21 enodes) 1546852766.176 * * [misc]simplify: iters left: 2 (23 enodes) 1546852766.180 * [exit]simplify: Simplified to (+ -1/2 (/ k 2)) 1546852766.180 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (pow (* PI (* n 2)) (+ -1/2 (/ k 2)))))) 1546852766.181 * * * * [misc]progress: [ 53 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 54 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 55 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 56 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 57 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 58 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 59 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 60 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 61 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 62 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 63 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 64 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 65 / 84 ] simplifiying candidate # 1546852766.181 * * * * [misc]progress: [ 66 / 84 ] simplifiying candidate # 1546852766.182 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852766.182 * * [misc]simplify: iters left: 5 (9 enodes) 1546852766.185 * * [misc]simplify: iters left: 4 (15 enodes) 1546852766.188 * * [misc]simplify: iters left: 3 (21 enodes) 1546852766.191 * * [misc]simplify: iters left: 2 (22 enodes) 1546852766.194 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852766.194 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546852766.194 * * * * [misc]progress: [ 67 / 84 ] simplifiying candidate # 1546852766.194 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852766.194 * * [misc]simplify: iters left: 5 (9 enodes) 1546852766.196 * * [misc]simplify: iters left: 4 (15 enodes) 1546852766.198 * * [misc]simplify: iters left: 3 (21 enodes) 1546852766.201 * * [misc]simplify: iters left: 2 (22 enodes) 1546852766.204 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852766.204 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (pow (* PI (* n 2)) 1/2)) (pow (* (* PI n) 2) (- (/ k 2))))))) 1546852766.204 * * * * [misc]progress: [ 68 / 84 ] simplifiying candidate # 1546852766.204 * [enter]simplify: Simplifying (pow (* n 2) (- 1/2 (/ k 2))) 1546852766.204 * * [misc]simplify: iters left: 5 (8 enodes) 1546852766.205 * * [misc]simplify: iters left: 4 (11 enodes) 1546852766.207 * * [misc]simplify: iters left: 3 (14 enodes) 1546852766.209 * [exit]simplify: Simplified to (pow (* n 2) (- 1/2 (/ k 2))) 1546852766.209 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (pow PI (- 1/2 (/ k 2)))) (pow (* n 2) (- 1/2 (/ k 2))))))) 1546852766.209 * * * * [misc]progress: [ 69 / 84 ] simplifiying candidate # 1546852766.209 * [enter]simplify: Simplifying (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852766.209 * * [misc]simplify: iters left: 6 (11 enodes) 1546852766.211 * * [misc]simplify: iters left: 5 (17 enodes) 1546852766.213 * * [misc]simplify: iters left: 4 (26 enodes) 1546852766.217 * * [misc]simplify: iters left: 3 (27 enodes) 1546852766.221 * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546852766.221 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546852766.221 * * * * [misc]progress: [ 70 / 84 ] simplifiying candidate # 1546852766.222 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1546852766.222 * * [misc]simplify: iters left: 6 (11 enodes) 1546852766.225 * * [misc]simplify: iters left: 5 (17 enodes) 1546852766.230 * * [misc]simplify: iters left: 4 (26 enodes) 1546852766.237 * * [misc]simplify: iters left: 3 (27 enodes) 1546852766.244 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1546852766.244 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))))) 1546852766.244 * * * * [misc]progress: [ 71 / 84 ] simplifiying candidate # 1546852766.244 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1546852766.244 * * [misc]simplify: iters left: 5 (10 enodes) 1546852766.248 * * [misc]simplify: iters left: 4 (16 enodes) 1546852766.253 * * [misc]simplify: iters left: 3 (25 enodes) 1546852766.259 * * [misc]simplify: iters left: 2 (26 enodes) 1546852766.266 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) 1546852766.266 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ (/ 1 1) (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))) 1546852766.266 * * * * [misc]progress: [ 72 / 84 ] simplifiying candidate # 1546852766.266 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852766.266 * * [misc]simplify: iters left: 5 (8 enodes) 1546852766.269 * * [misc]simplify: iters left: 4 (12 enodes) 1546852766.272 * * [misc]simplify: iters left: 3 (18 enodes) 1546852766.274 * * [misc]simplify: iters left: 2 (20 enodes) 1546852766.277 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852766.277 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (* (/ 1 (pow (* PI (* n 2)) 1/2)) (pow (* (* 2 n) PI) (/ k 2)))))) 1546852766.277 * * * * [misc]progress: [ 73 / 84 ] simplifiying candidate # 1546852766.277 * [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))))) 1546852766.277 * * [misc]simplify: iters left: 6 (37 enodes) 1546852766.286 * * [misc]simplify: iters left: 5 (105 enodes) 1546852766.316 * * [misc]simplify: iters left: 4 (339 enodes) 1546852766.516 * [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))))) 1546852766.516 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (+ (+ (* (* (* (* 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))))))))) 1546852766.516 * * * * [misc]progress: [ 74 / 84 ] simplifiying candidate # 1546852766.516 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546852766.517 * * [misc]simplify: iters left: 6 (15 enodes) 1546852766.520 * * [misc]simplify: iters left: 5 (33 enodes) 1546852766.527 * * [misc]simplify: iters left: 4 (64 enodes) 1546852766.544 * * [misc]simplify: iters left: 3 (171 enodes) 1546852766.618 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546852766.618 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))))))) 1546852766.618 * * * * [misc]progress: [ 75 / 84 ] simplifiying candidate # 1546852766.618 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546852766.618 * * [misc]simplify: iters left: 6 (15 enodes) 1546852766.621 * * [misc]simplify: iters left: 5 (30 enodes) 1546852766.627 * * [misc]simplify: iters left: 4 (65 enodes) 1546852766.641 * * [misc]simplify: iters left: 3 (200 enodes) 1546852766.751 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546852766.751 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))))) 1546852766.751 * * * * [misc]progress: [ 76 / 84 ] simplifiying candidate # 1546852766.751 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852766.751 * * [misc]simplify: iters left: 4 (5 enodes) 1546852766.753 * * [misc]simplify: iters left: 3 (9 enodes) 1546852766.756 * * [misc]simplify: iters left: 2 (15 enodes) 1546852766.760 * * [misc]simplify: iters left: 1 (17 enodes) 1546852766.764 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852766.764 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852766.764 * * * * [misc]progress: [ 77 / 84 ] simplifiying candidate # 1546852766.764 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852766.764 * * [misc]simplify: iters left: 4 (5 enodes) 1546852766.766 * * [misc]simplify: iters left: 3 (9 enodes) 1546852766.769 * * [misc]simplify: iters left: 2 (15 enodes) 1546852766.773 * * [misc]simplify: iters left: 1 (17 enodes) 1546852766.777 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852766.777 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852766.777 * * * * [misc]progress: [ 78 / 84 ] simplifiying candidate # 1546852766.777 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852766.777 * * [misc]simplify: iters left: 4 (5 enodes) 1546852766.779 * * [misc]simplify: iters left: 3 (9 enodes) 1546852766.781 * * [misc]simplify: iters left: 2 (15 enodes) 1546852766.783 * * [misc]simplify: iters left: 1 (17 enodes) 1546852766.785 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852766.785 * [misc]simplify: Simplified (2 2 2 2 1) to (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))) 1546852766.785 * * * * [misc]progress: [ 79 / 84 ] simplifiying candidate # 1546852766.785 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 1546852766.785 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546852766.785 * * * * [misc]progress: [ 80 / 84 ] simplifiying candidate # 1546852766.785 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 1546852766.785 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546852766.786 * * * * [misc]progress: [ 81 / 84 ] simplifiying candidate # 1546852766.786 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 1546852766.786 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ 1 +nan.0)) 1546852766.786 * * * * [misc]progress: [ 82 / 84 ] simplifiying candidate # 1546852766.786 * [enter]simplify: Simplifying (+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) 1546852766.786 * * [misc]simplify: iters left: 6 (39 enodes) 1546852766.795 * * [misc]simplify: iters left: 5 (105 enodes) 1546852766.816 * * [misc]simplify: iters left: 4 (297 enodes) 1546852766.966 * [exit]simplify: Simplified to (+ (+ (* (/ (* (* k k) 1/8) (pow n 1/2)) (/ (* (log (* PI 2)) (log (* PI 2))) (pow (* PI 2) 1/2))) (+ (/ (/ (* (log n) (* 1/2 k)) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (/ (* 1/2 k) (pow n 1/2)) (/ (log (* PI 2)) (pow (* PI 2) 1/2))))) (+ (+ (/ (* (* (log n) (* k k)) (* (log n) 1/8)) (* (pow (* PI 2) 1/2) (pow n 1/2))) (/ (/ 1 (pow n 1/2)) (pow (* PI 2) 1/2))) (* 1/4 (* (/ (* (log n) (* k k)) (pow n 1/2)) (/ (log (* PI 2)) (pow (* PI 2) 1/2)))))) 1546852766.966 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (+ (+ (* (/ (* (* k k) 1/8) (pow n 1/2)) (/ (* (log (* PI 2)) (log (* PI 2))) (pow (* PI 2) 1/2))) (+ (/ (/ (* (log n) (* 1/2 k)) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (/ (* 1/2 k) (pow n 1/2)) (/ (log (* PI 2)) (pow (* PI 2) 1/2))))) (+ (+ (/ (* (* (log n) (* k k)) (* (log n) 1/8)) (* (pow (* PI 2) 1/2) (pow n 1/2))) (/ (/ 1 (pow n 1/2)) (pow (* PI 2) 1/2))) (* 1/4 (* (/ (* (log n) (* k k)) (pow n 1/2)) (/ (log (* PI 2)) (pow (* PI 2) 1/2))))))))) 1546852766.967 * * * * [misc]progress: [ 83 / 84 ] simplifiying candidate # 1546852766.967 * [enter]simplify: Simplifying (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 1546852766.967 * * [misc]simplify: iters left: 6 (16 enodes) 1546852766.970 * * [misc]simplify: iters left: 5 (36 enodes) 1546852766.977 * * [misc]simplify: iters left: 4 (73 enodes) 1546852766.996 * * [misc]simplify: iters left: 3 (236 enodes) 1546852767.158 * [exit]simplify: Simplified to (pow (exp (- -1/2 (* -1/2 k))) (+ (log (* 2 PI)) (log n))) 1546852767.158 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (pow (exp (- -1/2 (* -1/2 k))) (+ (log (* 2 PI)) (log n)))))) 1546852767.158 * * * * [misc]progress: [ 84 / 84 ] simplifiying candidate # 1546852767.159 * [enter]simplify: Simplifying (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 1546852767.159 * * [misc]simplify: iters left: 6 (17 enodes) 1546852767.165 * * [misc]simplify: iters left: 5 (36 enodes) 1546852767.181 * * [misc]simplify: iters left: 4 (77 enodes) 1546852767.214 * * [misc]simplify: iters left: 3 (276 enodes) 1546852767.398 * [exit]simplify: Simplified to (pow (exp (- -1/2 (* k -1/2))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546852767.398 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt k) (pow (exp (- -1/2 (* k -1/2))) (- (log (* -2 PI)) (log (/ -1 n))))))) 1546852767.399 * * * [misc]progress: adding candidates to table 1546852768.460 * * [misc]progress: iteration 4 / 4 1546852768.460 * * * [misc]progress: picking best candidate 1546852768.513 * * * * [misc]pick: Picked # 1546852768.513 * * * [misc]progress: localizing error 1546852768.519 * * * [misc]progress: generating rewritten candidates 1546852768.519 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1 1) 1546852768.521 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1) 1546852768.522 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1 1 1) 1546852768.523 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1 1 1) 1546852768.525 * * * [misc]progress: generating series expansions 1546852768.525 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1 1) 1546852768.525 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546852768.525 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546852768.525 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852768.525 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852768.525 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852768.525 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852768.525 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.525 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.525 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852768.525 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.525 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.525 * [misc]taylor: Taking taylor expansion of k in k 1546852768.525 * [misc]backup-simplify: Simplify 0 into 0 1546852768.525 * [misc]backup-simplify: Simplify 1 into 1 1546852768.525 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852768.525 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852768.525 * [misc]taylor: Taking taylor expansion of 2 in k 1546852768.525 * [misc]backup-simplify: Simplify 2 into 2 1546852768.525 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852768.525 * [misc]taylor: Taking taylor expansion of n in k 1546852768.525 * [misc]backup-simplify: Simplify n into n 1546852768.525 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.525 * [misc]backup-simplify: Simplify PI into PI 1546852768.525 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852768.525 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852768.526 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852768.526 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852768.526 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.526 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852768.526 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852768.526 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852768.526 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852768.526 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852768.526 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852768.526 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852768.526 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.526 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.526 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852768.526 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.526 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.526 * [misc]taylor: Taking taylor expansion of k in n 1546852768.526 * [misc]backup-simplify: Simplify k into k 1546852768.526 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852768.526 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852768.526 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.526 * [misc]backup-simplify: Simplify 2 into 2 1546852768.526 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852768.526 * [misc]taylor: Taking taylor expansion of n in n 1546852768.526 * [misc]backup-simplify: Simplify 0 into 0 1546852768.526 * [misc]backup-simplify: Simplify 1 into 1 1546852768.526 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.527 * [misc]backup-simplify: Simplify PI into PI 1546852768.527 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852768.527 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852768.528 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852768.528 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852768.528 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.528 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852768.528 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852768.528 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852768.529 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.529 * [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)))) 1546852768.530 * [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))))) 1546852768.530 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852768.530 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852768.530 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852768.530 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852768.530 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.530 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.530 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852768.530 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.530 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.530 * [misc]taylor: Taking taylor expansion of k in n 1546852768.530 * [misc]backup-simplify: Simplify k into k 1546852768.530 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852768.530 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852768.530 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.530 * [misc]backup-simplify: Simplify 2 into 2 1546852768.530 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852768.530 * [misc]taylor: Taking taylor expansion of n in n 1546852768.530 * [misc]backup-simplify: Simplify 0 into 0 1546852768.530 * [misc]backup-simplify: Simplify 1 into 1 1546852768.530 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.530 * [misc]backup-simplify: Simplify PI into PI 1546852768.530 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852768.530 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852768.531 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852768.531 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852768.531 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.531 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852768.531 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852768.532 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852768.532 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.532 * [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)))) 1546852768.533 * [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))))) 1546852768.533 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546852768.533 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546852768.533 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852768.533 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.533 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852768.533 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.533 * [misc]taylor: Taking taylor expansion of k in k 1546852768.533 * [misc]backup-simplify: Simplify 0 into 0 1546852768.533 * [misc]backup-simplify: Simplify 1 into 1 1546852768.533 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546852768.533 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852768.533 * [misc]taylor: Taking taylor expansion of n in k 1546852768.533 * [misc]backup-simplify: Simplify n into n 1546852768.533 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852768.533 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852768.533 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852768.533 * [misc]taylor: Taking taylor expansion of 2 in k 1546852768.533 * [misc]backup-simplify: Simplify 2 into 2 1546852768.533 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.533 * [misc]backup-simplify: Simplify PI into PI 1546852768.533 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.534 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.534 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852768.534 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.534 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852768.534 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.535 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546852768.535 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852768.535 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852768.536 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852768.537 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852768.538 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852768.538 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546852768.539 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.539 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.539 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.539 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546852768.540 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852768.541 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.541 * [misc]backup-simplify: Simplify 0 into 0 1546852768.541 * [misc]backup-simplify: Simplify 0 into 0 1546852768.541 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546852768.541 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852768.543 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852768.543 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.543 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852768.544 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852768.544 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852768.544 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546852768.545 * [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))))))) 1546852768.546 * [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))))))) 1546852768.547 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.548 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852768.551 * [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 1546852768.551 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546852768.551 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.551 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.552 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.552 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852768.554 * [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 1546852768.554 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.554 * [misc]backup-simplify: Simplify 0 into 0 1546852768.554 * [misc]backup-simplify: Simplify 0 into 0 1546852768.554 * [misc]backup-simplify: Simplify 0 into 0 1546852768.555 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546852768.555 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.559 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1546852768.559 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.559 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852768.559 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.559 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.560 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852768.561 * [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))))) 1546852768.563 * [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))))) 1546852768.566 * [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))))) 1546852768.566 * [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)))) 1546852768.566 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546852768.566 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.566 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.566 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.566 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.566 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of k in k 1546852768.566 * [misc]backup-simplify: Simplify 0 into 0 1546852768.566 * [misc]backup-simplify: Simplify 1 into 1 1546852768.566 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852768.566 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of 2 in k 1546852768.566 * [misc]backup-simplify: Simplify 2 into 2 1546852768.566 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852768.566 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.566 * [misc]backup-simplify: Simplify PI into PI 1546852768.566 * [misc]taylor: Taking taylor expansion of n in k 1546852768.566 * [misc]backup-simplify: Simplify n into n 1546852768.566 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852768.567 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852768.567 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852768.567 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852768.567 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852768.567 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852768.567 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852768.567 * [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)))) 1546852768.567 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852768.567 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852768.567 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852768.567 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852768.567 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.567 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.567 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852768.567 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.567 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.567 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852768.567 * [misc]taylor: Taking taylor expansion of k in n 1546852768.567 * [misc]backup-simplify: Simplify k into k 1546852768.567 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852768.568 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852768.568 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852768.568 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.568 * [misc]backup-simplify: Simplify 2 into 2 1546852768.568 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.568 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.568 * [misc]backup-simplify: Simplify PI into PI 1546852768.568 * [misc]taylor: Taking taylor expansion of n in n 1546852768.568 * [misc]backup-simplify: Simplify 0 into 0 1546852768.568 * [misc]backup-simplify: Simplify 1 into 1 1546852768.568 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.568 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.569 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.569 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852768.569 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852768.569 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852768.570 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.571 * [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))) 1546852768.571 * [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)))) 1546852768.571 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852768.571 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852768.571 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852768.571 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852768.572 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.572 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.572 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852768.572 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.572 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.572 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852768.572 * [misc]taylor: Taking taylor expansion of k in n 1546852768.572 * [misc]backup-simplify: Simplify k into k 1546852768.572 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852768.572 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852768.572 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852768.572 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.572 * [misc]backup-simplify: Simplify 2 into 2 1546852768.572 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.572 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.572 * [misc]backup-simplify: Simplify PI into PI 1546852768.572 * [misc]taylor: Taking taylor expansion of n in n 1546852768.572 * [misc]backup-simplify: Simplify 0 into 0 1546852768.572 * [misc]backup-simplify: Simplify 1 into 1 1546852768.572 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.573 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.573 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.573 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852768.573 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852768.573 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852768.574 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.575 * [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))) 1546852768.575 * [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)))) 1546852768.575 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546852768.575 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546852768.575 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852768.576 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.576 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.576 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852768.576 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.576 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.576 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852768.576 * [misc]taylor: Taking taylor expansion of k in k 1546852768.576 * [misc]backup-simplify: Simplify 0 into 0 1546852768.576 * [misc]backup-simplify: Simplify 1 into 1 1546852768.576 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852768.576 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546852768.576 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852768.576 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852768.576 * [misc]taylor: Taking taylor expansion of 2 in k 1546852768.576 * [misc]backup-simplify: Simplify 2 into 2 1546852768.576 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.576 * [misc]backup-simplify: Simplify PI into PI 1546852768.576 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.577 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.577 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852768.577 * [misc]taylor: Taking taylor expansion of n in k 1546852768.577 * [misc]backup-simplify: Simplify n into n 1546852768.577 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852768.577 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852768.577 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852768.578 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852768.578 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852768.578 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546852768.579 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546852768.579 * [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)))) 1546852768.580 * [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)))) 1546852768.581 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852768.582 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852768.584 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852768.585 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852768.585 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852768.585 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.585 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.586 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.587 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852768.588 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852768.588 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.588 * [misc]backup-simplify: Simplify 0 into 0 1546852768.589 * [misc]backup-simplify: Simplify 0 into 0 1546852768.589 * [misc]backup-simplify: Simplify 0 into 0 1546852768.590 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.591 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.596 * [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 1546852768.596 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852768.597 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852768.597 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.597 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.598 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.599 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546852768.605 * [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 1546852768.605 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.605 * [misc]backup-simplify: Simplify 0 into 0 1546852768.605 * [misc]backup-simplify: Simplify 0 into 0 1546852768.605 * [misc]backup-simplify: Simplify 0 into 0 1546852768.605 * [misc]backup-simplify: Simplify 0 into 0 1546852768.607 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.609 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.617 * [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 1546852768.617 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852768.618 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852768.618 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.618 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.619 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.620 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546852768.623 * [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 1546852768.623 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.623 * [misc]backup-simplify: Simplify 0 into 0 1546852768.623 * [misc]backup-simplify: Simplify 0 into 0 1546852768.624 * [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))))) 1546852768.624 * [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)) 1546852768.624 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546852768.624 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852768.624 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852768.624 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852768.624 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852768.624 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852768.624 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.624 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.624 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852768.624 * [misc]taylor: Taking taylor expansion of k in k 1546852768.624 * [misc]backup-simplify: Simplify 0 into 0 1546852768.624 * [misc]backup-simplify: Simplify 1 into 1 1546852768.625 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852768.625 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.625 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.625 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852768.625 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852768.625 * [misc]taylor: Taking taylor expansion of -2 in k 1546852768.625 * [misc]backup-simplify: Simplify -2 into -2 1546852768.625 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852768.625 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.625 * [misc]backup-simplify: Simplify PI into PI 1546852768.625 * [misc]taylor: Taking taylor expansion of n in k 1546852768.625 * [misc]backup-simplify: Simplify n into n 1546852768.625 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852768.625 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852768.625 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852768.625 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852768.625 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852768.625 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852768.625 * [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))) 1546852768.625 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852768.625 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852768.625 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852768.625 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852768.625 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852768.625 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.625 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.625 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852768.625 * [misc]taylor: Taking taylor expansion of k in n 1546852768.625 * [misc]backup-simplify: Simplify k into k 1546852768.625 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852768.625 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.626 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.626 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852768.626 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852768.626 * [misc]taylor: Taking taylor expansion of -2 in n 1546852768.626 * [misc]backup-simplify: Simplify -2 into -2 1546852768.626 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.626 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.626 * [misc]backup-simplify: Simplify PI into PI 1546852768.626 * [misc]taylor: Taking taylor expansion of n in n 1546852768.626 * [misc]backup-simplify: Simplify 0 into 0 1546852768.626 * [misc]backup-simplify: Simplify 1 into 1 1546852768.626 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.626 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.626 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852768.626 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852768.627 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852768.627 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.627 * [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))) 1546852768.628 * [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)))) 1546852768.628 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.628 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.628 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of k in n 1546852768.628 * [misc]backup-simplify: Simplify k into k 1546852768.628 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852768.628 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.628 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.628 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of -2 in n 1546852768.628 * [misc]backup-simplify: Simplify -2 into -2 1546852768.628 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.628 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.628 * [misc]backup-simplify: Simplify PI into PI 1546852768.628 * [misc]taylor: Taking taylor expansion of n in n 1546852768.628 * [misc]backup-simplify: Simplify 0 into 0 1546852768.628 * [misc]backup-simplify: Simplify 1 into 1 1546852768.628 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.629 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.629 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852768.629 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852768.629 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852768.629 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.630 * [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))) 1546852768.630 * [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)))) 1546852768.630 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546852768.630 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546852768.630 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852768.630 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852768.630 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.630 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.630 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852768.630 * [misc]taylor: Taking taylor expansion of k in k 1546852768.630 * [misc]backup-simplify: Simplify 0 into 0 1546852768.631 * [misc]backup-simplify: Simplify 1 into 1 1546852768.631 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852768.631 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.631 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.631 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546852768.631 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546852768.631 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546852768.631 * [misc]taylor: Taking taylor expansion of -2 in k 1546852768.631 * [misc]backup-simplify: Simplify -2 into -2 1546852768.631 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.631 * [misc]backup-simplify: Simplify PI into PI 1546852768.631 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.631 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852768.631 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852768.631 * [misc]taylor: Taking taylor expansion of n in k 1546852768.631 * [misc]backup-simplify: Simplify n into n 1546852768.631 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852768.631 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852768.632 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852768.632 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852768.632 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546852768.632 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546852768.633 * [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)))) 1546852768.633 * [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)))) 1546852768.634 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852768.634 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852768.636 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852768.636 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852768.636 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852768.636 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.637 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.637 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546852768.638 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852768.638 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.638 * [misc]backup-simplify: Simplify 0 into 0 1546852768.638 * [misc]backup-simplify: Simplify 0 into 0 1546852768.638 * [misc]backup-simplify: Simplify 0 into 0 1546852768.639 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.640 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.645 * [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 1546852768.645 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852768.646 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852768.646 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.647 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.647 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546852768.650 * [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 1546852768.650 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.650 * [misc]backup-simplify: Simplify 0 into 0 1546852768.650 * [misc]backup-simplify: Simplify 0 into 0 1546852768.650 * [misc]backup-simplify: Simplify 0 into 0 1546852768.650 * [misc]backup-simplify: Simplify 0 into 0 1546852768.652 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.653 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.661 * [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 1546852768.662 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852768.662 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852768.662 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.663 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.664 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546852768.668 * [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 1546852768.668 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.668 * [misc]backup-simplify: Simplify 0 into 0 1546852768.669 * [misc]backup-simplify: Simplify 0 into 0 1546852768.669 * [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))))) 1546852768.669 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1) 1546852768.670 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1546852768.670 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1546852768.670 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1546852768.670 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1546852768.670 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1546852768.670 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852768.670 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.670 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.670 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852768.670 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.670 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.670 * [misc]taylor: Taking taylor expansion of k in k 1546852768.670 * [misc]backup-simplify: Simplify 0 into 0 1546852768.670 * [misc]backup-simplify: Simplify 1 into 1 1546852768.670 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1546852768.670 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1546852768.670 * [misc]taylor: Taking taylor expansion of 2 in k 1546852768.670 * [misc]backup-simplify: Simplify 2 into 2 1546852768.670 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1546852768.670 * [misc]taylor: Taking taylor expansion of n in k 1546852768.670 * [misc]backup-simplify: Simplify n into n 1546852768.670 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.670 * [misc]backup-simplify: Simplify PI into PI 1546852768.670 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1546852768.670 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1546852768.670 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1546852768.671 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852768.671 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.671 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852768.671 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1546852768.671 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1546852768.671 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852768.671 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852768.671 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852768.671 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852768.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.671 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852768.671 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.671 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.671 * [misc]taylor: Taking taylor expansion of k in n 1546852768.671 * [misc]backup-simplify: Simplify k into k 1546852768.671 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852768.672 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852768.672 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.672 * [misc]backup-simplify: Simplify 2 into 2 1546852768.672 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852768.672 * [misc]taylor: Taking taylor expansion of n in n 1546852768.672 * [misc]backup-simplify: Simplify 0 into 0 1546852768.672 * [misc]backup-simplify: Simplify 1 into 1 1546852768.672 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.672 * [misc]backup-simplify: Simplify PI into PI 1546852768.672 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852768.672 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852768.673 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852768.674 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852768.674 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.674 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852768.674 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852768.674 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852768.675 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.676 * [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)))) 1546852768.676 * [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))))) 1546852768.676 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1546852768.676 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1546852768.676 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1546852768.676 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1546852768.676 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.677 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.677 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1546852768.677 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.677 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.677 * [misc]taylor: Taking taylor expansion of k in n 1546852768.677 * [misc]backup-simplify: Simplify k into k 1546852768.677 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1546852768.677 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852768.677 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.677 * [misc]backup-simplify: Simplify 2 into 2 1546852768.677 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852768.677 * [misc]taylor: Taking taylor expansion of n in n 1546852768.677 * [misc]backup-simplify: Simplify 0 into 0 1546852768.677 * [misc]backup-simplify: Simplify 1 into 1 1546852768.677 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.677 * [misc]backup-simplify: Simplify PI into PI 1546852768.677 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852768.677 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852768.678 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852768.679 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852768.679 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.679 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1546852768.679 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1546852768.679 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1546852768.680 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.681 * [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)))) 1546852768.681 * [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))))) 1546852768.681 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1546852768.681 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1546852768.681 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1546852768.681 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.681 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.681 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1546852768.681 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.681 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.682 * [misc]taylor: Taking taylor expansion of k in k 1546852768.682 * [misc]backup-simplify: Simplify 0 into 0 1546852768.682 * [misc]backup-simplify: Simplify 1 into 1 1546852768.682 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1546852768.682 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852768.682 * [misc]taylor: Taking taylor expansion of n in k 1546852768.682 * [misc]backup-simplify: Simplify n into n 1546852768.682 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852768.682 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852768.682 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852768.682 * [misc]taylor: Taking taylor expansion of 2 in k 1546852768.682 * [misc]backup-simplify: Simplify 2 into 2 1546852768.682 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.682 * [misc]backup-simplify: Simplify PI into PI 1546852768.682 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.683 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.683 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1546852768.683 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.683 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852768.684 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.684 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1546852768.685 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852768.685 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1546852768.686 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852768.687 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852768.690 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852768.691 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1546852768.691 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.691 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.692 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.692 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1546852768.694 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852768.694 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.694 * [misc]backup-simplify: Simplify 0 into 0 1546852768.694 * [misc]backup-simplify: Simplify 0 into 0 1546852768.695 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1546852768.696 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852768.699 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852768.699 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.699 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1546852768.699 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852768.699 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852768.700 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1546852768.702 * [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))))))) 1546852768.703 * [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))))))) 1546852768.705 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.706 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852768.712 * [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 1546852768.712 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1546852768.712 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.712 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.713 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1546852768.714 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852768.716 * [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 1546852768.716 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.716 * [misc]backup-simplify: Simplify 0 into 0 1546852768.716 * [misc]backup-simplify: Simplify 0 into 0 1546852768.716 * [misc]backup-simplify: Simplify 0 into 0 1546852768.718 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1546852768.719 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.722 * [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 1546852768.722 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.723 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1546852768.723 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.723 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.723 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1546852768.725 * [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))))) 1546852768.726 * [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))))) 1546852768.729 * [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))))) 1546852768.729 * [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)))) 1546852768.729 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1546852768.729 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1546852768.729 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1546852768.729 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1546852768.729 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852768.729 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.729 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.729 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852768.729 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.729 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.730 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852768.730 * [misc]taylor: Taking taylor expansion of k in k 1546852768.730 * [misc]backup-simplify: Simplify 0 into 0 1546852768.730 * [misc]backup-simplify: Simplify 1 into 1 1546852768.730 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852768.730 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1546852768.730 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1546852768.730 * [misc]taylor: Taking taylor expansion of 2 in k 1546852768.730 * [misc]backup-simplify: Simplify 2 into 2 1546852768.730 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852768.730 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.730 * [misc]backup-simplify: Simplify PI into PI 1546852768.730 * [misc]taylor: Taking taylor expansion of n in k 1546852768.730 * [misc]backup-simplify: Simplify n into n 1546852768.730 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852768.730 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1546852768.730 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1546852768.730 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852768.730 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852768.730 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852768.730 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1546852768.730 * [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)))) 1546852768.730 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.731 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.731 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.731 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of k in n 1546852768.731 * [misc]backup-simplify: Simplify k into k 1546852768.731 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852768.731 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.731 * [misc]backup-simplify: Simplify 2 into 2 1546852768.731 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.731 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.731 * [misc]backup-simplify: Simplify PI into PI 1546852768.731 * [misc]taylor: Taking taylor expansion of n in n 1546852768.731 * [misc]backup-simplify: Simplify 0 into 0 1546852768.731 * [misc]backup-simplify: Simplify 1 into 1 1546852768.731 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.731 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.732 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.732 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852768.732 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852768.732 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852768.732 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.733 * [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))) 1546852768.733 * [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)))) 1546852768.733 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.733 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.733 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.733 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.733 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of k in n 1546852768.733 * [misc]backup-simplify: Simplify k into k 1546852768.733 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852768.733 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.733 * [misc]backup-simplify: Simplify 2 into 2 1546852768.733 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.733 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.733 * [misc]backup-simplify: Simplify PI into PI 1546852768.733 * [misc]taylor: Taking taylor expansion of n in n 1546852768.733 * [misc]backup-simplify: Simplify 0 into 0 1546852768.733 * [misc]backup-simplify: Simplify 1 into 1 1546852768.734 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.734 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.734 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.734 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852768.734 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1546852768.734 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1546852768.735 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.735 * [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))) 1546852768.735 * [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)))) 1546852768.735 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1546852768.735 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1546852768.735 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1546852768.736 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.736 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852768.736 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.736 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852768.736 * [misc]taylor: Taking taylor expansion of k in k 1546852768.736 * [misc]backup-simplify: Simplify 0 into 0 1546852768.736 * [misc]backup-simplify: Simplify 1 into 1 1546852768.736 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852768.736 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1546852768.736 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1546852768.736 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1546852768.736 * [misc]taylor: Taking taylor expansion of 2 in k 1546852768.736 * [misc]backup-simplify: Simplify 2 into 2 1546852768.736 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.736 * [misc]backup-simplify: Simplify PI into PI 1546852768.736 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.736 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1546852768.736 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852768.736 * [misc]taylor: Taking taylor expansion of n in k 1546852768.736 * [misc]backup-simplify: Simplify n into n 1546852768.736 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852768.737 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852768.737 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1546852768.737 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1546852768.737 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852768.737 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1546852768.737 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1546852768.738 * [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)))) 1546852768.738 * [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)))) 1546852768.739 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852768.739 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852768.741 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1546852768.741 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852768.741 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852768.741 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.741 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.742 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.742 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1546852768.743 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852768.743 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.743 * [misc]backup-simplify: Simplify 0 into 0 1546852768.743 * [misc]backup-simplify: Simplify 0 into 0 1546852768.743 * [misc]backup-simplify: Simplify 0 into 0 1546852768.744 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.745 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.749 * [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 1546852768.749 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852768.749 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852768.749 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.749 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.750 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.750 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1546852768.752 * [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 1546852768.752 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.752 * [misc]backup-simplify: Simplify 0 into 0 1546852768.752 * [misc]backup-simplify: Simplify 0 into 0 1546852768.752 * [misc]backup-simplify: Simplify 0 into 0 1546852768.752 * [misc]backup-simplify: Simplify 0 into 0 1546852768.753 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.755 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.763 * [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 1546852768.763 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852768.764 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852768.764 * [misc]backup-simplify: Simplify (- 0) into 0 1546852768.764 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.765 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1546852768.766 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1546852768.770 * [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 1546852768.770 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.770 * [misc]backup-simplify: Simplify 0 into 0 1546852768.770 * [misc]backup-simplify: Simplify 0 into 0 1546852768.771 * [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))))) 1546852768.771 * [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)) 1546852768.771 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1546852768.771 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1546852768.771 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1546852768.771 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1546852768.771 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852768.771 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852768.771 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.771 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.771 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852768.771 * [misc]taylor: Taking taylor expansion of k in k 1546852768.771 * [misc]backup-simplify: Simplify 0 into 0 1546852768.771 * [misc]backup-simplify: Simplify 1 into 1 1546852768.771 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852768.771 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.771 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.771 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1546852768.771 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1546852768.771 * [misc]taylor: Taking taylor expansion of -2 in k 1546852768.772 * [misc]backup-simplify: Simplify -2 into -2 1546852768.772 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1546852768.772 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.772 * [misc]backup-simplify: Simplify PI into PI 1546852768.772 * [misc]taylor: Taking taylor expansion of n in k 1546852768.772 * [misc]backup-simplify: Simplify n into n 1546852768.772 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1546852768.772 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1546852768.772 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1546852768.772 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852768.772 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852768.772 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1546852768.773 * [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))) 1546852768.773 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.773 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.773 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of k in n 1546852768.773 * [misc]backup-simplify: Simplify k into k 1546852768.773 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852768.773 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.773 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.773 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of -2 in n 1546852768.773 * [misc]backup-simplify: Simplify -2 into -2 1546852768.773 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.773 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.773 * [misc]backup-simplify: Simplify PI into PI 1546852768.773 * [misc]taylor: Taking taylor expansion of n in n 1546852768.773 * [misc]backup-simplify: Simplify 0 into 0 1546852768.773 * [misc]backup-simplify: Simplify 1 into 1 1546852768.774 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.774 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.774 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852768.774 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852768.775 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852768.775 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.776 * [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))) 1546852768.776 * [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)))) 1546852768.776 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.777 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.777 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of k in n 1546852768.777 * [misc]backup-simplify: Simplify k into k 1546852768.777 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1546852768.777 * [misc]taylor: Taking taylor expansion of 1/2 in n 1546852768.777 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.777 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of -2 in n 1546852768.777 * [misc]backup-simplify: Simplify -2 into -2 1546852768.777 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.777 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.777 * [misc]backup-simplify: Simplify PI into PI 1546852768.777 * [misc]taylor: Taking taylor expansion of n in n 1546852768.777 * [misc]backup-simplify: Simplify 0 into 0 1546852768.777 * [misc]backup-simplify: Simplify 1 into 1 1546852768.777 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.778 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.778 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852768.778 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1546852768.778 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1546852768.779 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.779 * [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))) 1546852768.780 * [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)))) 1546852768.780 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1546852768.780 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1546852768.780 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1546852768.780 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1546852768.780 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.780 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.780 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1546852768.780 * [misc]taylor: Taking taylor expansion of k in k 1546852768.780 * [misc]backup-simplify: Simplify 0 into 0 1546852768.780 * [misc]backup-simplify: Simplify 1 into 1 1546852768.780 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1546852768.780 * [misc]taylor: Taking taylor expansion of 1/2 in k 1546852768.780 * [misc]backup-simplify: Simplify 1/2 into 1/2 1546852768.780 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1546852768.780 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1546852768.780 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1546852768.780 * [misc]taylor: Taking taylor expansion of -2 in k 1546852768.780 * [misc]backup-simplify: Simplify -2 into -2 1546852768.780 * [misc]taylor: Taking taylor expansion of PI in k 1546852768.780 * [misc]backup-simplify: Simplify PI into PI 1546852768.780 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.781 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1546852768.781 * [misc]taylor: Taking taylor expansion of (log n) in k 1546852768.781 * [misc]taylor: Taking taylor expansion of n in k 1546852768.781 * [misc]backup-simplify: Simplify n into n 1546852768.781 * [misc]backup-simplify: Simplify (log n) into (log n) 1546852768.781 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1546852768.781 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1546852768.781 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1546852768.781 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1546852768.782 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1546852768.782 * [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)))) 1546852768.782 * [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)))) 1546852768.783 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852768.784 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852768.785 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1546852768.785 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1546852768.785 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1546852768.786 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.786 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.786 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1546852768.787 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1546852768.787 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.787 * [misc]backup-simplify: Simplify 0 into 0 1546852768.787 * [misc]backup-simplify: Simplify 0 into 0 1546852768.787 * [misc]backup-simplify: Simplify 0 into 0 1546852768.788 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.789 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.792 * [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 1546852768.792 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852768.792 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1546852768.792 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.793 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.793 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1546852768.795 * [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 1546852768.795 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.795 * [misc]backup-simplify: Simplify 0 into 0 1546852768.795 * [misc]backup-simplify: Simplify 0 into 0 1546852768.795 * [misc]backup-simplify: Simplify 0 into 0 1546852768.795 * [misc]backup-simplify: Simplify 0 into 0 1546852768.796 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.797 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.802 * [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 1546852768.802 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1546852768.802 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1546852768.802 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1546852768.803 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1546852768.803 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1546852768.805 * [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 1546852768.806 * [misc]taylor: Taking taylor expansion of 0 in k 1546852768.806 * [misc]backup-simplify: Simplify 0 into 0 1546852768.806 * [misc]backup-simplify: Simplify 0 into 0 1546852768.806 * [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))))) 1546852768.806 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1 1 1) 1546852768.806 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546852768.806 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546852768.806 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852768.806 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.806 * [misc]backup-simplify: Simplify 2 into 2 1546852768.806 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852768.806 * [misc]taylor: Taking taylor expansion of n in n 1546852768.806 * [misc]backup-simplify: Simplify 0 into 0 1546852768.806 * [misc]backup-simplify: Simplify 1 into 1 1546852768.806 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.806 * [misc]backup-simplify: Simplify PI into PI 1546852768.806 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852768.806 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.806 * [misc]backup-simplify: Simplify 2 into 2 1546852768.806 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852768.806 * [misc]taylor: Taking taylor expansion of n in n 1546852768.806 * [misc]backup-simplify: Simplify 0 into 0 1546852768.806 * [misc]backup-simplify: Simplify 1 into 1 1546852768.806 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.806 * [misc]backup-simplify: Simplify PI into PI 1546852768.807 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852768.807 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852768.807 * [misc]backup-simplify: Simplify 0 into 0 1546852768.807 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852768.808 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852768.808 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.808 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852768.809 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852768.809 * [misc]backup-simplify: Simplify 0 into 0 1546852768.810 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.811 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852768.811 * [misc]backup-simplify: Simplify 0 into 0 1546852768.813 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852768.815 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546852768.815 * [misc]backup-simplify: Simplify 0 into 0 1546852768.818 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852768.821 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546852768.821 * [misc]backup-simplify: Simplify 0 into 0 1546852768.824 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852768.827 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546852768.828 * [misc]backup-simplify: Simplify 0 into 0 1546852768.832 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546852768.836 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546852768.836 * [misc]backup-simplify: Simplify 0 into 0 1546852768.837 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546852768.837 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546852768.837 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546852768.837 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852768.837 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.837 * [misc]backup-simplify: Simplify 2 into 2 1546852768.837 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.837 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.837 * [misc]backup-simplify: Simplify PI into PI 1546852768.837 * [misc]taylor: Taking taylor expansion of n in n 1546852768.837 * [misc]backup-simplify: Simplify 0 into 0 1546852768.837 * [misc]backup-simplify: Simplify 1 into 1 1546852768.837 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.837 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852768.837 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.837 * [misc]backup-simplify: Simplify 2 into 2 1546852768.837 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.837 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.837 * [misc]backup-simplify: Simplify PI into PI 1546852768.837 * [misc]taylor: Taking taylor expansion of n in n 1546852768.837 * [misc]backup-simplify: Simplify 0 into 0 1546852768.838 * [misc]backup-simplify: Simplify 1 into 1 1546852768.838 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.838 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.838 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.840 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852768.840 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852768.840 * [misc]backup-simplify: Simplify 0 into 0 1546852768.842 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.843 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.843 * [misc]backup-simplify: Simplify 0 into 0 1546852768.844 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.846 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.846 * [misc]backup-simplify: Simplify 0 into 0 1546852768.848 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.850 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852768.850 * [misc]backup-simplify: Simplify 0 into 0 1546852768.852 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.855 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852768.855 * [misc]backup-simplify: Simplify 0 into 0 1546852768.858 * [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 1546852768.861 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852768.861 * [misc]backup-simplify: Simplify 0 into 0 1546852768.862 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546852768.862 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546852768.862 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546852768.862 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852768.862 * [misc]taylor: Taking taylor expansion of -2 in n 1546852768.862 * [misc]backup-simplify: Simplify -2 into -2 1546852768.862 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.862 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.862 * [misc]backup-simplify: Simplify PI into PI 1546852768.862 * [misc]taylor: Taking taylor expansion of n in n 1546852768.862 * [misc]backup-simplify: Simplify 0 into 0 1546852768.862 * [misc]backup-simplify: Simplify 1 into 1 1546852768.862 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.862 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852768.862 * [misc]taylor: Taking taylor expansion of -2 in n 1546852768.862 * [misc]backup-simplify: Simplify -2 into -2 1546852768.862 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.863 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.863 * [misc]backup-simplify: Simplify PI into PI 1546852768.863 * [misc]taylor: Taking taylor expansion of n in n 1546852768.863 * [misc]backup-simplify: Simplify 0 into 0 1546852768.863 * [misc]backup-simplify: Simplify 1 into 1 1546852768.863 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.863 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.863 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.865 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852768.865 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852768.865 * [misc]backup-simplify: Simplify 0 into 0 1546852768.867 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.868 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.868 * [misc]backup-simplify: Simplify 0 into 0 1546852768.869 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.871 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.871 * [misc]backup-simplify: Simplify 0 into 0 1546852768.873 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.875 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852768.875 * [misc]backup-simplify: Simplify 0 into 0 1546852768.878 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.881 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852768.881 * [misc]backup-simplify: Simplify 0 into 0 1546852768.884 * [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 1546852768.888 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852768.888 * [misc]backup-simplify: Simplify 0 into 0 1546852768.888 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546852768.888 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1 1 1) 1546852768.889 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1546852768.889 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1546852768.889 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852768.889 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.889 * [misc]backup-simplify: Simplify 2 into 2 1546852768.889 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852768.889 * [misc]taylor: Taking taylor expansion of n in n 1546852768.889 * [misc]backup-simplify: Simplify 0 into 0 1546852768.889 * [misc]backup-simplify: Simplify 1 into 1 1546852768.889 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.889 * [misc]backup-simplify: Simplify PI into PI 1546852768.889 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1546852768.889 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.889 * [misc]backup-simplify: Simplify 2 into 2 1546852768.889 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1546852768.889 * [misc]taylor: Taking taylor expansion of n in n 1546852768.889 * [misc]backup-simplify: Simplify 0 into 0 1546852768.889 * [misc]backup-simplify: Simplify 1 into 1 1546852768.889 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.889 * [misc]backup-simplify: Simplify PI into PI 1546852768.890 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1546852768.890 * [misc]backup-simplify: Simplify (* 2 0) into 0 1546852768.890 * [misc]backup-simplify: Simplify 0 into 0 1546852768.891 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1546852768.891 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1546852768.892 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.893 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1546852768.894 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1546852768.894 * [misc]backup-simplify: Simplify 0 into 0 1546852768.895 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.897 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1546852768.897 * [misc]backup-simplify: Simplify 0 into 0 1546852768.899 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852768.901 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1546852768.901 * [misc]backup-simplify: Simplify 0 into 0 1546852768.904 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852768.907 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1546852768.907 * [misc]backup-simplify: Simplify 0 into 0 1546852768.910 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852768.914 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1546852768.914 * [misc]backup-simplify: Simplify 0 into 0 1546852768.918 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1546852768.921 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1546852768.921 * [misc]backup-simplify: Simplify 0 into 0 1546852768.921 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1546852768.921 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1546852768.921 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1546852768.921 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852768.921 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.921 * [misc]backup-simplify: Simplify 2 into 2 1546852768.921 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.921 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.921 * [misc]backup-simplify: Simplify PI into PI 1546852768.921 * [misc]taylor: Taking taylor expansion of n in n 1546852768.921 * [misc]backup-simplify: Simplify 0 into 0 1546852768.921 * [misc]backup-simplify: Simplify 1 into 1 1546852768.922 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.922 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1546852768.922 * [misc]taylor: Taking taylor expansion of 2 in n 1546852768.922 * [misc]backup-simplify: Simplify 2 into 2 1546852768.922 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.922 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.922 * [misc]backup-simplify: Simplify PI into PI 1546852768.922 * [misc]taylor: Taking taylor expansion of n in n 1546852768.922 * [misc]backup-simplify: Simplify 0 into 0 1546852768.922 * [misc]backup-simplify: Simplify 1 into 1 1546852768.922 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.922 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.922 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1546852768.923 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852768.923 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1546852768.923 * [misc]backup-simplify: Simplify 0 into 0 1546852768.924 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.925 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.925 * [misc]backup-simplify: Simplify 0 into 0 1546852768.926 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.927 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.927 * [misc]backup-simplify: Simplify 0 into 0 1546852768.928 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.929 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852768.930 * [misc]backup-simplify: Simplify 0 into 0 1546852768.931 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.933 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852768.933 * [misc]backup-simplify: Simplify 0 into 0 1546852768.934 * [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 1546852768.936 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852768.936 * [misc]backup-simplify: Simplify 0 into 0 1546852768.937 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1546852768.937 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1546852768.937 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1546852768.937 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852768.937 * [misc]taylor: Taking taylor expansion of -2 in n 1546852768.937 * [misc]backup-simplify: Simplify -2 into -2 1546852768.937 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.937 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.937 * [misc]backup-simplify: Simplify PI into PI 1546852768.937 * [misc]taylor: Taking taylor expansion of n in n 1546852768.937 * [misc]backup-simplify: Simplify 0 into 0 1546852768.937 * [misc]backup-simplify: Simplify 1 into 1 1546852768.937 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.937 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1546852768.937 * [misc]taylor: Taking taylor expansion of -2 in n 1546852768.937 * [misc]backup-simplify: Simplify -2 into -2 1546852768.937 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1546852768.937 * [misc]taylor: Taking taylor expansion of PI in n 1546852768.937 * [misc]backup-simplify: Simplify PI into PI 1546852768.937 * [misc]taylor: Taking taylor expansion of n in n 1546852768.937 * [misc]backup-simplify: Simplify 0 into 0 1546852768.937 * [misc]backup-simplify: Simplify 1 into 1 1546852768.937 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1546852768.938 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.938 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1546852768.938 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1546852768.939 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1546852768.939 * [misc]backup-simplify: Simplify 0 into 0 1546852768.940 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.940 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1546852768.940 * [misc]backup-simplify: Simplify 0 into 0 1546852768.941 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.942 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1546852768.942 * [misc]backup-simplify: Simplify 0 into 0 1546852768.944 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.945 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1546852768.945 * [misc]backup-simplify: Simplify 0 into 0 1546852768.946 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1546852768.948 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1546852768.948 * [misc]backup-simplify: Simplify 0 into 0 1546852768.949 * [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 1546852768.951 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1546852768.952 * [misc]backup-simplify: Simplify 0 into 0 1546852768.952 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1546852768.952 * * * [misc]progress: simplifying candidates 1546852768.952 * * * * [misc]progress: [ 1 / 64 ] simplifiying candidate # 1546852768.952 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546852768.952 * * [misc]simplify: iters left: 6 (11 enodes) 1546852768.954 * * [misc]simplify: iters left: 5 (21 enodes) 1546852768.958 * * [misc]simplify: iters left: 4 (47 enodes) 1546852768.974 * * [misc]simplify: iters left: 3 (109 enodes) 1546852769.025 * * [misc]simplify: iters left: 2 (300 enodes) 1546852769.242 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546852769.243 * [misc]simplify: Simplified (2 2 1 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))))) 1546852769.243 * * * * [misc]progress: [ 2 / 64 ] simplifiying candidate # 1546852769.243 * * * * [misc]progress: [ 3 / 64 ] simplifiying candidate # 1546852769.243 * [enter]simplify: Simplifying (* PI (* n 2)) 1546852769.243 * * [misc]simplify: iters left: 4 (5 enodes) 1546852769.245 * * [misc]simplify: iters left: 3 (9 enodes) 1546852769.247 * * [misc]simplify: iters left: 2 (15 enodes) 1546852769.249 * * [misc]simplify: iters left: 1 (17 enodes) 1546852769.251 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546852769.251 * [misc]simplify: Simplified (2 2 1 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))))) 1546852769.252 * * * * [misc]progress: [ 4 / 64 ] simplifiying candidate # 1546852769.252 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852769.252 * * [misc]simplify: iters left: 5 (8 enodes) 1546852769.253 * * [misc]simplify: iters left: 4 (12 enodes) 1546852769.255 * * [misc]simplify: iters left: 3 (18 enodes) 1546852769.257 * * [misc]simplify: iters left: 2 (20 enodes) 1546852769.260 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852769.260 * [misc]simplify: Simplified (2 2 1 1 2) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))))) 1546852769.260 * * * * [misc]progress: [ 5 / 64 ] simplifiying candidate # 1546852769.260 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546852769.260 * * [misc]simplify: iters left: 5 (6 enodes) 1546852769.261 * * [misc]simplify: iters left: 4 (8 enodes) 1546852769.263 * * [misc]simplify: iters left: 3 (11 enodes) 1546852769.264 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546852769.264 * [misc]simplify: Simplified (2 2 1 1 2) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))))) 1546852769.264 * * * * [misc]progress: [ 6 / 64 ] simplifiying candidate # 1546852769.265 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546852769.265 * * [misc]simplify: iters left: 5 (6 enodes) 1546852769.265 * * [misc]simplify: iters left: 4 (8 enodes) 1546852769.267 * * [misc]simplify: iters left: 3 (11 enodes) 1546852769.268 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546852769.268 * [misc]simplify: Simplified (2 2 1 1 2) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))))) 1546852769.268 * * * * [misc]progress: [ 7 / 64 ] simplifiying candidate # 1546852769.268 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546852769.269 * * [misc]simplify: iters left: 4 (5 enodes) 1546852769.269 * * [misc]simplify: iters left: 3 (7 enodes) 1546852769.270 * * [misc]simplify: iters left: 2 (10 enodes) 1546852769.272 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546852769.272 * [misc]simplify: Simplified (2 2 1 1 2) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.272 * * * * [misc]progress: [ 8 / 64 ] simplifiying candidate # 1546852769.272 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852769.272 * * [misc]simplify: iters left: 5 (9 enodes) 1546852769.274 * * [misc]simplify: iters left: 4 (15 enodes) 1546852769.276 * * [misc]simplify: iters left: 3 (21 enodes) 1546852769.279 * * [misc]simplify: iters left: 2 (22 enodes) 1546852769.281 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852769.281 * [misc]simplify: Simplified (2 2 1 1 2) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))))) 1546852769.281 * * * * [misc]progress: [ 9 / 64 ] simplifiying candidate # 1546852769.282 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852769.282 * * [misc]simplify: iters left: 5 (9 enodes) 1546852769.283 * * [misc]simplify: iters left: 4 (15 enodes) 1546852769.288 * * [misc]simplify: iters left: 3 (21 enodes) 1546852769.297 * * [misc]simplify: iters left: 2 (22 enodes) 1546852769.302 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852769.302 * [misc]simplify: Simplified (2 2 1 1 2) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))))) 1546852769.302 * * * * [misc]progress: [ 10 / 64 ] simplifiying candidate # 1546852769.303 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546852769.303 * * [misc]simplify: iters left: 5 (7 enodes) 1546852769.305 * * [misc]simplify: iters left: 4 (9 enodes) 1546852769.308 * * [misc]simplify: iters left: 3 (12 enodes) 1546852769.311 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546852769.311 * [misc]simplify: Simplified (2 2 1 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))))) 1546852769.311 * * * * [misc]progress: [ 11 / 64 ] simplifiying candidate # 1546852769.311 * * * * [misc]progress: [ 12 / 64 ] simplifiying candidate # 1546852769.312 * * * * [misc]progress: [ 13 / 64 ] simplifiying candidate # 1546852769.312 * * * * [misc]progress: [ 14 / 64 ] simplifiying candidate # 1546852769.312 * * * * [misc]progress: [ 15 / 64 ] simplifiying candidate # 1546852769.312 * * * * [misc]progress: [ 16 / 64 ] simplifiying candidate # 1546852769.312 * * * * [misc]progress: [ 17 / 64 ] simplifiying candidate # 1546852769.312 * * * * [misc]progress: [ 18 / 64 ] simplifiying candidate # 1546852769.312 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1546852769.312 * * [misc]simplify: iters left: 6 (11 enodes) 1546852769.316 * * [misc]simplify: iters left: 5 (21 enodes) 1546852769.324 * * [misc]simplify: iters left: 4 (47 enodes) 1546852769.340 * * [misc]simplify: iters left: 3 (109 enodes) 1546852769.381 * * [misc]simplify: iters left: 2 (300 enodes) 1546852769.585 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1546852769.585 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (* (sqrt (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.585 * * * * [misc]progress: [ 19 / 64 ] simplifiying candidate # 1546852769.585 * * * * [misc]progress: [ 20 / 64 ] simplifiying candidate # 1546852769.586 * [enter]simplify: Simplifying (* PI (* n 2)) 1546852769.586 * * [misc]simplify: iters left: 4 (5 enodes) 1546852769.587 * * [misc]simplify: iters left: 3 (9 enodes) 1546852769.590 * * [misc]simplify: iters left: 2 (15 enodes) 1546852769.594 * * [misc]simplify: iters left: 1 (17 enodes) 1546852769.597 * [exit]simplify: Simplified to (* (* 2 n) PI) 1546852769.597 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (* (sqrt (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.597 * * * * [misc]progress: [ 21 / 64 ] simplifiying candidate # 1546852769.597 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1546852769.597 * * [misc]simplify: iters left: 5 (8 enodes) 1546852769.598 * * [misc]simplify: iters left: 4 (12 enodes) 1546852769.600 * * [misc]simplify: iters left: 3 (18 enodes) 1546852769.603 * * [misc]simplify: iters left: 2 (20 enodes) 1546852769.605 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1546852769.605 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (* (sqrt (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.605 * * * * [misc]progress: [ 22 / 64 ] simplifiying candidate # 1546852769.606 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1546852769.606 * * [misc]simplify: iters left: 5 (6 enodes) 1546852769.607 * * [misc]simplify: iters left: 4 (8 enodes) 1546852769.608 * * [misc]simplify: iters left: 3 (11 enodes) 1546852769.609 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1546852769.609 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (* (sqrt (/ (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.609 * * * * [misc]progress: [ 23 / 64 ] simplifiying candidate # 1546852769.610 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1546852769.610 * * [misc]simplify: iters left: 5 (6 enodes) 1546852769.610 * * [misc]simplify: iters left: 4 (8 enodes) 1546852769.612 * * [misc]simplify: iters left: 3 (11 enodes) 1546852769.613 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1546852769.613 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (* (sqrt (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.613 * * * * [misc]progress: [ 24 / 64 ] simplifiying candidate # 1546852769.613 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1546852769.613 * * [misc]simplify: iters left: 4 (5 enodes) 1546852769.614 * * [misc]simplify: iters left: 3 (7 enodes) 1546852769.615 * * [misc]simplify: iters left: 2 (10 enodes) 1546852769.617 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1546852769.617 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (* (sqrt (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.617 * * * * [misc]progress: [ 25 / 64 ] simplifiying candidate # 1546852769.617 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852769.617 * * [misc]simplify: iters left: 5 (9 enodes) 1546852769.618 * * [misc]simplify: iters left: 4 (15 enodes) 1546852769.621 * * [misc]simplify: iters left: 3 (21 enodes) 1546852769.624 * * [misc]simplify: iters left: 2 (22 enodes) 1546852769.629 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852769.629 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (* (sqrt (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.629 * * * * [misc]progress: [ 26 / 64 ] simplifiying candidate # 1546852769.629 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1546852769.630 * * [misc]simplify: iters left: 5 (9 enodes) 1546852769.632 * * [misc]simplify: iters left: 4 (15 enodes) 1546852769.637 * * [misc]simplify: iters left: 3 (21 enodes) 1546852769.642 * * [misc]simplify: iters left: 2 (22 enodes) 1546852769.648 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1546852769.648 * [misc]simplify: Simplified (2 1 1 1 2) to (λ (k n) (* (sqrt (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.648 * * * * [misc]progress: [ 27 / 64 ] simplifiying candidate # 1546852769.648 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1546852769.648 * * [misc]simplify: iters left: 5 (7 enodes) 1546852769.650 * * [misc]simplify: iters left: 4 (9 enodes) 1546852769.653 * * [misc]simplify: iters left: 3 (12 enodes) 1546852769.656 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1546852769.656 * [misc]simplify: Simplified (2 1 1 1 1) to (λ (k n) (* (sqrt (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852769.656 * * * * [misc]progress: [ 28 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 29 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 30 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 31 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 32 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 33 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 34 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 35 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 36 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 37 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 38 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 39 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 40 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 41 / 64 ] simplifiying candidate # 1546852769.657 * * * * [misc]progress: [ 42 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 43 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 44 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 45 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 46 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 47 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 48 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 49 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 50 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 51 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 52 / 64 ] simplifiying candidate # 1546852769.658 * * * * [misc]progress: [ 53 / 64 ] simplifiying candidate # 1546852769.659 * [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))))) 1546852769.659 * * [misc]simplify: iters left: 6 (37 enodes) 1546852769.674 * * [misc]simplify: iters left: 5 (105 enodes) 1546852769.710 * * [misc]simplify: iters left: 4 (339 enodes) 1546852769.900 * [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))))) 1546852769.900 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (+ (+ (* (* (* (* 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))))) 1546852769.900 * * * * [misc]progress: [ 54 / 64 ] simplifiying candidate # 1546852769.900 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546852769.900 * * [misc]simplify: iters left: 6 (15 enodes) 1546852769.904 * * [misc]simplify: iters left: 5 (33 enodes) 1546852769.910 * * [misc]simplify: iters left: 4 (64 enodes) 1546852769.922 * * [misc]simplify: iters left: 3 (171 enodes) 1546852770.037 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546852770.037 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))))) 1546852770.037 * * * * [misc]progress: [ 55 / 64 ] simplifiying candidate # 1546852770.037 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546852770.037 * * [misc]simplify: iters left: 6 (15 enodes) 1546852770.043 * * [misc]simplify: iters left: 5 (30 enodes) 1546852770.053 * * [misc]simplify: iters left: 4 (65 enodes) 1546852770.068 * * [misc]simplify: iters left: 3 (200 enodes) 1546852770.158 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546852770.158 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))))) 1546852770.158 * * * * [misc]progress: [ 56 / 64 ] simplifiying candidate # 1546852770.159 * [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))))) 1546852770.159 * * [misc]simplify: iters left: 6 (37 enodes) 1546852770.167 * * [misc]simplify: iters left: 5 (105 enodes) 1546852770.193 * * [misc]simplify: iters left: 4 (339 enodes) 1546852770.377 * [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))))) 1546852770.377 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (+ (+ (* (* (* (* 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))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852770.377 * * * * [misc]progress: [ 57 / 64 ] simplifiying candidate # 1546852770.378 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1546852770.378 * * [misc]simplify: iters left: 6 (15 enodes) 1546852770.384 * * [misc]simplify: iters left: 5 (33 enodes) 1546852770.395 * * [misc]simplify: iters left: 4 (64 enodes) 1546852770.419 * * [misc]simplify: iters left: 3 (171 enodes) 1546852770.522 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1546852770.522 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852770.522 * * * * [misc]progress: [ 58 / 64 ] simplifiying candidate # 1546852770.522 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1546852770.522 * * [misc]simplify: iters left: 6 (15 enodes) 1546852770.525 * * [misc]simplify: iters left: 5 (30 enodes) 1546852770.532 * * [misc]simplify: iters left: 4 (65 enodes) 1546852770.557 * * [misc]simplify: iters left: 3 (200 enodes) 1546852770.657 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1546852770.657 * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (* (sqrt (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))) 1546852770.657 * * * * [misc]progress: [ 59 / 64 ] simplifiying candidate # 1546852770.658 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852770.658 * * [misc]simplify: iters left: 4 (5 enodes) 1546852770.659 * * [misc]simplify: iters left: 3 (9 enodes) 1546852770.660 * * [misc]simplify: iters left: 2 (15 enodes) 1546852770.662 * * [misc]simplify: iters left: 1 (17 enodes) 1546852770.665 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852770.665 * [misc]simplify: Simplified (2 2 1 1 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))) (sqrt k))))) 1546852770.665 * * * * [misc]progress: [ 60 / 64 ] simplifiying candidate # 1546852770.665 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852770.665 * * [misc]simplify: iters left: 4 (5 enodes) 1546852770.667 * * [misc]simplify: iters left: 3 (9 enodes) 1546852770.670 * * [misc]simplify: iters left: 2 (15 enodes) 1546852770.673 * * [misc]simplify: iters left: 1 (17 enodes) 1546852770.681 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852770.681 * [misc]simplify: Simplified (2 2 1 1 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))) (sqrt k))))) 1546852770.681 * * * * [misc]progress: [ 61 / 64 ] simplifiying candidate # 1546852770.681 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852770.682 * * [misc]simplify: iters left: 4 (5 enodes) 1546852770.683 * * [misc]simplify: iters left: 3 (9 enodes) 1546852770.686 * * [misc]simplify: iters left: 2 (15 enodes) 1546852770.689 * * [misc]simplify: iters left: 1 (17 enodes) 1546852770.691 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852770.691 * [misc]simplify: Simplified (2 2 1 1 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))) (sqrt k))))) 1546852770.691 * * * * [misc]progress: [ 62 / 64 ] simplifiying candidate # 1546852770.691 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852770.691 * * [misc]simplify: iters left: 4 (5 enodes) 1546852770.692 * * [misc]simplify: iters left: 3 (9 enodes) 1546852770.693 * * [misc]simplify: iters left: 2 (15 enodes) 1546852770.696 * * [misc]simplify: iters left: 1 (17 enodes) 1546852770.697 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852770.698 * [misc]simplify: Simplified (2 1 1 1 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))) (sqrt k))))) 1546852770.698 * * * * [misc]progress: [ 63 / 64 ] simplifiying candidate # 1546852770.698 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852770.698 * * [misc]simplify: iters left: 4 (5 enodes) 1546852770.699 * * [misc]simplify: iters left: 3 (9 enodes) 1546852770.700 * * [misc]simplify: iters left: 2 (15 enodes) 1546852770.702 * * [misc]simplify: iters left: 1 (17 enodes) 1546852770.704 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852770.704 * [misc]simplify: Simplified (2 1 1 1 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))) (sqrt k))))) 1546852770.704 * * * * [misc]progress: [ 64 / 64 ] simplifiying candidate # 1546852770.704 * [enter]simplify: Simplifying (* 2 (* n PI)) 1546852770.704 * * [misc]simplify: iters left: 4 (5 enodes) 1546852770.705 * * [misc]simplify: iters left: 3 (9 enodes) 1546852770.707 * * [misc]simplify: iters left: 2 (15 enodes) 1546852770.709 * * [misc]simplify: iters left: 1 (17 enodes) 1546852770.711 * [exit]simplify: Simplified to (* (* PI n) 2) 1546852770.711 * [misc]simplify: Simplified (2 1 1 1 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))) (sqrt k))))) 1546852770.711 * * * [misc]progress: adding candidates to table 1546852771.708 * [misc]progress: [Phase 3 of 3] Extracting. 1546852771.708 * * [misc]regime: Finding splitpoints for: (# # # # # # # #) 1546852771.711 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1546852771.711 * * * * [misc]regimes: Trying to branch on n from (# # # # # # # #) 1546852771.772 * * * * [misc]regimes: Trying to branch on k from (# # # # # # # #) 1546852771.845 * * * [misc]regime: Found split indices: #