* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * [misc]progress: [2/2] Setting up program. * [misc]progress: [Phase 2 of 3] Improving. * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]progress: iteration 1 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 3 ] rewriting at (2) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 3 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 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 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (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 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* n (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 3 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 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 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 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 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 2 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 3 / 81 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (+ PI PI))) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (254 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 5 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (+ PI PI))) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (254 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 6 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (120 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 7 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (119 enodes) * * [misc]simplify: iters left: 1 (204 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 8 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 9 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (341 enodes) * [exit]simplify: Simplified to (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (* k (sqrt k)))) * [exit]simplify: Simplified to (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (* k (sqrt k)))) * * * * [misc]progress: [ 10 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 11 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (155 enodes) * [exit]simplify: Simplified to (/ (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (pow (* (+ n n) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (pow (* (+ n n) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 12 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 13 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (- (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (- (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 14 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 15 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 16 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) 1) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) 1) * [enter]simplify: Simplifying (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 17 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 18 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 19 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)) * [enter]simplify: Simplifying (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 20 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 21 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 22 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1) * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 23 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 24 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 25 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 26 / 81 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 28 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 29 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 30 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 31 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1) * * * * [misc]progress: [ 32 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 33 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 34 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 35 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 36 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (* PI (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (* PI (+ n n)) (/ k 2))) * * * * [misc]progress: [ 37 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * * * * [misc]progress: [ 38 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * * * * [misc]progress: [ 39 / 81 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * * [misc]simplify: iters left: 1 (46 enodes) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * * * * [misc]progress: [ 41 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * * * * [misc]progress: [ 42 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [enter]simplify: Simplifying (cbrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * * * * [misc]progress: [ 43 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (426 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * * * * [misc]progress: [ 44 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * * * * [misc]progress: [ 45 / 81 ] simplifiying candidate # * * * * [misc]progress: [ 46 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 47 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 48 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * * * [misc]progress: [ 49 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (sqrt (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * * * * [misc]progress: [ 50 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to n * [exit]simplify: Simplified to n * * * * [misc]progress: [ 51 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (+ n n) * [exit]simplify: Simplified to (+ n n) * * * * [misc]progress: [ 52 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (+ (pow PI 3) (pow PI 3))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * * * * [misc]progress: [ 53 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (- (* PI PI) (* PI PI))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to 0 * [exit]simplify: Simplified to 0 * * * * [misc]progress: [ 54 / 81 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 56 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 57 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (+ PI PI))) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (142 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k))) * * * * [misc]progress: [ 58 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (+ PI PI))) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (142 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k))) * * * * [misc]progress: [ 59 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (37 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 60 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ 1 2)) * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ k 2)) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ k 2)) * * * * [misc]progress: [ 61 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 62 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 63 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * [exit]simplify: Simplified to (* n (+ PI PI)) * [exit]simplify: Simplified to (* n (+ PI PI)) * * * * [misc]progress: [ 64 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (- 1 k)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (pow (+ (* PI n) (* PI n)) (- 1 k)) * [exit]simplify: Simplified to (pow (+ (* PI n) (* PI n)) (- 1 k)) * * * * [misc]progress: [ 65 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow (+ PI PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (pow (+ PI PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ PI PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 66 / 81 ] simplifiying candidate # * * * * [misc]progress: [ 67 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* n (+ PI PI)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* n (+ PI PI)))) * * * * [misc]progress: [ 68 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 69 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 70 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 71 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 72 / 81 ] simplifiying candidate # * * * * [misc]progress: [ 73 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 74 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * * * * [misc]progress: [ 75 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 76 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 77 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 78 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 79 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) (sqrt k)) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (112 enodes) * * [misc]simplify: iters left: 4 (355 enodes) * [exit]simplify: Simplified to (/ (+ (* (* (* (pow (+ PI PI) 1/2) (* (pow n 1/2) 1/8)) (* k k)) (+ (* (log (+ PI PI)) (log (+ PI PI))) (* (log n) (log n)))) (- (fma (* (pow (+ PI PI) 1/2) (* (pow n 1/2) 1/4)) (* (log (+ PI PI)) (* (* k k) (log n))) (* (pow n 1/2) (pow (+ PI PI) 1/2))) (* (* (pow (+ PI PI) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (+ PI PI)) (* (log n) k))))) (sqrt k)) * * * * [misc]progress: [ 80 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (236 enodes) * [exit]simplify: Simplified to (/ (pow (exp (* (- 1 k) 1/2)) (- (log (+ PI PI)) (- (log n)))) (sqrt k)) * * * * [misc]progress: [ 81 / 81 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * [exit]simplify: Simplified to (/ (pow (exp (* (- 1 k) 1/2)) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k)) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 2 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ k 2) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* n (* 2 PI))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (sqrt (* n (* 2 PI))) +nan.0) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (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 (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) +nan.0) (* (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (* (sqrt (/ PI n)) (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 2 1) * [misc]approximate: Taking taylor expansion of (* n (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1 1) * [misc]approximate: Taking taylor expansion of (* n (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 2 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 3 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (+ PI PI))) (/ 1 2)) (* (log (* n (+ PI PI))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (242 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 5 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (+ PI PI))) (/ 1 2)) (* (log (* n (+ PI PI))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (242 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 6 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (+ PI PI))) (/ 1 2)) (log (pow (* n (+ PI PI)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 7 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (+ PI PI))) (/ 1 2)) (* (log (* n (+ PI PI))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (242 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 8 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (+ PI PI))) (/ 1 2)) (* (log (* n (+ PI PI))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (242 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 9 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* n (+ PI PI))) (/ 1 2)) (log (pow (* n (+ PI PI)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 10 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* n (+ PI PI)) (/ 1 2))) (* (log (* n (+ PI PI))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 11 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* n (+ PI PI)) (/ 1 2))) (* (log (* n (+ PI PI))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 12 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* n (+ PI PI)) (/ 1 2))) (log (pow (* n (+ PI PI)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (330 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 13 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI)))) (log (sqrt k))) * * * * [misc]progress: [ 14 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 15 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (exp (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 16 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ 1 2))) (* (* (pow (* n (+ PI PI)) (/ k 2)) (pow (* n (+ PI PI)) (/ k 2))) (pow (* n (+ PI PI)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (395 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (* (sqrt k) k) (/ (pow (* n (+ PI PI)) (/ k 2)) (pow (* n (+ PI PI)) (/ 1 2))))) * [exit]simplify: Simplified to (/ (* (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (* (sqrt k) k) (/ (pow (* n (+ PI PI)) (/ k 2)) (pow (* n (+ PI PI)) (/ 1 2))))) * * * * [misc]progress: [ 17 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (103 enodes) * * [misc]simplify: iters left: 3 (276 enodes) * [exit]simplify: Simplified to (* (* (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (pow (* n (+ PI PI)) (/ k 2)) (* (sqrt k) k)))) * [exit]simplify: Simplified to (* (* (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (pow (* n (+ PI PI)) (/ k 2)) (* (sqrt k) k)))) * * * * [misc]progress: [ 18 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2)))))) * [enter]simplify: Simplifying (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 19 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (201 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k))) (/ (* k (pow (* (+ n n) PI) (/ k 2))) (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (* (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k))) (/ (* k (pow (* (+ n n) PI) (/ k 2))) (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) * * * * [misc]progress: [ 20 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * [enter]simplify: Simplifying (sqrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 21 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (- (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (- (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 22 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 23 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 24 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 25 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 26 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 27 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 28 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (sqrt k))) (pow (+ PI PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (sqrt k))) (pow (+ PI PI) (/ k 2))) * * * * [misc]progress: [ 29 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (sqrt k))) (pow (+ PI PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (sqrt k))) (pow (+ PI PI) (/ k 2))) * * * * [misc]progress: [ 30 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * * [misc]simplify: iters left: 1 (26 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt k)) (pow (+ PI PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt k)) (pow (+ PI PI) (/ k 2))) * * * * [misc]progress: [ 31 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (82 enodes) * [exit]simplify: Simplified to (/ (/ (/ (pow n (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (/ (pow n (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* PI (+ n n)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* PI (+ n n)) (/ k 2)))) * * * * [misc]progress: [ 32 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* PI (+ n n)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* PI (+ n n)) (/ k 2)))) * * * * [misc]progress: [ 33 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt k)) (cbrt (pow (* (+ n n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt k)) (cbrt (pow (* (+ n n) PI) (/ k 2)))) * * * * [misc]progress: [ 34 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* PI (+ n n)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* PI (+ n n)) (/ k 2)))) * * * * [misc]progress: [ 35 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (+ n n)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (+ n n)) (/ k 2)))) * * * * [misc]progress: [ 36 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt k)) (sqrt (pow (* (+ n n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt k)) (sqrt (pow (* (+ n n) PI) (/ k 2)))) * * * * [misc]progress: [ 37 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* (+ n n) PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* (+ n n) PI) (/ k 2))) * * * * [misc]progress: [ 38 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * * [misc]simplify: iters left: 1 (24 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* (+ n n) PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* (+ n n) PI) (/ k 2))) * * * * [misc]progress: [ 39 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow n (/ 1 2)) 1) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) 1) * [enter]simplify: Simplifying (/ (/ (pow (+ PI PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt k)) (pow (* (+ n n) PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (+ PI PI) (/ 1 2)) (sqrt k)) (pow (* (+ n n) PI) (/ k 2))) * * * * [misc]progress: [ 40 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (154 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow n (/ k 2))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow n (/ k 2))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * * * * [misc]progress: [ 41 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (sqrt (sqrt k)) (pow n (/ k 2)))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (sqrt (sqrt k)) (pow n (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * * * * [misc]progress: [ 42 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (119 enodes) * * [misc]simplify: iters left: 1 (151 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow (+ PI PI) (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow (+ PI PI) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 43 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (257 enodes) * * [misc]simplify: iters left: 1 (320 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 44 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (134 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 45 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (199 enodes) * * [misc]simplify: iters left: 1 (347 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 46 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (155 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (+ n n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (+ n n) PI) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 47 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 48 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (155 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 49 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 50 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (226 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 51 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 52 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow n (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow n (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * * * * [misc]progress: [ 53 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow n (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow n (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * * * * [misc]progress: [ 54 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow (+ PI PI) (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow (+ PI PI) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 55 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 56 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 57 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 58 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 59 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 60 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 61 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 62 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 63 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) 1) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 64 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (cbrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (cbrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * * * * [misc]progress: [ 65 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (+ PI PI) (/ k 2)))) * * * * [misc]progress: [ 66 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n (/ k 2))) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * [exit]simplify: Simplified to (/ 1 (pow n (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow n (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (+ PI PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (+ PI PI) (/ k 2)))) * * * * [misc]progress: [ 67 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 68 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (* (cbrt (pow (* (+ PI PI) n) (/ k 2))) (cbrt (pow (* (+ PI PI) n) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (* (cbrt (pow (* (+ PI PI) n) (/ k 2))) (cbrt (pow (* (+ PI PI) n) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 69 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (pow (* PI (+ n n)) (/ k 2))) (cbrt (pow (* PI (+ n n)) (/ k 2))))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (pow (* PI (+ n n)) (/ k 2))) (cbrt (pow (* PI (+ n n)) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 70 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * [exit]simplify: Simplified to (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (+ PI PI) n) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (+ PI PI) n) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 71 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 72 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (+ n n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (+ n n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 73 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 74 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 75 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) 1) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 76 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 77 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 78 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 79 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* n (+ PI PI)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* (+ n n) PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* (+ n n) PI) (/ k 2))) * * * * [misc]progress: [ 80 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* (+ n n) PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* (+ n n) PI) (/ k 2))) * * * * [misc]progress: [ 81 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (+ PI PI)) (/ 1 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (pow (+ (* PI n) (* PI n)) (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow (+ (* PI n) (* PI n)) (/ 1 2)) 1) * [enter]simplify: Simplifying (/ (/ 1 (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* (+ n n) PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* (+ n n) PI) (/ k 2))) * * * * [misc]progress: [ 82 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 83 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 84 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (pow (* (+ n n) PI) (/ k 2)) (/ (sqrt k) (pow (* (+ n n) PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (pow (* (+ n n) PI) (/ k 2)) (/ (sqrt k) (pow (* (+ n n) PI) (/ 1 2)))) * * * * [misc]progress: [ 85 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 86 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 87 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 88 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 89 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 90 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) * * * * [misc]progress: [ 91 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (+ n n)) (/ k 2))) (/ (sqrt k) (pow (+ PI PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (+ n n)) (/ k 2))) (/ (sqrt k) (pow (+ PI PI) (/ 1 2)))) * * * * [misc]progress: [ 92 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* PI (+ n n)) (/ k 2))) (/ (sqrt k) (pow (+ PI PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (sqrt (pow (* PI (+ n n)) (/ k 2))) (/ (sqrt k) (pow (+ PI PI) (/ 1 2)))) * * * * [misc]progress: [ 93 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (+ PI PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (pow (* (+ n n) PI) (/ k 2)) (/ (sqrt k) (pow (+ PI PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (pow (* (+ n n) PI) (/ k 2)) (/ (sqrt k) (pow (+ PI PI) (/ 1 2)))) * * * * [misc]progress: [ 94 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (* (pow (+ PI PI) (/ k 2)) (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (+ PI PI) (/ k 2)) (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) * * * * [misc]progress: [ 95 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 96 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 97 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) * * * * [misc]progress: [ 98 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (* (pow (+ PI PI) (/ k 2)) (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (+ PI PI) (/ k 2)) (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) * * * * [misc]progress: [ 99 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 100 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 101 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) * * * * [misc]progress: [ 102 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (* (pow (+ PI PI) (/ k 2)) (sqrt k)) (pow (* (+ n n) PI) (/ 1 2))) * [exit]simplify: Simplified to (/ (* (pow (+ PI PI) (/ k 2)) (sqrt k)) (pow (* (+ n n) PI) (/ 1 2))) * * * * [misc]progress: [ 103 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (/ (sqrt k) (pow (* n (+ PI PI)) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (/ (sqrt k) (pow (* n (+ PI PI)) (/ 1 2)))) * * * * [misc]progress: [ 104 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (/ (sqrt k) (pow (* n (+ PI PI)) (/ 1 2)))) * [exit]simplify: Simplified to (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (/ (sqrt k) (pow (* n (+ PI PI)) (/ 1 2)))) * * * * [misc]progress: [ 105 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (pow (* (+ n n) PI) (/ k 2)) (/ (sqrt k) (pow (* (+ n n) PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (pow (* (+ n n) PI) (/ k 2)) (/ (sqrt k) (pow (* (+ n n) PI) (/ 1 2)))) * * * * [misc]progress: [ 106 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (pow (* (+ n n) PI) (/ k 2)) (/ (sqrt k) (pow (* (+ n n) PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (pow (* (+ n n) PI) (/ k 2)) (/ (sqrt k) (pow (* (+ n n) PI) (/ 1 2)))) * * * * [misc]progress: [ 107 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) 1) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) 1) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 108 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (* PI (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (* PI (+ n n)) (/ k 2))) * * * * [misc]progress: [ 109 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * * * * [misc]progress: [ 110 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * * * * [misc]progress: [ 111 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 112 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * * [misc]simplify: iters left: 1 (46 enodes) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * * * * [misc]progress: [ 113 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * * * * [misc]progress: [ 114 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [enter]simplify: Simplifying (cbrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * * * * [misc]progress: [ 115 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (426 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * * * * [misc]progress: [ 116 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * * * * [misc]progress: [ 117 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 118 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 119 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 120 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * * * [misc]progress: [ 121 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (sqrt (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * * * * [misc]progress: [ 122 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to n * [exit]simplify: Simplified to n * * * * [misc]progress: [ 123 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (+ n n) * [exit]simplify: Simplified to (+ n n) * * * * [misc]progress: [ 124 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (+ (pow PI 3) (pow PI 3))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * * * * [misc]progress: [ 125 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (- (* PI PI) (* PI PI))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to 0 * [exit]simplify: Simplified to 0 * * * * [misc]progress: [ 126 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 127 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * * * * [misc]progress: [ 128 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * * * * [misc]progress: [ 129 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 130 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * * [misc]simplify: iters left: 1 (46 enodes) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * * * * [misc]progress: [ 131 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * * * * [misc]progress: [ 132 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [enter]simplify: Simplifying (cbrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * * * * [misc]progress: [ 133 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (426 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * * * * [misc]progress: [ 134 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * * * * [misc]progress: [ 135 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 136 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 137 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 138 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * * * [misc]progress: [ 139 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (sqrt (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * * * * [misc]progress: [ 140 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to n * [exit]simplify: Simplified to n * * * * [misc]progress: [ 141 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (+ n n) * [exit]simplify: Simplified to (+ n n) * * * * [misc]progress: [ 142 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (+ (pow PI 3) (pow PI 3))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * * * * [misc]progress: [ 143 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (- (* PI PI) (* PI PI))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to 0 * [exit]simplify: Simplified to 0 * * * * [misc]progress: [ 144 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 145 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* n (+ PI PI)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (expm1 (pow (+ (* PI n) (* PI n)) (/ 1 2))) * [exit]simplify: Simplified to (expm1 (pow (+ (* PI n) (* PI n)) (/ 1 2))) * * * * [misc]progress: [ 146 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* n (+ PI PI)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (log1p (pow (+ (* PI n) (* PI n)) (/ 1 2))) * [exit]simplify: Simplified to (log1p (pow (+ (* PI n) (* PI n)) (/ 1 2))) * * * * [misc]progress: [ 147 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (+ PI PI))) (/ 1 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (174 enodes) * * [misc]simplify: iters left: 1 (355 enodes) * [exit]simplify: Simplified to (fma (log (+ PI PI)) (/ 1 2) (/ (log n) 2)) * [exit]simplify: Simplified to (fma (log (+ PI PI)) (/ 1 2) (/ (log n) 2)) * * * * [misc]progress: [ 148 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n (+ PI PI))) (/ 1 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (174 enodes) * * [misc]simplify: iters left: 1 (355 enodes) * [exit]simplify: Simplified to (fma (log (+ PI PI)) (/ 1 2) (/ (log n) 2)) * [exit]simplify: Simplified to (fma (log (+ PI PI)) (/ 1 2) (/ (log n) 2)) * * * * [misc]progress: [ 149 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ 1 2)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (/ 1 2) * [exit]simplify: Simplified to (/ 1 2) * * * * [misc]progress: [ 150 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (pow (* (+ n n) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * [exit]simplify: Simplified to (pow (* (+ n n) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * * * [misc]progress: [ 151 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (sqrt (/ 1 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (pow (+ (* PI n) (* PI n)) (sqrt (/ 1 2))) * [exit]simplify: Simplified to (pow (+ (* PI n) (* PI n)) (sqrt (/ 1 2))) * * * * [misc]progress: [ 152 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * [exit]simplify: Simplified to (* n (+ PI PI)) * [exit]simplify: Simplified to (* n (+ PI PI)) * * * * [misc]progress: [ 153 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n (+ PI PI)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * [exit]simplify: Simplified to (* n (+ PI PI)) * [exit]simplify: Simplified to (* n (+ PI PI)) * * * * [misc]progress: [ 154 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (/ 1 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow n (/ 1 2)) * [exit]simplify: Simplified to (pow n (/ 1 2)) * [enter]simplify: Simplifying (pow (+ PI PI) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * * [misc]simplify: iters left: 1 (10 enodes) * [exit]simplify: Simplified to (pow (+ PI PI) (/ 1 2)) * [exit]simplify: Simplified to (pow (+ PI PI) (/ 1 2)) * * * * [misc]progress: [ 155 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 156 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* n (+ PI PI)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (270 enodes) * [exit]simplify: Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2)) * [exit]simplify: Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2)) * * * * [misc]progress: [ 157 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* n (+ PI PI)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (exp (pow (+ (* PI n) (* PI n)) (/ 1 2))) * [exit]simplify: Simplified to (exp (pow (+ (* PI n) (* PI n)) (/ 1 2))) * * * * [misc]progress: [ 158 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) * [enter]simplify: Simplifying (cbrt (pow (* n (+ PI PI)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (cbrt (pow (+ (* PI n) (* PI n)) (/ 1 2))) * [exit]simplify: Simplified to (cbrt (pow (+ (* PI n) (* PI n)) (/ 1 2))) * * * * [misc]progress: [ 159 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ 1 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (pow (pow (* (+ n n) PI) (/ 1 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (+ n n) PI) (/ 1 2)) 3) * * * * [misc]progress: [ 160 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* n (+ PI PI)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2))) * [enter]simplify: Simplifying (sqrt (pow (* n (+ PI PI)) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2))) * * * * [misc]progress: [ 161 / 173 ] simplifiying candidate # * * * * [misc]progress: [ 162 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 163 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * * * * [misc]progress: [ 164 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))) * * * * [misc]progress: [ 165 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 166 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 167 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 168 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 169 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 170 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 171 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (205 enodes) * * [misc]simplify: iters left: 1 (318 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (+ n n)) (/ (sqrt PI) (sqrt k))) (pow (* (+ PI PI) n) (/ k 2))) * * * * [misc]progress: [ 172 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (247 enodes) * [exit]simplify: Simplified to (/ (exp (fma 1/2 (- (log PI) (log 1)) (* (log 2) 1/2))) (* (pow (* n (+ PI PI)) (/ k 2)) (/ (sqrt k) (sqrt n)))) * * * * [misc]progress: [ 173 / 173 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (128 enodes) * * [misc]simplify: iters left: 1 (245 enodes) * [exit]simplify: Simplified to (/ (exp (fma (- (log -2) (log -1)) 1/2 (* 1/2 (log PI)))) (* (pow (* PI (+ n n)) (/ k 2)) (/ (sqrt k) (sqrt n)))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 3 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]backup-simplify: Simplify (* +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (sqrt (* n (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (sqrt (* n (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (* n (* 2 PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (* 2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 n)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* 0 (sqrt 2)) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 PI)) * [misc]backup-simplify: Simplify (- (* +nan.0 PI)) into (- (* +nan.0 PI)) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 n))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 * [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 (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))) (+ (* (- +nan.0) (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (log (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (log (+ (log (* 2 PI)) (log n))) into (log (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 2 (log (+ (log (* 2 PI)) (log n)))) into (* 2 (log (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 2 (log (+ (log (* 2 PI)) (log n))))) into (pow (+ (log (* 2 PI)) (log n)) 2) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log (* 2 PI)) (log n)) 2)) into (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* 0 (sqrt 2)) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (* (+ (log (* 2 PI)) (log n)) (sqrt 2)))) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))) (* 0 0)) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (sqrt 2))) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* PI (sqrt 2))))) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) (- (* +nan.0 (* PI (sqrt 2))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (pow PI 2))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI 2))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) (* n 1)) (* (- (* +nan.0 PI)) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- (log (* 2 PI)) (log n)) 0) (* 0 (- 1 (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (+ 1 (/ 1 k)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) k) (+ (- +nan.0) (* +nan.0 (/ 1 k)))) into (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 2)) (+ (* (- +nan.0) (/ 1 k)) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) n) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 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 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 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 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 2 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 3 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (187 enodes) * * [misc]simplify: iters left: 1 (288 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 5 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (187 enodes) * * [misc]simplify: iters left: 1 (288 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 6 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (169 enodes) * * [misc]simplify: iters left: 1 (285 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 7 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * * [misc]simplify: iters left: 1 (399 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 8 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (235 enodes) * * [misc]simplify: iters left: 1 (399 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 9 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (422 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k)))) * * * * [misc]progress: [ 10 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (178 enodes) * * [misc]simplify: iters left: 1 (366 enodes) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 11 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 12 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (196 enodes) * * [misc]simplify: iters left: 2 (422 enodes) * [exit]simplify: Simplified to (* (* (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (* (sqrt k) k))) * [exit]simplify: Simplified to (* (* (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (* (sqrt k) k))) * * * * [misc]progress: [ 13 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 14 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (209 enodes) * * [misc]simplify: iters left: 2 (441 enodes) * [exit]simplify: Simplified to (* (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (* (sqrt k) k)) (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (* (sqrt k) k)) (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 15 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 16 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (pow (* (+ n n) PI) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (+ n n) PI) (/ 1 2)) * [enter]simplify: Simplifying (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) * * * * [misc]progress: [ 17 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (45 enodes) * [exit]simplify: Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 19 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)) * * * * [misc]progress: [ 20 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 21 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) 1) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 22 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* PI (+ n n)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 23 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* PI (+ n n)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 24 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 25 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 26 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) * * * * [misc]progress: [ 27 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 28 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (expm1 (/ 1 (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ 1 (sqrt k))) * * * * [misc]progress: [ 30 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (log1p (/ 1 (sqrt k))) * [exit]simplify: Simplified to (log1p (/ 1 (sqrt k))) * * * * [misc]progress: [ 31 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- 1/2) * [exit]simplify: Simplified to (- 1/2) * * * * [misc]progress: [ 33 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (- 1) * [exit]simplify: Simplified to (- 1) * * * * [misc]progress: [ 34 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 35 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 36 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 37 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * * * * [misc]progress: [ 38 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 39 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (100 enodes) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * * * * [misc]progress: [ 40 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 41 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (- 1) * [exit]simplify: Simplified to (- 1) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 42 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 43 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 44 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ (sqrt k) 1) * [exit]simplify: Simplified to (/ (sqrt k) 1) * * * * [misc]progress: [ 45 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 46 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * * * * [misc]progress: [ 47 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * * * * [misc]progress: [ 48 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (expm1 (* (+ PI PI) n)) * [exit]simplify: Simplified to (expm1 (* (+ PI PI) n)) * * * * [misc]progress: [ 49 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (log1p (* (+ PI PI) n)) * [exit]simplify: Simplified to (log1p (* (+ PI PI) n)) * * * * [misc]progress: [ 50 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 51 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (log (* (+ PI PI) n)) * [exit]simplify: Simplified to (log (* (+ PI PI) n)) * * * * [misc]progress: [ 52 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (42 enodes) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * * * * [misc]progress: [ 53 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (cbrt (* (+ n n) PI)) (cbrt (* (+ n n) PI))) * [exit]simplify: Simplified to (* (cbrt (* (+ n n) PI)) (cbrt (* (+ n n) PI))) * [enter]simplify: Simplifying (cbrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (cbrt (* (+ PI PI) n)) * [exit]simplify: Simplified to (cbrt (* (+ PI PI) n)) * * * * [misc]progress: [ 54 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (241 enodes) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) 3) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) 3) * * * * [misc]progress: [ 55 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (sqrt (* (+ PI PI) n)) * [exit]simplify: Simplified to (sqrt (* (+ PI PI) n)) * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (sqrt (* (+ PI PI) n)) * [exit]simplify: Simplified to (sqrt (* (+ PI PI) n)) * * * * [misc]progress: [ 56 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 57 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 58 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 59 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (expm1 (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 60 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (log1p (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 61 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (230 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * * * * [misc]progress: [ 62 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (230 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * * * * [misc]progress: [ 63 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (37 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 64 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * [exit]simplify: Simplified to (pow (* (+ PI PI) n) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (+ PI PI) n) (/ 1 2)) * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (+ PI PI) n) (/ k 2)) * [exit]simplify: Simplified to (pow (* (+ PI PI) n) (/ k 2)) * * * * [misc]progress: [ 65 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 66 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (pow (* (+ PI PI) n) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* (+ PI PI) n) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 67 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * [exit]simplify: Simplified to (* (+ PI PI) n) * [exit]simplify: Simplified to (* (+ PI PI) n) * * * * [misc]progress: [ 68 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) (- 1 k)) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) (- 1 k)) * * * * [misc]progress: [ 69 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (pow (+ PI PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ PI PI) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 70 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 71 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (207 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * * * * [misc]progress: [ 72 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (exp (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 73 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 74 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (pow (pow (* (+ n n) PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (+ n n) PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 75 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 76 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 77 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))) * * * * [misc]progress: [ 78 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * * * * [misc]progress: [ 79 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 80 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 81 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 82 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 83 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 84 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 85 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 86 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (373 enodes) * [exit]simplify: Simplified to (/ (+ (* (* 1/8 (* (pow (+ PI PI) 1/2) (* (pow n 1/2) (* k k)))) (+ (* (log n) (log n)) (* (log (+ PI PI)) (log (+ PI PI))))) (- (fma (* (* (log n) (* k k)) (log (+ PI PI))) (* (pow (+ PI PI) 1/2) (* (pow n 1/2) 1/4)) (* (pow n 1/2) (pow (+ PI PI) 1/2))) (* (* (pow (+ PI PI) 1/2) (* (pow n 1/2) 1/2)) (fma (log (+ PI PI)) k (* (log n) k))))) (sqrt k)) * * * * [misc]progress: [ 87 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (121 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (/ (pow (/ (+ PI PI) (/ 1 n)) (* (- 1 k) 1/2)) (sqrt k)) * * * * [misc]progress: [ 88 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (/ (pow (/ (* PI -2) (/ -1 n)) (* (- 1 k) 1/2)) (sqrt k)) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 4 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1 1 2 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 1 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ k 2) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* n (* 2 PI))) * [misc]backup-simplify: Simplify (sqrt (sqrt (* n (* 2 PI)))) into (* (pow (* n PI) 1/4) (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* 2 (* n PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (* n (* 2 PI))) (/ (* 1/2 (log (* 2 (* n PI)))) 1)))) into (- (* 1/2 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))) * [misc]backup-simplify: Simplify (/ (- (* 1/2 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))) (* 2 (sqrt (sqrt (* n (* 2 PI)))))) into (* -1/4 (* (pow (* n PI) 1/4) (* (sqrt (sqrt 2)) (log (* 2 (* n PI)))))) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (* (pow (* n PI) 1/4) (sqrt (sqrt 2))) 1) into (* (pow (* n PI) 1/4) (sqrt (sqrt 2))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ k 2) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* n (* 2 PI))) * [misc]backup-simplify: Simplify (sqrt (sqrt (* n (* 2 PI)))) into (* (pow (* n PI) 1/4) (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* 2 (* n PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (* n (* 2 PI))) (/ (* 1/2 (log (* 2 (* n PI)))) 1)))) into (- (* 1/2 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))) * [misc]backup-simplify: Simplify (/ (- (* 1/2 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))) (* 2 (sqrt (sqrt (* n (* 2 PI)))))) into (* -1/4 (* (pow (* n PI) 1/4) (* (sqrt (sqrt 2)) (log (* 2 (* n PI)))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (* (pow (* n PI) 1/4) (sqrt (sqrt 2))) +nan.0) into (* +nan.0 (* (pow (* n PI) 1/4) (sqrt (sqrt 2)))) * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) 1) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (sqrt k)) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) 1) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (sqrt k)) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k)))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) 0) (* 0 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (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 (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) +nan.0) (* (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) 1) (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) 1) (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) 1) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (sqrt (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 n) 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (/ PI n)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* 2 (/ PI n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) (+ (* (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) 1) into (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (sqrt (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 n) 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (/ PI n)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* 2 (/ PI n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) (+ (* (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) +nan.0) into (* +nan.0 (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) 1) (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) 1) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (sqrt (/ 1 k))) into (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) 1) (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) 1) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 1) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (sqrt (/ 1 k))) into (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 0) (* 0 (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 0) (+ (* 0 0) (* 0 (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) 1) (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) 1) (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) 1) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (sqrt (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 n) (/ 0 (- n))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ -1 n) 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 (/ PI n)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* -2 (/ PI n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* -2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (+ (* (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 1) into (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (sqrt (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 n) (/ 0 (- n))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ -1 n) 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 (/ PI n)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* -2 (/ PI n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* -2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (+ (* (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) 1) (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) 1) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (sqrt (/ -1 k))) into (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (* (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) 1) (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) 1) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 1) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (sqrt (/ -1 k))) into (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) * [misc]backup-simplify: Simplify (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k))))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 0) (* 0 (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 0) (+ (* 0 0) (* 0 (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ k 2) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* n (* 2 PI))) * [misc]backup-simplify: Simplify (sqrt (sqrt (* n (* 2 PI)))) into (* (pow (* n PI) 1/4) (sqrt (sqrt 2))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* 2 (* n PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (* n (* 2 PI))) (/ (* 1/2 (log (* 2 (* n PI)))) 1)))) into (- (* 1/2 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))) * [misc]backup-simplify: Simplify (/ (- (* 1/2 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))) (* 2 (sqrt (sqrt (* n (* 2 PI)))))) into (* -1/4 (* (pow (* n PI) 1/4) (* (sqrt (sqrt 2)) (log (* 2 (* n PI)))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (* (pow (* n PI) 1/4) (sqrt (sqrt 2))) +nan.0) into (* +nan.0 (* (pow (* n PI) 1/4) (sqrt (sqrt 2)))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (sqrt k)) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* n (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (sqrt k)) into (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) * [misc]taylor: Taking taylor expansion of (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 1 0) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (+ (* 1 1) (* (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 0)) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* 2 (sqrt 0))) into (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) (* (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 0))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) * [misc]backup-simplify: Simplify (/ (- (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (pow (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) 2) (+)) (* 2 0)) into (* +nan.0 (+ (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2)) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (+ (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2)) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))) into (* +nan.0 (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (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 (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 0) (+ (* (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1) (* (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 0)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log (* 2 PI)) (log n))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (/ (- (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (+ (* 2 (* (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (* +nan.0 (+ (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2)) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))))) (* 2 0)) into (* +nan.0 (- (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (log (* 2 PI)))) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (log n))) (- (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 3)))))))) * [misc]backup-simplify: Simplify (* +nan.0 (- (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (log (* 2 PI)))) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (log n))) (- (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 3)))))))) into (* +nan.0 (- (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (log (* 2 PI)))) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (log n))) (- (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 3)))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (- (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (log (* 2 PI)))) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (log n))) (- (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 3)))))))) (pow (* k 1) 2)) (+ (* (* +nan.0 (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (* +nan.0 (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2)))) (* k 1)) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) k)) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2))))) (- (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 3) (pow k 2)))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (sqrt (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 n) 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (/ PI n)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* 2 (/ PI n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) (+ (* (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) +nan.0) into (* +nan.0 (* (pow (/ PI n) 1/4) (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (sqrt (/ 1 k))) into (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (sqrt (/ 1 k))) into (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 1) (* 0 0)) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* 2 (sqrt 0))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 2) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 2) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2))) into (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 2) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [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 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 2) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2))))))) (* 2 0)) into (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 3) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 3))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 3) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 3))) into (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log n)))) 3) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 3))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) 3) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) 3))) (pow (* (/ 1 k) 1) 3)) (+ (* (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) 2) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) 2))) (pow (* (/ 1 k) 1) 2)) (* (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) 3) (* (pow k 3) (pow (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))) 3)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) 2) (* (pow k 2) (pow (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))) 2))))))))) * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (+ PI PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (sqrt (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 n) (/ 0 (- n))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ -1 n) 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 (/ PI n)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* -2 (/ PI n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* -2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (+ (* (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (sqrt (/ -1 k))) into (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (+ PI PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (sqrt (/ -1 k))) into (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) +nan.0) into (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- +nan.0)) (* 0 +nan.0)) into (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [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 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 1 (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [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 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- +nan.0)) (+ (* 0 (- +nan.0)) (* 0 +nan.0))) into (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))))) into (- (+ (* +nan.0 (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (/ 1 (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (/ 1 k))) (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1 1 2 1) * [misc]approximate: Taking taylor expansion of (* n (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 1 1 1 1) * [misc]approximate: Taking taylor expansion of (* n (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* n (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (+ PI PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ PI PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (expm1 (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (expm1 (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 2 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (log1p (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (log1p (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 3 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (141 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 4 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (- (log (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (fma (log (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 2 (- (+ (log 1) (log (sqrt k))))) * [exit]simplify: Simplified to (fma (log (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 2 (- (+ (log 1) (log (sqrt k))))) * * * * [misc]progress: [ 6 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (log (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (+ (log (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (log (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * [exit]simplify: Simplified to (+ (log (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (log (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * * * [misc]progress: [ 7 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (154 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (- (* (log (* (+ n n) PI)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* (+ n n) PI)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 8 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k)))) * [exit]simplify: Simplified to (exp (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (pow (* n (+ PI PI)) (/ k 2)) (sqrt k)))) * * * * [misc]progress: [ 9 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (166 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (* 1 1)) (* (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (* k (sqrt k))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) 1))) * [exit]simplify: Simplified to (* (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (* 1 1)) (* (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (* k (sqrt k))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) 1))) * * * * [misc]progress: [ 10 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (* (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (133 enodes) * * [misc]simplify: iters left: 3 (390 enodes) * [exit]simplify: Simplified to (* (* (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (* (sqrt k) 1))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) k)) * [exit]simplify: Simplified to (* (* (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (* (sqrt k) 1))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) k)) * * * * [misc]progress: [ 11 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) (cbrt (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))))) * [enter]simplify: Simplifying (cbrt (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (cbrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 12 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (351 enodes) * [exit]simplify: Simplified to (pow (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) 3) * [exit]simplify: Simplified to (pow (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)) 3) * * * * [misc]progress: [ 13 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [enter]simplify: Simplifying (sqrt (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2)))) * * * * [misc]progress: [ 14 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) * [enter]simplify: Simplifying (* 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 15 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (* (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) (/ 1 (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))))) * [exit]simplify: Simplified to (/ (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) (/ 1 (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))))) * * * * [misc]progress: [ 17 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * * * [misc]progress: [ 18 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * * [misc]simplify: iters left: 2 (457 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 19 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * * [misc]simplify: iters left: 1 (472 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) (* (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))))) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) (* (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))))) * * * * [misc]progress: [ 20 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (133 enodes) * * [misc]simplify: iters left: 1 (203 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 21 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 22 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (182 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) (fabs (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) (fabs (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 23 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 24 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (200 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 25 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (179 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 26 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 27 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 28 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (181 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))))) * * * * [misc]progress: [ 29 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 30 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (pow n (/ 1 2)) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (pow n (/ 1 2)) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 31 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (189 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 32 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) 1)) * [exit]simplify: Simplified to (* (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) 1)) * * * * [misc]progress: [ 33 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 34 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (181 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 35 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 36 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (202 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow n (/ 1 2)) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow n (/ 1 2)) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 37 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) 1)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (186 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (/ (pow n (/ 1 2)) 1)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (/ (pow n (/ 1 2)) 1)))) * * * * [misc]progress: [ 38 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow n (/ 1 2)) 1)) 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow n (/ 1 2)) 1)) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow n (/ 1 2)) 1)) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 39 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (209 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow n (/ k 2))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))))) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow n (/ k 2))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))))) * * * * [misc]progress: [ 40 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (113 enodes) * * [misc]simplify: iters left: 1 (194 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (pow n (/ k 2)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (pow n (/ k 2)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 41 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2)))) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow n (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2))))) (/ 1 (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (* (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow n (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2))))) (/ 1 (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 42 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (227 enodes) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 43 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* PI (+ n n)) (/ 1 2))) (cbrt (pow (* PI (+ n n)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* PI (+ n n)) (/ 1 2))) (cbrt (pow (* PI (+ n n)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2)))))) * * * * [misc]progress: [ 44 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (91 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 45 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (209 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))))) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))))) * * * * [misc]progress: [ 46 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (113 enodes) * * [misc]simplify: iters left: 1 (194 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (sqrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (sqrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 47 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (93 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (pow (* (+ n n) PI) (/ 1 2))))) (/ 1 (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (* (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (pow (* (+ n n) PI) (/ 1 2))))) (/ 1 (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 48 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (208 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))))) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))))) * * * * [misc]progress: [ 49 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (111 enodes) * * [misc]simplify: iters left: 1 (192 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ 1 (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ 1 (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 50 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) 1)) (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) 1)) * [exit]simplify: Simplified to (* (sqrt (/ (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) 1)) (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) 1)) * * * * [misc]progress: [ 51 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))))) * * * * [misc]progress: [ 52 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (181 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (pow n (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (pow n (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 53 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 54 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 55 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (189 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 56 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) 1)) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) 1)) * * * * [misc]progress: [ 57 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 58 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (181 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 59 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (/ 1 (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 60 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (202 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 61 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (186 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) 1)) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) 1)) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 62 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) * * * * [misc]progress: [ 63 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (202 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 64 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (pow n (/ k 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (186 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (/ 1 (pow n (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (/ 1 (pow n (/ k 2)))))) * * * * [misc]progress: [ 65 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (pow n (/ k 2)))) 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (pow n (/ k 2)))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ 1 (pow n (/ k 2)))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 66 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (205 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))))) * * * * [misc]progress: [ 67 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (183 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 68 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) (/ 1 (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) (/ 1 (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 69 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (202 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 70 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (186 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* (+ n n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* (+ n n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 71 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) * * * * [misc]progress: [ 72 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (201 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt 1))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt 1))) * * * * [misc]progress: [ 73 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 1)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (175 enodes) * [exit]simplify: Simplified to (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 74 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ 1 1)) 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (sqrt 1) 1)) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (sqrt 1) 1)) * * * * [misc]progress: [ 75 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (200 enodes) * [exit]simplify: Simplified to (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 76 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt 1) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (179 enodes) * [exit]simplify: Simplified to (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 77 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt 1) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (* (/ (sqrt 1) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt 1) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 78 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (200 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 79 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (179 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 80 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 81 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (200 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 82 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (179 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 83 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 84 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (225 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 85 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (257 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 86 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ 1 1)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) * * * * [misc]progress: [ 87 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) * * * * [misc]progress: [ 88 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 89 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 90 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1)) (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 91 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (141 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 92 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 93 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 94 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) (pow (* (+ n n) PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) (pow (* (+ n n) PI) (/ k 2))) * * * * [misc]progress: [ 95 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 96 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (expm1 (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 97 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (log1p (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 98 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 99 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (- (log (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (log (sqrt k))) * * * * [misc]progress: [ 100 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (log (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (sqrt k))) * [exit]simplify: Simplified to (log (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 101 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (exp (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 102 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (352 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (* (pow (* n (+ PI PI)) (/ k 2)) k))) * [exit]simplify: Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (* (pow (* n (+ PI PI)) (/ k 2)) k))) * * * * [misc]progress: [ 103 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 104 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (134 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (/ (* (sqrt k) k) (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (/ (* (sqrt k) k) (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) * * * * [misc]progress: [ 105 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) k) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) k) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) k) * * * * [misc]progress: [ 106 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 107 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (- (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (- (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (- (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 108 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 109 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 110 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1)) * [exit]simplify: Simplified to (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1)) * [enter]simplify: Simplifying (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 111 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 112 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 113 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (* (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 114 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 115 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 116 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 117 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 118 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 119 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (pow n (/ k 2)))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 120 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (+ (* PI n) (* PI n)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (+ (* PI n) (* PI n)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 121 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (+ (* PI n) (* PI n)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (+ (* PI n) (* PI n)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 122 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* (+ n n) PI) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* (+ n n) PI) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 123 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (+ (* PI n) (* PI n)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (+ (* PI n) (* PI n)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 124 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (+ (* PI n) (* PI n)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (+ (* PI n) (* PI n)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 125 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 126 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 127 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) 1)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) 1)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) 1)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 128 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow n (/ 1 2)) 1)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) 1)) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (pow n (/ 1 2)) 1)) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 129 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 130 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (pow n (/ k 2)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (pow n (/ k 2)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 131 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow n (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (pow n (/ k 2)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (pow n (/ k 2)) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 132 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 133 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 134 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 135 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ 1 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (* (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ 1 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 136 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 137 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))))) 1) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (pow (* (+ n n) PI) (/ k 2)))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 138 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 139 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 140 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) 1)) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 141 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 142 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 143 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow n (/ k 2)))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 144 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 145 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 146 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))) (cbrt (pow (* (+ n n) PI) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 147 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 148 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 149 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 150 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 151 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 152 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1)) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 153 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow n (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 154 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (pow n (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow n (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow n (/ k 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 155 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (pow n (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow n (/ k 2)))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow n (/ k 2)))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 156 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (+ (* PI n) (* PI n)) (/ k 2))) (cbrt (pow (+ (* PI n) (* PI n)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (+ (* PI n) (* PI n)) (/ k 2))) (cbrt (pow (+ (* PI n) (* PI n)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 157 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* PI (+ n n)) (/ k 2))) (cbrt (pow (* PI (+ n n)) (/ k 2)))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* PI (+ n n)) (/ k 2))) (cbrt (pow (* PI (+ n n)) (/ k 2)))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 158 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (* (cbrt (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 159 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* PI (+ n n)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* PI (+ n n)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 160 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* (+ n n) PI) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 161 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* (+ n n) PI) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (pow (* (+ n n) PI) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 162 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt 1) (cbrt (sqrt k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt 1) (cbrt (sqrt k))) (cbrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 163 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 1)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to (/ (sqrt 1) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt 1) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 164 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 1)) 1) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to (/ (sqrt 1) 1) * [exit]simplify: Simplified to (/ (sqrt 1) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 165 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt 1) (cbrt (sqrt k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (sqrt 1) (cbrt (sqrt k))) (cbrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 166 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (8 enodes) * [exit]simplify: Simplified to (/ (sqrt 1) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt 1) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 167 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 1) 1) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (/ (sqrt 1) 1) * [exit]simplify: Simplified to (/ (sqrt 1) 1) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 168 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow (* (+ n n) PI) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 169 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow (* (+ n n) PI) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 170 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) 1) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow (* (+ n n) PI) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (pow (* (+ n n) PI) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 171 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (cbrt (sqrt k))) * * * * [misc]progress: [ 172 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt (sqrt k))) * * * * [misc]progress: [ 173 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) 1) * [enter]simplify: Simplifying (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)) * * * * [misc]progress: [ 174 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 175 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 176 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 177 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 178 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 179 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 180 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 181 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 182 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) * * * * [misc]progress: [ 183 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 184 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 185 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 186 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2))))) * * * * [misc]progress: [ 187 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 188 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 189 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))))) * * * * [misc]progress: [ 190 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow (+ PI PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow (+ PI PI) (/ k 2))))) * * * * [misc]progress: [ 191 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 192 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 193 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ k 2))))) * * * * [misc]progress: [ 194 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (+ PI PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (pow (+ PI PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (pow (+ PI PI) (/ k 2))))) * * * * [misc]progress: [ 195 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 196 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * * * * [misc]progress: [ 197 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ k 2))))) * * * * [misc]progress: [ 198 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ PI PI) (/ k 2))))) * * * * [misc]progress: [ 199 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (cbrt (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 200 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 201 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 202 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 203 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ 1 (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ 1 (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ 1 (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 204 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2)))))) * * * * [misc]progress: [ 205 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))) * * * * [misc]progress: [ 206 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (+ (* n PI) (* n PI)) (/ k 2))) (sqrt k)) * [exit]simplify: Simplified to (* (sqrt (pow (+ (* n PI) (* n PI)) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 207 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * * * * [misc]progress: [ 208 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * * * * [misc]progress: [ 209 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 210 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * * [misc]simplify: iters left: 1 (46 enodes) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * * * * [misc]progress: [ 211 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * * * * [misc]progress: [ 212 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [enter]simplify: Simplifying (cbrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * * * * [misc]progress: [ 213 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (426 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * * * * [misc]progress: [ 214 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * * * * [misc]progress: [ 215 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 216 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 217 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 218 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * * * [misc]progress: [ 219 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (sqrt (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * * * * [misc]progress: [ 220 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to n * [exit]simplify: Simplified to n * * * * [misc]progress: [ 221 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (+ n n) * [exit]simplify: Simplified to (+ n n) * * * * [misc]progress: [ 222 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (+ (pow PI 3) (pow PI 3))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * * * * [misc]progress: [ 223 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (- (* PI PI) (* PI PI))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to 0 * [exit]simplify: Simplified to 0 * * * * [misc]progress: [ 224 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 225 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * [exit]simplify: Simplified to (expm1 (* n (+ PI PI))) * * * * [misc]progress: [ 226 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * [exit]simplify: Simplified to (log1p (* n (+ PI PI))) * * * * [misc]progress: [ 227 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 228 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * * [misc]simplify: iters left: 1 (46 enodes) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * [exit]simplify: Simplified to (log (* (+ n n) PI)) * * * * [misc]progress: [ 229 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * * * * [misc]progress: [ 230 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [exit]simplify: Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) * [enter]simplify: Simplifying (cbrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * [exit]simplify: Simplified to (cbrt (* n (+ PI PI))) * * * * [misc]progress: [ 231 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (426 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) 3) * * * * [misc]progress: [ 232 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [enter]simplify: Simplifying (sqrt (* n (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * [exit]simplify: Simplified to (sqrt (* n (+ PI PI))) * * * * [misc]progress: [ 233 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 234 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 235 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 236 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * [exit]simplify: Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) * * * * [misc]progress: [ 237 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (sqrt (+ PI PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * [exit]simplify: Simplified to (* (sqrt (+ PI PI)) n) * * * * [misc]progress: [ 238 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to n * [exit]simplify: Simplified to n * * * * [misc]progress: [ 239 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (+ n n) * [exit]simplify: Simplified to (+ n n) * * * * [misc]progress: [ 240 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (+ (pow PI 3) (pow PI 3))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * [exit]simplify: Simplified to (* (+ n n) (pow PI 3)) * * * * [misc]progress: [ 241 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* n (- (* PI PI) (* PI PI))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to 0 * [exit]simplify: Simplified to 0 * * * * [misc]progress: [ 242 / 254 ] simplifiying candidate # * * * * [misc]progress: [ 243 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 244 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * * * * [misc]progress: [ 245 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))) * * * * [misc]progress: [ 246 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) k)) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 2) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2))))) (- (* +nan.0 (* (pow (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 3) (pow k 2))))))))))))))))))))))) * * * * [misc]progress: [ 247 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (- (+ (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) 3) (* (pow k 3) (pow (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))) 3)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (pow (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) 2) (* (pow k 2) (pow (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))) 2)))))))))) * * * * [misc]progress: [ 248 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (- (+ (* +nan.0 (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (/ 1 (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (/ 1 k))) (- (* +nan.0 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))))))))))) * * * * [misc]progress: [ 249 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (180 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 250 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (180 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 251 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (180 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 252 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (182 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 253 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (182 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 254 / 254 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (182 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * [misc]progress: adding candidates to table * [misc]progress: [Phase 3 of 3] Extracting. * * [misc]regime-changes: Finding splitpoints for: (# # # # # # # # # # # # # # #) * [misc]regimes: Found splitpoints: (#s(sp 0 (* (* 2 PI) n) +inf.0)) , with alts (#) * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (13 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ 1 2)) * [enter]simplify: Simplifying (pow (* n (+ PI PI)) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ k 2)) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ k 2))