* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Setting MPFR precision to 832 * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 256 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 198 additional inputs, on iter 1 have 58 / 256 * * * * [misc]points: Computing exacts on every 12 of 198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 198 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 146 additional inputs, on iter 2 have 110 / 256 * * * * [misc]points: Computing exacts on every 9 of 146 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 146 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 146 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 146 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 119 additional inputs, on iter 3 have 137 / 256 * * * * [misc]points: Computing exacts on every 7 of 119 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 119 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 119 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 90 additional inputs, on iter 4 have 166 / 256 * * * * [misc]points: Computing exacts on every 5 of 90 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 90 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 90 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 68 additional inputs, on iter 5 have 188 / 256 * * * * [misc]points: Computing exacts on every 4 of 68 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 68 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 68 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 52 additional inputs, on iter 6 have 204 / 256 * * * * [misc]points: Computing exacts on every 3 of 52 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 52 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 41 additional inputs, on iter 7 have 215 / 256 * * * * [misc]points: Computing exacts on every 2 of 41 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 41 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 32 additional inputs, on iter 8 have 224 / 256 * * * * [misc]points: Computing exacts on every 2 of 32 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 32 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 23 additional inputs, on iter 9 have 233 / 256 * * * * [misc]points: Computing exacts for 23 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 20 additional inputs, on iter 10 have 236 / 256 * * * * [misc]points: Computing exacts for 20 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 16 additional inputs, on iter 11 have 240 / 256 * * * * [misc]points: Computing exacts for 16 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 12 additional inputs, on iter 12 have 244 / 256 * * * * [misc]points: Computing exacts for 12 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 9 additional inputs, on iter 13 have 247 / 256 * * * * [misc]points: Computing exacts for 9 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 7 additional inputs, on iter 14 have 249 / 256 * * * * [misc]points: Computing exacts for 7 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 6 additional inputs, on iter 15 have 250 / 256 * * * * [misc]points: Computing exacts for 6 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 16 have 252 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 17 have 253 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 18 have 253 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 19 have 253 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [exit]points: Sampled 257 points with exact outputs * * * [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 (27 enodes) * * [misc]simplify: iters left: 4 (43 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 2) 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 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) * [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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 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 n) (log (* 2 PI)))) 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 n) (log (* 2 PI))) in k * [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 (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]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 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 (/ (+ (* 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 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 (+ 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 n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) 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 (+ 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 n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) * [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 (* (- 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]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 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) * [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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [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 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [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 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (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) 1) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in k * [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 (+ 1 0) 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 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1)) (/ 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) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1)) (/ 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) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1)) (/ 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) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * * [misc]progress: [ 2 / 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: [ 3 / 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) * [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 (* PI (* n 2)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (sqrt (* PI (* n 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 (* PI (* n 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) 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 2) 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 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* PI 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* PI 2) (* 0 0)) 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 (* PI (* n 2))) (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 (* PI (* n 2))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* 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 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n * [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 (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 (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* 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 2) (sqrt (* 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 (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]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) 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 (* PI (* n 2))) (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 (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* (- +nan.0) (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* 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 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n * [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 (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 (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* 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 2) (sqrt (* 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 (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 (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* 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 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n * [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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (log (+ (log n) (log (* 2 PI)))) into (log (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* 2 (log (+ (log n) (log (* 2 PI))))) into (* 2 (log (+ (log n) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 2 (log (+ (log n) (log (* 2 PI)))))) into (pow (+ (log n) (log (* 2 PI))) 2) * [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]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) 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 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n 1)) (* (- (* +nan.0 PI)) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI))))))))))))))) * [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 (* (- 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]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 (* (- 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 k)) into (- (/ 1 k)) * [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 (- (+ (* 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 k)) into (- (/ 1 k)) * [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) 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 (- (+ (* 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 k)) into (- (/ 1 k)) * [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)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) * [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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [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 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) * [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 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 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 k) 1)))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) 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 k) 1)) 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 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 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 k) 1)))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) 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 k) 1)) 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 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 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 k) 1))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) 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 k) 1)))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) 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 k) 1)) 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 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (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)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) * * * * [misc]progress: [ 4 / 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 (/ 1 k)) (- (+ +nan.0 (- (* +nan.0 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 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) * [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 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * * * * [misc]progress: [ 2 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * * * * [misc]progress: [ 3 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 4 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ 1 2)) * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * * * * [misc]progress: [ 5 / 80 ] 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 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 6 / 80 ] 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 7 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* 2 PI) n) * [exit]simplify: Simplified to (* (* 2 PI) n) * * * * [misc]progress: [ 8 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (* n PI) 2) (- 1 k)) * [exit]simplify: Simplified to (pow (* (* n PI) 2) (- 1 k)) * * * * [misc]progress: [ 9 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 10 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 80 ] 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 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * [exit]simplify: Simplified to (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 12 / 80 ] 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 13 / 80 ] 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 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 14 / 80 ] 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 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 15 / 80 ] 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 16 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* 2 PI) n)) * [exit]simplify: Simplified to (log (* (* 2 PI) n)) * * * * [misc]progress: [ 19 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* n PI)) * [exit]simplify: Simplified to (pow (exp 2) (* n PI)) * * * * [misc]progress: [ 20 / 80 ] 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 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) * [exit]simplify: Simplified to (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) * [enter]simplify: Simplifying (cbrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* 2 PI) n)) * [exit]simplify: Simplified to (cbrt (* (* 2 PI) n)) * * * * [misc]progress: [ 21 / 80 ] 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 (18 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (170 enodes) * [exit]simplify: Simplified to (pow (* (* n PI) 2) 3) * [exit]simplify: Simplified to (pow (* (* n PI) 2) 3) * * * * [misc]progress: [ 22 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) * * * * [misc]progress: [ 23 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 80 ] 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 (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 25 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 80 ] 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 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * [exit]simplify: Simplified to (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 28 / 80 ] 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 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * [exit]simplify: Simplified to (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 29 / 80 ] 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 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (286 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* 2 (* n PI)))) (log (sqrt k))) * * * * [misc]progress: [ 30 / 80 ] 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 (37 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * [exit]simplify: Simplified to (- (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 31 / 80 ] 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 (37 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * [exit]simplify: Simplified to (- (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 32 / 80 ] 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 (33 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (418 enodes) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 33 / 80 ] 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 (31 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (201 enodes) * [exit]simplify: Simplified to (- (* (log (* 2 (* n PI))) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* 2 (* n PI))) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 34 / 80 ] 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 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 35 / 80 ] 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 (41 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (180 enodes) * * [misc]simplify: iters left: 2 (358 enodes) * [exit]simplify: Simplified to (* (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 36 / 80 ] 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 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 (* 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 (28 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 (65 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 37 / 80 ] 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 (36 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * * [misc]simplify: iters left: 2 (428 enodes) * [exit]simplify: Simplified to (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (* (sqrt k) k))) * [exit]simplify: Simplified to (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (* (sqrt k) k))) * * * * [misc]progress: [ 38 / 80 ] 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 (28 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 (65 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* n 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 (28 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 (65 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 39 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (pow (* PI (* 2 n)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* PI (* 2 n)) (/ 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 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 40 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 80 ] 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 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 42 / 80 ] 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 (31 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 43 / 80 ] 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 (28 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 (65 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 44 / 80 ] 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: [ 45 / 80 ] 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 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 46 / 80 ] 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 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 47 / 80 ] 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 (27 enodes) * * [misc]simplify: iters left: 4 (43 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 2) PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 48 / 80 ] 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 (27 enodes) * * [misc]simplify: iters left: 4 (43 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 2) PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 49 / 80 ] 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 (21 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) * * * * [misc]progress: [ 50 / 80 ] 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 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (pow (* (* n PI) 2) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* n PI) 2) (/ (- 1 k) 2)) * * * * [misc]progress: [ 51 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 52 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 53 / 80 ] 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: [ 54 / 80 ] 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: [ 55 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 56 / 80 ] 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: [ 57 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * * [misc]simplify: iters left: 2 (12 enodes) * * [misc]simplify: iters left: 1 (16 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 58 / 80 ] 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: [ 59 / 80 ] 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: [ 60 / 80 ] 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 (36 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (78 enodes) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * * * * [misc]progress: [ 61 / 80 ] 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: [ 62 / 80 ] 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: [ 63 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 64 / 80 ] 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: [ 65 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * * [misc]simplify: iters left: 1 (8 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 66 / 80 ] 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: [ 67 / 80 ] 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: [ 68 / 80 ] 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: [ 69 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (375 enodes) * [exit]simplify: Simplified to (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* 2 PI) 1/2)) (+ (log (* 2 PI)) (log n))) (- 1/2)) (+ (* (pow n 1/2) (pow (* 2 PI) 1/2)) (* (* (* 1/8 (pow n 1/2)) (pow (* 2 PI) 1/2)) (* (* (log n) k) (* (log n) k))))) (* (* (pow n 1/2) (pow (* 2 PI) 1/2)) (+ (* (* 1/8 (log (* 2 PI))) (* (* k k) (log (* 2 PI)))) (* 1/4 (* (log (* 2 PI)) (* (log n) (* k k))))))) (sqrt k)) * * * * [misc]progress: [ 70 / 80 ] 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 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (285 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (- 1/2 (* k 1/2))) (pow n (- 1/2 (* k 1/2)))) (sqrt k)) * * * * [misc]progress: [ 71 / 80 ] 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 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (299 enodes) * [exit]simplify: Simplified to (/ (pow (pow (exp 1/2) (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k)) * * * * [misc]progress: [ 72 / 80 ] 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 (27 enodes) * * [misc]simplify: iters left: 4 (43 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 (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 73 / 80 ] 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 (27 enodes) * * [misc]simplify: iters left: 4 (43 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 (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 74 / 80 ] 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 (27 enodes) * * [misc]simplify: iters left: 4 (43 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 (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 75 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI))))))))))))))) * * * * [misc]progress: [ 76 / 80 ] 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)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) * * * * [misc]progress: [ 77 / 80 ] 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)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) * * * * [misc]progress: [ 78 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ (* +nan.0 (/ 1 k)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 79 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 80 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * [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 1 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]backup-simplify: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2) * [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) 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 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) * [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 (- 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 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) * [misc]backup-simplify: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) * [misc]approximate: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * [misc]approximate: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [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 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* PI 2))) * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* PI 2))) * [misc]backup-simplify: Simplify (* +nan.0 (sqrt (* PI 2))) into (* +nan.0 (* (sqrt 2) (sqrt PI))) * [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) 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 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) +nan.0) (+ (* (* +nan.0 (sqrt (* PI 2))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) * [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 (- 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 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) +nan.0) (+ (* (* +nan.0 (sqrt (* PI 2))) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) k) (+ (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) (* (* +nan.0 (* (sqrt 2) (sqrt PI))) (/ 1 k)))) into (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) k)) (sqrt PI))) (- (+ (* +nan.0 (* (/ (sqrt 2) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [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 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [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 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (/ 1 k)) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [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 k) 1) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [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 k) 1) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [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 (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * [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))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n)))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* PI 2))) * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* PI 2))) * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]backup-simplify: Simplify (* (* +nan.0 (sqrt (* PI 2))) (pow n 1/2)) into (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* 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 2) (sqrt (* 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 (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]backup-simplify: Simplify (* (sqrt 2) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 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 n))) into (- (* 1/2 (log n))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) * [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) 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 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) +nan.0) (+ (* (* +nan.0 (sqrt (* PI 2))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (sqrt (* PI 2))) (* -1/2 (* (sqrt n) (log n)))) (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) (pow n 1/2))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* 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 2) (log (* 2 PI))) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 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 PI)) 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]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 (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 (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* 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 2) (sqrt (* 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 (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 (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* 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 2) (log n)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) 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 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 (log 1) into 0 * [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]backup-simplify: Simplify (* (sqrt 2) (log (* 2 PI))) into (* (sqrt 2) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log (* 2 PI))) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log n)) 0) 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 (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) * [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 (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) * [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 (- 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 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) +nan.0) (+ (* (* +nan.0 (sqrt (* PI 2))) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (sqrt (* PI 2))) (* 1/8 (* (sqrt n) (pow (log n) 2)))) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) (* -1/2 (* (sqrt n) (log n)))) (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) (pow n 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))))))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* 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 2) (pow (log n) 2)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log n) 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 n) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log n)))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log 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 (log (log n)) in n * [misc]taylor: Taking taylor expansion of (log 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (log (log n)) into (log (log n)) * [misc]backup-simplify: Simplify (* 2 (log (log n))) into (* 2 (log (log n))) * [misc]backup-simplify: Simplify (exp (* 2 (log (log n)))) into (pow (log n) 2) * [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 (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* 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 2) (log n)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) 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 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 (log 1) into 0 * [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 (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* 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 2) (log (* 2 PI))) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 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 PI)) 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]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 (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 (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* 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 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 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 PI)) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log (* 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 (log (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (log (log (* 2 PI))) into (log (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 2 (log (log (* 2 PI)))) into (* 2 (log (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 2 (log (log (* 2 PI))))) into (pow (log (* 2 PI)) 2) * [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 (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* 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 2) (sqrt (* 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 (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 (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* 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 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log n) (log (* 2 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 n) (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (log 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 (log 1) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]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 (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]backup-simplify: Simplify (* (sqrt 2) (pow (log n) 2)) into (* (sqrt 2) (pow (log n) 2)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log n) 2)) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log n)) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) (log (* 2 PI))) into (* (sqrt 2) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log (* 2 PI))) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log (* 2 PI)) 2)) into (* (sqrt 2) (pow (log (* 2 PI)) 2)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (log n) (log (* 2 PI))) into (* (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (sqrt 2) (* (log n) (log (* 2 PI)))) into (* (sqrt 2) (* (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) 0) 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 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 (+ (* 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 (+ (* (sqrt 2) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log (* 2 PI))) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log n)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 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 (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n 1)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n (/ 1 k))))) into (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (pow PI 2))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) * [misc]backup-simplify: Simplify (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))) into (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 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 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 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 (/ 1 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [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) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log n))) into (* -1 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (* (- 1 (/ 1 k)) (log n)))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [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)) (log (* 2 PI))) into (* (- 1 (/ 1 k)) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [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 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 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 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 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 (/ 1 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [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) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log n))) into (* -1 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (* (- 1 (/ 1 k)) (log n)))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [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)) (log (* 2 PI))) into (* (- 1 (/ 1 k)) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 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 (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* -1 (* (- 1 (/ 1 k)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) 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 (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) 0) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 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 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 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 (/ 1 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [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) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (- 1 (/ 1 k)) (- (log n))) into (* -1 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (* (- 1 (/ 1 k)) (log n)))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [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)) (log (* 2 PI))) into (* (- 1 (/ 1 k)) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (* 1 (/ 1 k))) (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [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 k) 1) (log (* 2 PI))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (/ 1 (- n))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [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 k) 1) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [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 k) 1) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) * [misc]backup-simplify: Simplify (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n)))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 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 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 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 k) 1) (log (/ -1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (- (log -1) (log n))) into (* (+ (/ 1 k) 1) (- (log -1) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) 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 k) 1) (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (log (* 2 PI))) into (* (+ (/ 1 k) 1) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (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 (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) 0) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 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 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 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 k) 1) (log (/ -1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (- (log -1) (log n))) into (* (+ (/ 1 k) 1) (- (log -1) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) 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 k) 1) (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (log (* 2 PI))) into (* (+ (/ 1 k) 1) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) * [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 k) 1) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 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 -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (+ (/ 1 k) 1) 0) (* 0 (- (log -1) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (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 (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) 0) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) 0) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 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 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 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 k) 1) (log (/ -1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (- (log -1) (log n))) into (* (+ (/ 1 k) 1) (- (log -1) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) 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 k) 1) (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (log (* 2 PI))) into (* (+ (/ 1 k) 1) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n)))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n)))) * [misc]taylor: Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (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 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 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 (* 1 (log n)) into (log n) * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]backup-simplify: Simplify (pow n 1/2) into (pow n 1/2) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 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)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) 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 n))) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) * [misc]backup-simplify: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 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)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (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 (/ (+ (* -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 0) (+ (* -1 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) * [misc]backup-simplify: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k)))) * [misc]approximate: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 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 (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (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 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 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 (* -1 (log n)) into (* -1 (log n)) * [misc]backup-simplify: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]backup-simplify: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (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 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 * [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)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (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 (/ 1 n))))) into (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) * [misc]approximate: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 (/ 1 (- n))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (/ 1 (- n))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (/ 1 (- n))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (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) 1) (- (log -1) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log -1) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -1) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify (log -1) into (log -1) * [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 0) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 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 k) 1)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -1) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 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 k) 1)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (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 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0 * [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 k) 1)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (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 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* 2 PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (369 enodes) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 2 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* 2 PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (369 enodes) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 3 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 4 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ 1 2)) * [enter]simplify: Simplifying (pow (* 2 PI) (/ k 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ k 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ k 2)) * * * * [misc]progress: [ 5 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 6 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* 2 PI) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 7 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) 1) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * [exit]simplify: Simplified to (* 2 PI) * [exit]simplify: Simplified to (* 2 PI) * * * * [misc]progress: [ 8 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (- 1 k)) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (12 enodes) * * [misc]simplify: iters left: 1 (13 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (- 1 k)) * [exit]simplify: Simplified to (pow (* 2 PI) (- 1 k)) * * * * [misc]progress: [ 9 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow 2 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow PI (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * * * * [misc]progress: [ 10 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* 2 PI))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* 2 PI))) * * * * [misc]progress: [ 12 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (exp (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 13 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 14 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (pow (pow (* 2 PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* 2 PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 15 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 16 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (429 enodes) * [exit]simplify: Simplified to (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 19 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (429 enodes) * [exit]simplify: Simplified to (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 20 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (sqrt k))) * * [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 (63 enodes) * * [misc]simplify: iters left: 2 (164 enodes) * [exit]simplify: Simplified to (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 21 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (178 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* 2 PI))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* 2 PI))) (log (sqrt k))) * * * * [misc]progress: [ 22 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 23 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 24 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 25 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (141 enodes) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 26 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 27 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (- (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (- (pow (* 2 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: [ 28 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 29 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 30 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 31 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 32 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 33 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) 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 (37 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 34 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 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 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 35 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 36 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 37 / 115 ] 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 (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 38 / 115 ] 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 (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 39 / 115 ] 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 (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 40 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 115 ] 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: [ 42 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 43 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 44 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 45 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 PI) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 46 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 47 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 48 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 49 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 50 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* 2 PI) (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (* (pow (* 2 PI) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* 2 PI) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 51 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 52 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (226 enodes) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 53 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) (log (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 54 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (226 enodes) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 55 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) (log (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 56 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (489 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 57 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (sqrt k))) (log (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (373 enodes) * [exit]simplify: Simplified to (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 58 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (* (log n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (282 enodes) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 59 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (log (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log n) (log (* 2 PI)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log n) (log (* 2 PI)))) (log (sqrt k))) * * * * [misc]progress: [ 60 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (240 enodes) * [exit]simplify: Simplified to (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 61 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (exp (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (exp (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 62 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (118 enodes) * * [misc]simplify: iters left: 3 (442 enodes) * [exit]simplify: Simplified to (* (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))) * * * * [misc]progress: [ 63 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (241 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (/ k (pow (* 2 PI) (/ (- 1 k) 2)))) (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (/ k (pow (* 2 PI) (/ (- 1 k) 2)))) (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))) * * * * [misc]progress: [ 64 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) (cbrt (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))) * [exit]simplify: Simplified to (* (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))) * [enter]simplify: Simplifying (cbrt (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 65 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (213 enodes) * [exit]simplify: Simplified to (pow (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) 3) * [exit]simplify: Simplified to (pow (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) 3) * * * * [misc]progress: [ 66 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (sqrt (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 67 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) * [exit]simplify: Simplified to (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) * [enter]simplify: Simplifying (* (sqrt k) (pow n (/ k 2))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 68 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 69 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (* (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (cbrt (pow n (/ (- 1 k) 2)))) (cbrt (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (cbrt (pow n (/ (- 1 k) 2)))) (cbrt (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 70 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (sqrt (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (sqrt (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (sqrt (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 71 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) 1) * * [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) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 72 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 73 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 74 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 75 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * * * [misc]progress: [ 76 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 77 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 78 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 79 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 80 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 81 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 82 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 83 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 84 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * * * [misc]progress: [ 85 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 86 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 87 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 88 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2)))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2)))) * * * * [misc]progress: [ 89 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 90 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 91 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log n) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (289 enodes) * [exit]simplify: Simplified to (* (- 1 k) (/ (log n) 2)) * [exit]simplify: Simplified to (* (- 1 k) (/ (log n) 2)) * * * * [misc]progress: [ 92 / 115 ] 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 n (/ k 2)) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (pow n (/ k 2)) * [exit]simplify: Simplified to (pow n (/ k 2)) * * * * [misc]progress: [ 93 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 94 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (pow n (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow n (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 95 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n 1) * * [misc]simplify: iters left: 1 (3 enodes) * [exit]simplify: Simplified to n * [exit]simplify: Simplified to n * * * * [misc]progress: [ 96 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (- 1 k)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * * [misc]simplify: iters left: 1 (10 enodes) * [exit]simplify: Simplified to (pow n (- 1 k)) * [exit]simplify: Simplified to (pow n (- 1 k)) * * * * [misc]progress: [ 97 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 98 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (120 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log n)) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log n)) * * * * [misc]progress: [ 99 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (exp (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 100 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (cbrt (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 101 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (pow (pow n (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow n (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 102 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (sqrt (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow n (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (sqrt (pow n (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 103 / 115 ] simplifiying candidate # * * * * [misc]progress: [ 104 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (75 enodes) * * [misc]simplify: iters left: 4 (204 enodes) * [exit]simplify: Simplified to (/ (- (sqrt (* PI 2)) (- (* (* (sqrt PI) (* (sqrt 2) 1/2)) (* k (log (* PI 2)))) (* (* (* (sqrt PI) 1/8) (* (* k k) (sqrt 2))) (* (log (* PI 2)) (log (* PI 2)))))) (/ (sqrt k) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 105 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * [exit]simplify: Simplified to (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 106 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k)) (pow n (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (156 enodes) * [exit]simplify: Simplified to (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 107 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) k)) (sqrt PI))) (- (+ (* +nan.0 (* (/ (sqrt 2) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI)))))))))))))) (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 108 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))))) (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 109 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))))) (pow n (/ (- 1 k) 2))) * * * * [misc]progress: [ 110 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (pow PI 2))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) * * * * [misc]progress: [ 111 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k))))))) * * * * [misc]progress: [ 112 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k))))))) * * * * [misc]progress: [ 113 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (59 enodes) * * [misc]simplify: iters left: 4 (163 enodes) * * [misc]simplify: iters left: 3 (462 enodes) * [exit]simplify: Simplified to (+ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (sqrt n))) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (sqrt n))) (- (* (* 1/8 (log n)) (* (log n) (* k k))) (* (* 1/2 k) (log n))))) * * * * [misc]progress: [ 114 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * [exit]simplify: Simplified to (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (/ 1 n) (- -1/2 (* k -1/2)))) (sqrt k)) * * * * [misc]progress: [ 115 / 115 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (228 enodes) * [exit]simplify: Simplified to (* (pow (exp (log n)) (- 1/2 (* k 1/2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) * * * [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 1 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]backup-simplify: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2) * [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) 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 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) * [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 (- 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 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) * [misc]backup-simplify: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) * [misc]approximate: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [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 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * [misc]approximate: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [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 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow n (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log n)) 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) 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow n (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log n)) 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) 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow n (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log n)) 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) 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]backup-simplify: Simplify (* (pow (* 2 PI) 1/2) (pow n 1/2)) into (sqrt (* PI (* n 2))) * [misc]taylor: Taking taylor expansion of (sqrt (* PI (* n 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) 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 2) 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 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* PI 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* PI 2) (* 0 0)) 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 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow 0 1) 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) 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 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (+ (* (pow (* 2 PI) 1/2) 0) (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) (pow n 1/2))) into (- (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI))))) * [misc]taylor: Taking taylor expansion of (- (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) 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 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 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 PI)) 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]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 (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]backup-simplify: Simplify (* (sqrt 2) (log (* 2 PI))) into (* (sqrt 2) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log (* 2 PI))) 0) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* +nan.0 PI) into (* +nan.0 PI) * [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 (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (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 (- 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 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) * [misc]backup-simplify: Simplify (+ (* (pow (* 2 PI) 1/2) 0) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 0) (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) (pow n 1/2)))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) * [misc]taylor: Taking taylor expansion of (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) in n * [misc]taylor: Taking taylor expansion of 1/8 in n * [misc]backup-simplify: Simplify 1/8 into 1/8 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 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 PI)) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log (* 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 (log (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (log (log (* 2 PI))) into (log (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 2 (log (log (* 2 PI)))) into (* 2 (log (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 2 (log (log (* 2 PI))))) into (pow (log (* 2 PI)) 2) * [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]backup-simplify: Simplify (* (sqrt 2) (pow (log (* 2 PI)) 2)) into (* (sqrt 2) (pow (log (* 2 PI)) 2)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) 0) into 0 * [misc]backup-simplify: Simplify (* 1/8 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 (+ (* (sqrt 2) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log (* 2 PI))) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))) into (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) into (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) 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 (pow PI 2)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (pow PI 2)) (pow (* n 1) 2)) (+ (* (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) (* n k)) (* (* +nan.0 PI) (* n 1)))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (pow n 2) (pow PI 2))) (- (* +nan.0 (* n PI))))))) * [misc]approximate: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 n))) 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)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log n))) into (* -1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* -1/2 (log n))) into (pow n -1/2) * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 n))) 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)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 1 n)))) into (pow (/ 1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 n))) 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)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 1 n)))) into (pow (/ 1 n) 1/2) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (pow (/ 1 n) 1/2)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ 1 n))) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [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)) (log (* 2 PI))) into (* (- 1 (/ 1 k)) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) 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]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (/ 1 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ 1 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) 0) (* 0 (pow (/ 1 n) 1/2))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [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 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 (+ (* (- 1 (/ 1 k)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)) (* 0 (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 1 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 1 n) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (log (/ 1 n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ 1 n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (pow (/ 1 n) 1/2)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [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 (- (+ (* (/ 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 (+ (* (- 1 (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (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 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (* (/ 1 n) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (* (/ 1 n) 1)) (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow n 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) n)) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))))) * [misc]approximate: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 (- n)))) 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))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -1) (log n)))) into (exp (* 1/2 (- (log -1) (log n)))) * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 (- n)))) 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))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ -1 n)))) into (pow (/ -1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 (- n)))) 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))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ -1 n)))) into (pow (/ -1 n) 1/2) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (pow (/ -1 n) 1/2)) into (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (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) 1) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) 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 k) 1) (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (log (* 2 PI))) into (* (+ (/ 1 k) 1) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [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 k) 1) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [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 (/ (* (pow (* 1 0) 1)) (pow (/ -1 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (/ -1 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ -1 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) 0) (* 0 (pow (/ -1 n) 1/2))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [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 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (+ (/ 1 k) 1) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (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 (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 n) (/ 0 (- n))) (* 0 (/ 0 (- n))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ -1 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ -1 n) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (log (/ -1 n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ -1 n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (pow (/ -1 n) 1/2)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [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 (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (+ (/ 1 k) 1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (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 (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))) (pow (* (/ 1 (- n)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))) (* (/ 1 (- n)) 1)) (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow n 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) n)) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow n (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log n)) 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) 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow n (/ k 2))) 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]taylor: Taking taylor expansion of (pow n (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log n)) 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) 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 k) (log n)) into (* 1/2 (* (log n) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log n) k))) into (exp (* 1/2 (* (log n) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow n 1/2)) into (* (sqrt n) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* 1/2 (* (log n) k)))) into (* (exp (* 1/2 (* (log n) k))) (sqrt k)) * [misc]backup-simplify: Simplify (/ (* (sqrt n) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (* (exp (* 1/2 (* (log n) k))) (sqrt k))) into (* (sqrt (/ n k)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (log n) k))))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow n (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log n)) 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) 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow n (/ k 2))) 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]taylor: Taking taylor expansion of (pow n (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log n)) 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) 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* (pow (* 2 PI) 1/2) (pow n 1/2)) into (sqrt (* PI (* n 2))) * [misc]backup-simplify: Simplify (* 0 1) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log n)) 1) 1)))) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (+ (* 0 (* 1/2 (log n))) (* +nan.0 1)) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (sqrt (* PI (* n 2))) (- +nan.0)) into (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow n (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log n)) 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) 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow n (/ k 2))) 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]taylor: Taking taylor expansion of (pow n (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log n)) 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) 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* (pow (* 2 PI) 1/2) (pow n 1/2)) into (sqrt (* PI (* n 2))) * [misc]backup-simplify: Simplify (* 0 1) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log n)) 1) 1)))) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (+ (* 0 (* 1/2 (log n))) (* +nan.0 1)) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (sqrt (* PI (* n 2))) (- +nan.0)) into (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* 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 2) (sqrt (* 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 (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]backup-simplify: Simplify (* (sqrt 2) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow 0 1) 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) 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 PI)))) into (- (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (+ (* (pow (* 2 PI) 1/2) 0) (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) (pow n 1/2))) into (- (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI))))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log n)) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (pow (log n) 2)) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (pow (log n) 2))) (+ (* +nan.0 (* 1/2 (log n))) (* +nan.0 1))) into (- (+ +nan.0 (- (* +nan.0 (log n))))) * [misc]backup-simplify: Simplify (- (/ (- (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI))))) (- +nan.0)) (+ (* (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (/ (- (+ +nan.0 (- (* +nan.0 (log n))))) (- +nan.0))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* 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 2) (log (* 2 PI))) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 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 PI)) 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]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 (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 (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* 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 2) (sqrt (* 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 (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 (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* 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 2) (log n)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) 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 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 (log 1) into 0 * [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]backup-simplify: Simplify (* (sqrt 2) (log (* 2 PI))) into (* (sqrt 2) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log (* 2 PI))) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log n)) 0) 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 (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) * [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 (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (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 (- 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 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) * [misc]backup-simplify: Simplify (+ (* (pow (* 2 PI) 1/2) 0) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 0) (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) (pow n 1/2)))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) * [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 2) (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log n)) 3) 6)) (* (/ (pow (* 1/2 (log n)) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* 1/48 (pow (log n) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/48 (pow (log n) 3))) (+ (* +nan.0 (* 1/8 (pow (log n) 2))) (+ (* +nan.0 (* 1/2 (log n))) (* +nan.0 1)))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- +nan.0)) (+ (* (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (/ (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) (- +nan.0))) (* (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) (/ (- (+ +nan.0 (- (* +nan.0 (log n))))) (- +nan.0))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* 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 2) (pow (log n) 2)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log n) 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 n) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log n)))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log 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 (log (log n)) in n * [misc]taylor: Taking taylor expansion of (log 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (log (log n)) into (log (log n)) * [misc]backup-simplify: Simplify (* 2 (log (log n))) into (* 2 (log (log n))) * [misc]backup-simplify: Simplify (exp (* 2 (log (log n)))) into (pow (log n) 2) * [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 (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* 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 2) (log n)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) 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 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 (log 1) into 0 * [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 (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* 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 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 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 PI)) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log (* 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 (log (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (log (log (* 2 PI))) into (log (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 2 (log (log (* 2 PI)))) into (* 2 (log (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 2 (log (log (* 2 PI))))) into (pow (log (* 2 PI)) 2) * [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 (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* 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 2) (log (* 2 PI))) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 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 PI)) 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]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 (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 (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* 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 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log n) (log (* 2 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 n) (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (log 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 (log 1) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]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 (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 (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* 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 2) (sqrt (* 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 (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]backup-simplify: Simplify (* (sqrt 2) (pow (log n) 2)) into (* (sqrt 2) (pow (log n) 2)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log n) 2)) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log n)) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log (* 2 PI)) 2)) into (* (sqrt 2) (pow (log (* 2 PI)) 2)) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) (log (* 2 PI))) into (* (sqrt 2) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log (* 2 PI))) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (log n) (log (* 2 PI))) into (* (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (sqrt 2) (* (log n) (log (* 2 PI)))) into (* (sqrt 2) (* (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) 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 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 (+ (* 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 (+ (* (sqrt 2) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log (* 2 PI))) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log n)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 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 (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n 1)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n (/ 1 k))))) into (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (pow PI 2))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2)))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 n))) 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)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log n))) into (* -1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* -1/2 (log n))) into (pow n -1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2))) 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]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (/ 1 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 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)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log n))) into (* -1/2 (/ (log n) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (log n) k))) into (exp (* -1/2 (/ (log n) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (pow n -1/2)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ 1 n))) * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* -1/2 (/ (log n) k)))) into (* (exp (* -1/2 (/ (log n) k))) (sqrt (/ 1 k))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ 1 n))) (* (exp (* -1/2 (/ (log n) k))) (sqrt (/ 1 k)))) into (* (sqrt (/ k n)) (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k))))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 n))) 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)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 1 n)))) into (pow (/ 1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2))) 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 (pow (/ 1 n) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (/ 1 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 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)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) into (exp (* 1/2 (/ (log (/ 1 n)) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (pow (/ 1 n) 1/2)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ 1 n))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (log (/ 1 n)) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ 1 n))) (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k)))))) into (* +nan.0 (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 n)))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (pow (/ 1 n) (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 n))) 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)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 1 n)))) into (pow (/ 1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2))) 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 (pow (/ 1 n) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (/ 1 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 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)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) into (exp (* 1/2 (/ (log (/ 1 n)) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (pow (/ 1 n) 1/2)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ 1 n))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (log (/ 1 n)) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ 1 n))) (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k)))))) into (* +nan.0 (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 n)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 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))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [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)) (log (* 2 PI))) into (* (- 1 (/ 1 k)) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (/ 1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (/ 1 n)) 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 (/ 1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (/ (- (log n)) k) into (* -1 (/ (log n) k)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (/ (log n) k))) into (* -1/2 (/ (log n) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (log n) k))) into (exp (* -1/2 (/ (log n) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) 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]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (* -1 (/ (log n) k)) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* -1 (/ (log n) k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log n) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (log n) k)))) (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) (/ 0 (exp (* -1/2 (/ (log n) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k))))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (/ 1 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ 1 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) 0) (* 0 (pow (/ 1 n) 1/2))) 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 (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k)))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k)))))) (+ (* (* +nan.0 (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 n)))) (/ (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))))))) into (- (* +nan.0 (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 n))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 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))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* 1/2 (/ (log (/ 1 n)) k)))) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) 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))) 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)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [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)) (log (* 2 PI))) into (* (- 1 (/ 1 k)) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (/ 1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (/ 1 n)) 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 (/ 1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (/ (- (log n)) k) into (* -1 (/ (log n) k)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (/ (log n) k))) into (* -1/2 (/ (log n) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (log n) k))) into (exp (* -1/2 (/ (log n) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) 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]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (* -1 (/ (log n) k)) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* -1 (/ (log n) k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log n) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (log n) k)))) (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) (/ 0 (exp (* -1/2 (/ (log n) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k))))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k))))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [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 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 (+ (* (- 1 (/ 1 k)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (* -1 (/ (log n) k)) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (* -1 (/ (log n) k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log n) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (log n) k)))) (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) (/ 0 (exp (* -1/2 (/ (log n) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (log n) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k))))))) (+ (* 0 (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k))))))) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (/ (log n) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) (exp (* -1/2 (/ (log (/ 1 n)) (/ 1 k))))))) (* (/ 1 n) 1)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) (exp (* -1/2 (/ (log (/ 1 n)) (/ 1 k))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) (exp (* -1/2 (/ (log (/ 1 n)) (/ 1 k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (* (exp (* -1/2 (* (log (/ 1 n)) k))) k))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (log (/ 1 n)) k))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (* (exp (* -1/2 (* (log (/ 1 n)) k))) n)))))))) * [misc]approximate: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 (- n)))) 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))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -1) (log n)))) into (exp (* 1/2 (- (log -1) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2))) 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]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (/ 1 (- 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 (- 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))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -1) (log n))) into (* -1/2 (/ (- (log -1) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -1) (log n)) k))) into (exp (* -1/2 (/ (- (log -1) (log n)) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (- (log -1) (log n))))) into (* (exp (* 1/2 (- (log -1) (log n)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log -1) (log n)) k)))) into (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log -1) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (- (log -1) (log n)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) into (/ (* (exp (* 1/2 (- (log -1) (log n)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 (- n)))) 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))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ -1 n)))) into (pow (/ -1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2))) 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]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (/ 1 (- 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 (- 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))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ -1 n))) into (* -1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) into (exp (* -1/2 (/ (log (/ -1 n)) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (pow (/ -1 n) 1/2)) into (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (log (/ -1 n)) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) * [misc]backup-simplify: Simplify (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k)))))) into (* +nan.0 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (pow (/ 1 (- n)) (/ 1 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 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 (* 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]backup-simplify: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (/ 1 (- n)))) 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))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ -1 n)))) into (pow (/ -1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2))) 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]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (/ 1 (- 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 (- 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))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ -1 n))) into (* -1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) into (exp (* -1/2 (/ (log (/ -1 n)) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (pow (/ -1 n) 1/2)) into (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (log (/ -1 n)) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) * [misc]backup-simplify: Simplify (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k)))))) into (* +nan.0 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) k))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) 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 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) k)))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (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) 1) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) 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 k) 1) (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (log (* 2 PI))) into (* (+ (/ 1 k) 1) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (/ -1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (/ -1 n)) 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 (/ -1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (log -1) into (log -1) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -1) (log n)) k) into (/ (- (log -1) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log -1) (log n)) k)) into (* -1/2 (/ (- (log -1) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -1) (log n)) k))) into (exp (* -1/2 (/ (- (log -1) (log n)) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) 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 k) 1) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))) into (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [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 (/ (* (pow (* 1 0) 1)) (pow (/ -1 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (/ -1 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ -1 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) 0) (* 0 (pow (/ -1 n) 1/2))) 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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k)))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k)))))) (+ (* (* +nan.0 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))))))) into (- (* +nan.0 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) k)))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) k)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) 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 (/ (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (exp (* -1/2 (/ (log (/ -1 n)) k)))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt (/ -1 n)) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (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) 1) (log (* 2 PI))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) 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 k) 1) (log (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) 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]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (* (+ (/ 1 k) 1) (log (* 2 PI))) into (* (+ (/ 1 k) 1) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (/ -1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (/ -1 n)) 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 (/ -1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (log -1) into (log -1) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -1) (log n)) k) into (/ (- (log -1) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log -1) (log n)) k)) into (* -1/2 (/ (- (log -1) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -1) (log n)) k))) into (exp (* -1/2 (/ (- (log -1) (log n)) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) 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 k) 1) 0) (* 0 (log (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (/ (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))) into (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) * [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 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (+ (/ 1 k) 1) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (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 (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log -1) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log -1) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -1) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))) (+ (* (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))) (/ 0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))))) (* 0 (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k))))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- n)) 1)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* -1/2 (/ (- (log -1) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (* (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))) k))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (* (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))) n)))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow n (/ k 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow n (/ k 2))) 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]taylor: Taking taylor expansion of (pow n (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log n))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log n)) 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) 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* (* 1/2 k) (log n)) into (* 1/2 (* (log n) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log n) k))) into (exp (* 1/2 (* (log n) k))) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow n (/ k 2))) 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]taylor: Taking taylor expansion of (pow n (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log n)) 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) 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow n (/ k 2))) 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]taylor: Taking taylor expansion of (pow n (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log n)) 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) 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 (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* 0 1) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log n)) 1) 1)))) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (+ (* 0 (* 1/2 (log n))) (* +nan.0 1)) into (- +nan.0) * [misc]taylor: Taking taylor expansion of (- +nan.0) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (- +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 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log n)) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (pow (log n) 2)) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (pow (log n) 2))) (+ (* +nan.0 (* 1/2 (log n))) (* +nan.0 1))) into (- (+ +nan.0 (- (* +nan.0 (log n))))) * [misc]taylor: Taking taylor expansion of (- (+ +nan.0 (- (* +nan.0 (log n))))) in n * [misc]taylor: Taking taylor expansion of (+ +nan.0 (- (* +nan.0 (log 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 (- (* +nan.0 (log n))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (log 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 (log 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* +nan.0 (log n)) into (* +nan.0 (log n)) * [misc]backup-simplify: Simplify (- (* +nan.0 (log n))) into (- (* +nan.0 (log n))) * [misc]backup-simplify: Simplify (+ +nan.0 (- (* +nan.0 (log n)))) into (- (+ +nan.0 (- (* +nan.0 (log n))))) * [misc]backup-simplify: Simplify (- (- (+ +nan.0 (- (* +nan.0 (log n)))))) into (- (+ +nan.0 (- (* +nan.0 (log n))))) * [misc]backup-simplify: Simplify (- (+ +nan.0 (- (* +nan.0 (log n))))) into (- (+ +nan.0 (- (* +nan.0 (log n))))) * [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 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log n)) 3) 6)) (* (/ (pow (* 1/2 (log n)) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* 1/48 (pow (log n) 3)) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/48 (pow (log n) 3))) (+ (* +nan.0 (* 1/8 (pow (log n) 2))) (+ (* +nan.0 (* 1/2 (log n))) (* +nan.0 1)))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (pow (log n) 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 (pow (log n) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log n)))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log 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 (log (log n)) in n * [misc]taylor: Taking taylor expansion of (log 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (log (log n)) into (log (log n)) * [misc]backup-simplify: Simplify (* 2 (log (log n))) into (* 2 (log (log n))) * [misc]backup-simplify: Simplify (exp (* 2 (log (log n)))) into (pow (log n) 2) * [misc]taylor: Taking taylor expansion of (- (+ +nan.0 (- (* +nan.0 (log n))))) in n * [misc]taylor: Taking taylor expansion of (+ +nan.0 (- (* +nan.0 (log 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 (- (* +nan.0 (log n))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (log 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 (log 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 (log 1) into 0 * [misc]backup-simplify: Simplify (* +nan.0 (pow (log n) 2)) into (* +nan.0 (pow (log n) 2)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* +nan.0 (log n)) into (* +nan.0 (log n)) * [misc]backup-simplify: Simplify (- (* +nan.0 (log n))) into (- (* +nan.0 (log n))) * [misc]backup-simplify: Simplify (+ +nan.0 (- (* +nan.0 (log n)))) into (- (+ +nan.0 (- (* +nan.0 (log n))))) * [misc]backup-simplify: Simplify (- (- (+ +nan.0 (- (* +nan.0 (log n)))))) into (- (+ +nan.0 (- (* +nan.0 (log n))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n)))))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n)))))))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) into (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (pow (log n) 2)) (- (+ +nan.0 (- (* +nan.0 (log n))))))) (pow (* 1 k) 3)) (+ (* (- (+ +nan.0 (- (* +nan.0 (log n))))) (pow (* 1 k) 2)) (* (- +nan.0) (* 1 k)))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow k 3))) (- (+ (* +nan.0 (pow k 2)) (- (+ (* +nan.0 (pow k 3)) (- (+ (* +nan.0 (* (log n) (pow k 2))) (- (+ (* +nan.0 k) (- (* +nan.0 (* (log n) (pow k 3)))))))))))))) * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2))) 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]taylor: Taking taylor expansion of (pow (/ 1 n) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (/ 1 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 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)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log n))) into (* -1/2 (/ (log n) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (log n) k))) into (exp (* -1/2 (/ (log n) k))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2))) 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 (pow (/ 1 n) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (/ 1 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 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)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) into (exp (* 1/2 (/ (log (/ 1 n)) k))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (/ 1 n) (/ (/ 1 k) 2))) 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 (pow (/ 1 n) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (/ 1 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 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)) 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]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (/ 1 n)))) into (exp (* 1/2 (/ (log (/ 1 n)) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (log (/ 1 n)) k)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) 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 (/ 1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (/ 1 n)) 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 (/ 1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (/ (- (log n)) k) into (* -1 (/ (log n) k)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (/ (log n) k))) into (* -1/2 (/ (log n) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (log n) k))) into (exp (* -1/2 (/ (log n) k))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* -1/2 (/ (log n) k)))) into (* +nan.0 (exp (* -1/2 (/ (log n) k)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) * [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 (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k)))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) 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 (/ 1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (/ 1 n)) 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 (/ 1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (/ (- (log n)) k) into (* -1 (/ (log n) k)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (/ (log n) k))) into (* -1/2 (/ (log n) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (log n) k))) into (exp (* -1/2 (/ (log n) k))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* -1/2 (/ (log n) k)))) into (* +nan.0 (exp (* -1/2 (/ (log n) k)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (* -1 (/ (log n) k)) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* -1 (/ (log n) k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (log n) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* -1/2 (/ (log n) k))))) 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)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) k))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (/ (log (/ 1 n)) 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 (/ 1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (/ 1 n)) 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 (/ 1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) 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]backup-simplify: Simplify (log 1) into 0 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (/ (- (log n)) k) into (* -1 (/ (log n) k)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (/ (log n) k))) into (* -1/2 (/ (log n) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (log n) k))) into (exp (* -1/2 (/ (log n) k))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* -1/2 (/ (log n) k)))) into (* +nan.0 (exp (* -1/2 (/ (log n) k)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log n) k))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* -1/2 (/ (log (/ 1 n)) (/ 1 k)))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (exp (* -1/2 (/ (log (/ 1 n)) (/ 1 k)))))) (* 1 (/ 1 k))) (- (* +nan.0 (exp (* -1/2 (/ (log (/ 1 n)) (/ 1 k)))))))) into (- (+ (* +nan.0 (/ (exp (* -1/2 (* (log (/ 1 n)) k))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* -1/2 (* (log (/ 1 n)) k))) k)) (- (* +nan.0 (exp (* -1/2 (* (log (/ 1 n)) k))))))))) * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2))) 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]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (/ 1 (- 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 (- 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))) 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]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -1) (log n))) into (* -1/2 (/ (- (log -1) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -1) (log n)) k))) into (exp (* -1/2 (/ (- (log -1) (log n)) k))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2))) 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]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (/ 1 (- 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 (- 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))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ -1 n))) into (* -1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) into (exp (* -1/2 (/ (log (/ -1 n)) k))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2))) 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]taylor: Taking taylor expansion of (pow (/ 1 (- n)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (/ 1 (- 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 (- 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))) 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]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ -1 n))) into (* -1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (/ 1 (- n))))) into (exp (* -1/2 (/ (log (/ -1 n)) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (log (/ -1 n)) k)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) 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 (/ -1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (/ -1 n)) 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 (/ -1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (log -1) into (log -1) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -1) (log n)) k) into (/ (- (log -1) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log -1) (log n)) k)) into (* -1/2 (/ (- (log -1) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -1) (log n)) k))) into (exp (* -1/2 (/ (- (log -1) (log n)) k))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k)))) into (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [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 (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k)))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) 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 (/ -1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (/ -1 n)) 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 (/ -1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (log -1) into (log -1) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -1) (log n)) k) into (/ (- (log -1) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log -1) (log n)) k)) into (* -1/2 (/ (- (log -1) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -1) (log n)) k))) into (exp (* -1/2 (/ (- (log -1) (log n)) k))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k)))) into (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log -1) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log -1) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -1) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) 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 (- (+ (* -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 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) k))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* -1/2 (/ (log (/ -1 n)) 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 (/ -1 n)) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (/ -1 n)) 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 (/ -1 n)) k) in n * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [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 (log -1) into (log -1) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -1) (log n)) k) into (/ (- (log -1) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log -1) (log n)) k)) into (* -1/2 (/ (- (log -1) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -1) (log n)) k))) into (exp (* -1/2 (/ (- (log -1) (log n)) k))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k)))) into (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log n)) k))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log (/ 1 (- n)))) (/ 1 (- k))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log (/ 1 (- n)))) (/ 1 (- k))))))) (* 1 (/ 1 (- k)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -1) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))) k))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* 2 PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (369 enodes) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 2 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* 2 PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (369 enodes) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 3 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 4 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ 1 2)) * [enter]simplify: Simplifying (pow (* 2 PI) (/ k 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ k 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ k 2)) * * * * [misc]progress: [ 5 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 6 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* 2 PI) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 7 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) 1) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * [exit]simplify: Simplified to (* 2 PI) * [exit]simplify: Simplified to (* 2 PI) * * * * [misc]progress: [ 8 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (- 1 k)) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (12 enodes) * * [misc]simplify: iters left: 1 (13 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (- 1 k)) * [exit]simplify: Simplified to (pow (* 2 PI) (- 1 k)) * * * * [misc]progress: [ 9 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow 2 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow PI (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * * * * [misc]progress: [ 10 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (451 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* 2 PI))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* 2 PI))) * * * * [misc]progress: [ 12 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (exp (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 13 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 14 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (pow (pow (* 2 PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* 2 PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 15 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 16 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (* (log n) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (444 enodes) * [exit]simplify: Simplified to (+ (/ (log n) 2) (* (log (* 2 PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (+ (/ (log n) 2) (* (log (* 2 PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 19 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (420 enodes) * [exit]simplify: Simplified to (+ (/ (log n) 2) (/ (log (* 2 PI)) (/ 2 (- 1 k)))) * [exit]simplify: Simplified to (+ (/ (log n) 2) (/ (log (* 2 PI)) (/ 2 (- 1 k)))) * * * * [misc]progress: [ 20 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (* (log n) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (444 enodes) * [exit]simplify: Simplified to (+ (/ (log n) 2) (* (log (* 2 PI)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (+ (/ (log n) 2) (* (log (* 2 PI)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 21 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (420 enodes) * [exit]simplify: Simplified to (+ (/ (log n) 2) (/ (log (* 2 PI)) (/ 2 (- 1 k)))) * [exit]simplify: Simplified to (+ (/ (log n) 2) (/ (log (* 2 PI)) (/ 2 (- 1 k)))) * * * * [misc]progress: [ 22 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow (* 2 PI) (/ (- 1 k) 2))) (* (log n) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (197 enodes) * [exit]simplify: Simplified to (+ (/ (log n) 2) (/ (log (* 2 PI)) (/ 2 (- 1 k)))) * [exit]simplify: Simplified to (+ (/ (log n) 2) (/ (log (* 2 PI)) (/ 2 (- 1 k)))) * * * * [misc]progress: [ 23 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (169 enodes) * [exit]simplify: Simplified to (+ (/ (log n) 2) (/ (log (* 2 PI)) (/ 2 (- 1 k)))) * [exit]simplify: Simplified to (+ (/ (log n) 2) (/ (log (* 2 PI)) (/ 2 (- 1 k)))) * * * * [misc]progress: [ 24 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (180 enodes) * [exit]simplify: Simplified to (+ (* (/ (- 1 k) 2) (log (* 2 PI))) (/ (log n) 2)) * [exit]simplify: Simplified to (+ (* (/ (- 1 k) 2) (log (* 2 PI))) (/ (log n) 2)) * * * * [misc]progress: [ 25 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (exp (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * [exit]simplify: Simplified to (exp (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * * * [misc]progress: [ 26 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (* (* (pow n (/ 1 2)) (pow n (/ 1 2))) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (113 enodes) * * [misc]simplify: iters left: 1 (114 enodes) * [exit]simplify: Simplified to (pow (* (pow n (/ 1 2)) (pow (* 2 PI) (/ (- 1 k) 2))) 3) * [exit]simplify: Simplified to (pow (* (pow n (/ 1 2)) (pow (* 2 PI) (/ (- 1 k) 2))) 3) * * * * [misc]progress: [ 27 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (* (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))))) * [exit]simplify: Simplified to (* (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))))) * [enter]simplify: Simplifying (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * [exit]simplify: Simplified to (cbrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * * * [misc]progress: [ 28 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (pow (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) 3) * [exit]simplify: Simplified to (pow (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) 3) * * * * [misc]progress: [ 29 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * [exit]simplify: Simplified to (sqrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * [enter]simplify: Simplifying (sqrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * [exit]simplify: Simplified to (sqrt (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * * * [misc]progress: [ 30 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (pow n (/ 1 2))) (cbrt (pow n (/ 1 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (* (* (cbrt (pow n (/ 1 2))) (cbrt (pow n (/ 1 2)))) (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (* (cbrt (pow n (/ 1 2))) (cbrt (pow n (/ 1 2)))) (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 32 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (* (sqrt (pow n (/ 1 2))) (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (pow n (/ 1 2))) (pow (* 2 PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 33 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 PI) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 34 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow PI (/ (- 1 k) 2)) (pow n (/ 1 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (* (pow n (/ 1 2)) (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow n (/ 1 2)) (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 35 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ 1 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (* (pow n (/ 1 2)) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (pow n (/ 1 2)) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 36 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ 1 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (* (pow n (/ 1 2)) (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (pow n (/ 1 2)) (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 37 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) * [exit]simplify: Simplified to (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) * * * * [misc]progress: [ 38 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 PI) (/ 1 2)) (pow n (/ 1 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * [exit]simplify: Simplified to (* (pow n (/ 1 2)) (pow (* 2 PI) (/ 1 2))) * [exit]simplify: Simplified to (* (pow n (/ 1 2)) (pow (* 2 PI) (/ 1 2))) * * * * [misc]progress: [ 39 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (* (log n) (/ 1 2))) (+ (log (sqrt k)) (* (log n) (/ k 2)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (257 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (+ (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 42 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (* (log n) (/ 1 2))) (+ (log (sqrt k)) (log (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k)))) * [exit]simplify: Simplified to (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k)))) * * * * [misc]progress: [ 43 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (* (log n) (/ 1 2))) (log (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (214 enodes) * [exit]simplify: Simplified to (- (* (log n) (/ (- 1 k) 2)) (- (log (sqrt k)) (* (log (* 2 PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (- (* (log n) (/ (- 1 k) 2)) (- (log (sqrt k)) (* (log (* 2 PI)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 44 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (pow n (/ 1 2)))) (+ (log (sqrt k)) (* (log n) (/ k 2)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (251 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 45 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (pow n (/ 1 2)))) (+ (log (sqrt k)) (log (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (245 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 46 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (pow n (/ 1 2)))) (log (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (209 enodes) * [exit]simplify: Simplified to (+ (/ (log n) 2) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (+ (log (sqrt k)) (* (log n) (/ k 2))))) * [exit]simplify: Simplified to (+ (/ (log n) 2) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (+ (log (sqrt k)) (* (log n) (/ k 2))))) * * * * [misc]progress: [ 47 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (* (log n) (/ 1 2))) (+ (log (sqrt k)) (* (log n) (/ k 2)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (257 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (+ (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 48 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (* (log n) (/ 1 2))) (+ (log (sqrt k)) (log (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k)))) * [exit]simplify: Simplified to (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k)))) * * * * [misc]progress: [ 49 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (* (log n) (/ 1 2))) (log (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (214 enodes) * [exit]simplify: Simplified to (- (* (log n) (/ (- 1 k) 2)) (- (log (sqrt k)) (* (log (* 2 PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (- (* (log n) (/ (- 1 k) 2)) (- (log (sqrt k)) (* (log (* 2 PI)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 50 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (pow n (/ 1 2)))) (+ (log (sqrt k)) (* (log n) (/ k 2)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (251 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 51 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (pow n (/ 1 2)))) (+ (log (sqrt k)) (log (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (245 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 52 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (pow n (/ 1 2)))) (log (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (209 enodes) * [exit]simplify: Simplified to (+ (/ (log n) 2) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (+ (log (sqrt k)) (* (log n) (/ k 2))))) * [exit]simplify: Simplified to (+ (/ (log n) 2) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (+ (log (sqrt k)) (* (log n) (/ k 2))))) * * * * [misc]progress: [ 53 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (log (pow (* 2 PI) (/ (- 1 k) 2))) (* (log n) (/ 1 2))) (+ (log (sqrt k)) (* (log n) (/ k 2)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * [exit]simplify: Simplified to (+ (- (* (/ (- 1 k) 2) (log (* 2 PI))) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (+ (- (* (/ (- 1 k) 2) (log (* 2 PI))) (log (sqrt k))) (* (log n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 54 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (log (pow (* 2 PI) (/ (- 1 k) 2))) (* (log n) (/ 1 2))) (+ (log (sqrt k)) (log (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * [exit]simplify: Simplified to (- (+ (* (log n) (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (log (* 2 PI)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (+ (* (log n) (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (log (* 2 PI)))) (log (sqrt k))) * * * * [misc]progress: [ 55 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (log (pow (* 2 PI) (/ (- 1 k) 2))) (* (log n) (/ 1 2))) (log (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (482 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 56 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (pow n (/ 1 2)))) (+ (log (sqrt k)) (* (log n) (/ k 2)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 57 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (pow n (/ 1 2)))) (+ (log (sqrt k)) (log (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (169 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 58 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (pow n (/ 1 2)))) (log (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (439 enodes) * [exit]simplify: Simplified to (- (+ (* (log n) (/ (- 1 k) 2)) (* (log (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (+ (* (log n) (/ (- 1 k) 2)) (* (log (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k))) * * * * [misc]progress: [ 59 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (+ (log (sqrt k)) (* (log n) (/ k 2)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (265 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log n) (log (* 2 PI)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log n) (log (* 2 PI)))) (log (sqrt k))) * * * * [misc]progress: [ 60 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (+ (log (sqrt k)) (log (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 61 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (log (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* 2 PI)) (log n))) (log (sqrt k))) * * * * [misc]progress: [ 62 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (403 enodes) * [exit]simplify: Simplified to (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 63 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (102 enodes) * [exit]simplify: Simplified to (exp (/ (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 64 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (* (* (pow n (/ 1 2)) (pow n (/ 1 2))) (pow n (/ 1 2)))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow n (/ k 2)) (pow n (/ k 2))) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (241 enodes) * [exit]simplify: Simplified to (* (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ k (pow (* 2 PI) (/ (- 1 k) 2)))) (* (/ (pow n (/ 1 2)) (* (sqrt k) (pow n (/ k 2)))) (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (/ (pow n (/ 1 2)) (pow n (/ k 2)))))) * [exit]simplify: Simplified to (* (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ k (pow (* 2 PI) (/ (- 1 k) 2)))) (* (/ (pow n (/ 1 2)) (* (sqrt k) (pow n (/ k 2)))) (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (/ (pow n (/ 1 2)) (pow n (/ k 2)))))) * * * * [misc]progress: [ 65 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (* (* (pow n (/ 1 2)) (pow n (/ 1 2))) (pow n (/ 1 2)))) (* (* (* (sqrt k) (pow n (/ k 2))) (* (sqrt k) (pow n (/ k 2)))) (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (225 enodes) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (* k (pow n (/ k 2))) (/ (pow n (/ 1 2)) (pow n (/ k 2))))) (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (* (/ (pow n (/ k 2)) (pow n (/ 1 2))) (/ (sqrt k) (pow n (/ 1 2)))))) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (* k (pow n (/ k 2))) (/ (pow n (/ 1 2)) (pow n (/ k 2))))) (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (* (/ (pow n (/ k 2)) (pow n (/ 1 2))) (/ (sqrt k) (pow n (/ 1 2)))))) * * * * [misc]progress: [ 66 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow n (/ k 2)) (pow n (/ k 2))) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (217 enodes) * [exit]simplify: Simplified to (* (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (/ (* (pow n (/ k 2)) (pow n (/ k 2))) (/ (pow n (/ 1 2)) (pow n (/ k 2))))) (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (/ (* k (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (/ (* (pow n (/ k 2)) (pow n (/ k 2))) (/ (pow n (/ 1 2)) (pow n (/ k 2))))) (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (/ (* k (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 67 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) (* (* (* (sqrt k) (pow n (/ k 2))) (* (sqrt k) (pow n (/ k 2)))) (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (202 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (pow n (/ k 2)) (pow n (/ 1 2))))) (/ (* (pow n (/ k 2)) k) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (pow n (/ k 2)) (pow n (/ 1 2)))))) * [exit]simplify: Simplified to (/ (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (pow n (/ k 2)) (pow n (/ 1 2))))) (/ (* (pow n (/ k 2)) k) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (pow n (/ k 2)) (pow n (/ 1 2)))))) * * * * [misc]progress: [ 68 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2))))) (cbrt (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))) (/ (sqrt k) (pow n (/ 1 2))))) (cbrt (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))) (/ (sqrt k) (pow n (/ 1 2)))))) * [exit]simplify: Simplified to (* (cbrt (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))) (/ (sqrt k) (pow n (/ 1 2))))) (cbrt (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))) (/ (sqrt k) (pow n (/ 1 2)))))) * [enter]simplify: Simplifying (cbrt (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (100 enodes) * [exit]simplify: Simplified to (cbrt (* (/ (pow n (/ 1 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))))) * [exit]simplify: Simplified to (cbrt (* (/ (pow n (/ 1 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))))) * * * * [misc]progress: [ 69 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))) (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2))))) (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (138 enodes) * [exit]simplify: Simplified to (pow (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) 3) * [exit]simplify: Simplified to (pow (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) 3) * * * * [misc]progress: [ 70 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (100 enodes) * [exit]simplify: Simplified to (sqrt (* (/ (pow n (/ 1 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))))) * [exit]simplify: Simplified to (sqrt (* (/ (pow n (/ 1 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))))) * [enter]simplify: Simplifying (sqrt (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (100 enodes) * [exit]simplify: Simplified to (sqrt (* (/ (pow n (/ 1 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))))) * [exit]simplify: Simplified to (sqrt (* (/ (pow n (/ 1 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ k 2))))) * * * * [misc]progress: [ 71 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (* (- (pow n (/ 1 2))) (pow (* 2 PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (- (pow n (/ 1 2))) (pow (* 2 PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (- (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (* (- (sqrt k)) (pow n (/ k 2))) * [exit]simplify: Simplified to (* (- (sqrt k)) (pow n (/ k 2))) * * * * [misc]progress: [ 72 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (pow n (/ k 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 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))) * * * * [misc]progress: [ 73 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 74 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow n (/ k 2))) * * * * [misc]progress: [ 75 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow n (/ k 2))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (pow (* 2 PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (pow (* 2 PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 76 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (37 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2)))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2)))) * * * * [misc]progress: [ 77 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow n (/ k 2))) (pow n (/ 1 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 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 (/ k 2)) (sqrt k)) (pow n (/ 1 2))) * [exit]simplify: Simplified to (/ (* (pow n (/ k 2)) (sqrt k)) (pow n (/ 1 2))) * * * * [misc]progress: [ 78 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (sqrt k) (pow n (/ k 2))) (pow (* 2 PI) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2)))) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2)))) * * * * [misc]progress: [ 79 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 80 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (sqrt k)) (* (log n) (/ k 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * * [misc]simplify: iters left: 1 (22 enodes) * [exit]simplify: Simplified to (+ (* (/ k 2) (log n)) (log (sqrt k))) * [exit]simplify: Simplified to (+ (* (/ k 2) (log n)) (log (sqrt k))) * * * * [misc]progress: [ 81 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (sqrt k)) (log (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (+ (* (log n) (/ k 2)) (log (sqrt k))) * [exit]simplify: Simplified to (+ (* (log n) (/ k 2)) (log (sqrt k))) * * * * [misc]progress: [ 82 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (sqrt k) (pow n (/ k 2)))) * * [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 (18 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (/ k 2) (log n))) * [exit]simplify: Simplified to (+ (log (sqrt k)) (* (/ k 2) (log n))) * * * * [misc]progress: [ 83 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (pow (exp (sqrt k)) (pow n (/ k 2))) * [exit]simplify: Simplified to (pow (exp (sqrt k)) (pow n (/ k 2))) * * * * [misc]progress: [ 84 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow n (/ k 2)) (pow n (/ k 2))) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (* (* (* k (sqrt k)) (pow n (/ k 2))) (* (pow n (/ k 2)) (pow n (/ k 2)))) * [exit]simplify: Simplified to (* (* (* k (sqrt k)) (pow n (/ k 2))) (* (pow n (/ k 2)) (pow n (/ k 2)))) * * * * [misc]progress: [ 85 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (sqrt k) (pow n (/ k 2)))) (cbrt (* (sqrt k) (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (* (cbrt (* (pow n (/ k 2)) (sqrt k))) (cbrt (* (pow n (/ k 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (* (pow n (/ k 2)) (sqrt k))) (cbrt (* (pow n (/ k 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (cbrt (* (pow n (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (* (pow n (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 86 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (sqrt k) (pow n (/ k 2))) (* (sqrt k) (pow n (/ k 2)))) (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (* (* (* k (sqrt k)) (pow n (/ k 2))) (* (pow n (/ k 2)) (pow n (/ k 2)))) * [exit]simplify: Simplified to (* (* (* k (sqrt k)) (pow n (/ k 2))) (* (pow n (/ k 2)) (pow n (/ k 2)))) * * * * [misc]progress: [ 87 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (sqrt (* (pow n (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (* (pow n (/ k 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (sqrt (* (pow n (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (* (pow n (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 88 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 89 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (* (cbrt (pow n (/ k 2))) (cbrt (pow n (/ k 2))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (* (sqrt k) (* (cbrt (pow n (/ k 2))) (cbrt (pow n (/ k 2))))) * [exit]simplify: Simplified to (* (sqrt k) (* (cbrt (pow n (/ k 2))) (cbrt (pow n (/ k 2))))) * * * * [misc]progress: [ 90 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (sqrt (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (* (sqrt (pow n (/ k 2))) (sqrt k)) * [exit]simplify: Simplified to (* (sqrt (pow n (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 91 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) 1) * * [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: [ 92 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (pow n (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 93 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (pow n (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 94 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow n (/ k 2))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 95 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 96 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (32 enodes) * * [misc]simplify: iters left: 5 (75 enodes) * * [misc]simplify: iters left: 4 (226 enodes) * [exit]simplify: Simplified to (/ (- (sqrt (* PI 2)) (- (* (* (log (* PI 2)) (* (sqrt 2) k)) (* 1/2 (sqrt PI))) (* (* (* (sqrt PI) 1/8) (* (* k k) (sqrt 2))) (* (log (* PI 2)) (log (* PI 2)))))) (/ (* (pow n (/ k 2)) (sqrt k)) (pow n (/ 1 2)))) * * * * [misc]progress: [ 97 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (201 enodes) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (sqrt k) (pow n (/ k 2)))) (pow n (/ 1 2))) * * * * [misc]progress: [ 98 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow n (/ 1 2))) (* (sqrt k) (pow n (/ k 2)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (201 enodes) * [exit]simplify: Simplified to (* (/ (pow (* 2 PI) (- 1/2 (* 1/2 k))) (* (sqrt k) (pow n (/ k 2)))) (pow n (/ 1 2))) * * * * [misc]progress: [ 99 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (pow n 2) (pow PI 2))) (- (* +nan.0 (* n PI))))))) (* (sqrt k) (pow n (/ k 2)))) * * * * [misc]progress: [ 100 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow n 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) n)) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))))) (* (sqrt k) (pow n (/ k 2)))) * * * * [misc]progress: [ 101 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow n 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) n)) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))))) (* (sqrt k) (pow n (/ k 2)))) * * * * [misc]progress: [ 102 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow n 2) (pow PI 2))) k)) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log n)))))))))))))) * * * * [misc]progress: [ 103 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (* (exp (* -1/2 (* (log (/ 1 n)) k))) k))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (log (/ 1 n)) k))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (* (exp (* -1/2 (* (log (/ 1 n)) k))) n)))))))) * * * * [misc]progress: [ 104 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (* (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))) k))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (* (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))) n)))))))) * * * * [misc]progress: [ 105 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow k 3))) (- (+ (* +nan.0 (pow k 2)) (- (+ (* +nan.0 (pow k 3)) (- (+ (* +nan.0 (* (log n) (pow k 2))) (- (+ (* +nan.0 k) (- (* +nan.0 (* (log n) (pow k 3))))))))))))))) * * * * [misc]progress: [ 106 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (- (+ (* +nan.0 (/ (exp (* -1/2 (* (log (/ 1 n)) k))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* -1/2 (* (log (/ 1 n)) k))) k)) (- (* +nan.0 (exp (* -1/2 (* (log (/ 1 n)) k)))))))))) * * * * [misc]progress: [ 107 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log -1) (log (/ -1 n))) k))) 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 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 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) * [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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) 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 n) (log (* 2 PI)))) 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 n) (log (* 2 PI))) in k * [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 (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]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 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 (/ (+ (* 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 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 (+ 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 n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) 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 (+ 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 n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) * [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 (* (- 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]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 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) * [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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [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 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [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 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (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) 1) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in k * [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 (+ 1 0) 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 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1)) (/ 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) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1)) (/ 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) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1)) (/ 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) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ +nan.0 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ +nan.0 +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 (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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (- +nan.0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (- +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 (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (- +nan.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 (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (- +nan.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) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (- +nan.0) (+ (* (- +nan.0) (/ 1 k)) (* +nan.0 (pow (/ 1 k) 2)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) * [misc]approximate: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (/ 1 (sqrt +nan.0)) (sqrt +nan.0)) into (/ 1 (pow (sqrt +nan.0) 2)) * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (/ 1 (sqrt +nan.0)) (sqrt +nan.0)) into (/ 1 (pow (sqrt +nan.0) 2)) * [misc]backup-simplify: Simplify (/ 1 (pow (sqrt +nan.0) 2)) into (/ 1 (pow (sqrt +nan.0) 2)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (sqrt +nan.0)) (+ (* (/ 1 (pow (sqrt +nan.0) 2)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) * [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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) * [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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) * [misc]backup-simplify: Simplify (- (/ (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) (sqrt +nan.0)) (+ (* (/ 1 (pow (sqrt +nan.0) 2)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) (/ 1 k)) (/ 1 (pow (sqrt +nan.0) 2)))) into (- (/ 1 (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 6) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 4) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 4) (pow k 2))))))))) * [misc]approximate: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (/ 1 (sqrt +nan.0)) (sqrt +nan.0)) into (/ 1 (pow (sqrt +nan.0) 2)) * [misc]taylor: Taking taylor expansion of (/ (/ 1 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (/ 1 (sqrt +nan.0)) (sqrt +nan.0)) into (/ 1 (pow (sqrt +nan.0) 2)) * [misc]backup-simplify: Simplify (/ 1 (pow (sqrt +nan.0) 2)) into (/ 1 (pow (sqrt +nan.0) 2)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (sqrt +nan.0)) (+ (* (/ 1 (pow (sqrt +nan.0) 2)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) * [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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) * [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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) * [misc]backup-simplify: Simplify (- (/ (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) (sqrt +nan.0)) (+ (* (/ 1 (pow (sqrt +nan.0) 2)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 4)))) (/ 1 (- k))) (/ 1 (pow (sqrt +nan.0) 2)))) into (- (/ 1 (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 6) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 4) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 4) (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 1 1) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ +nan.0 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ +nan.0 (* 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 (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 (+ (* 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 (/ 1 k)) (- (+ +nan.0 (- (* +nan.0 k)))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) * [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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ 1 k)) (/ 1 (sqrt +nan.0)))) into (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k)))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) * [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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ 1 (- k))) (/ 1 (sqrt +nan.0)))) into (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k)))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * * * * [misc]progress: [ 2 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * * * * [misc]progress: [ 3 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 4 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ 1 2)) * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * * * * [misc]progress: [ 5 / 108 ] 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 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 6 / 108 ] 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* PI (* n 2)) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 7 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* 2 PI) n) * [exit]simplify: Simplified to (* (* 2 PI) n) * * * * [misc]progress: [ 8 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (* n PI) 2) (- 1 k)) * [exit]simplify: Simplified to (pow (* (* n PI) 2) (- 1 k)) * * * * [misc]progress: [ 9 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 10 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 108 ] 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 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * [exit]simplify: Simplified to (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 12 / 108 ] 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 13 / 108 ] 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 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 14 / 108 ] 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 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 15 / 108 ] 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 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 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 16 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (- -1 1) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (7 enodes) * [exit]simplify: Simplified to (- -1 1) * [exit]simplify: Simplified to (- -1 1) * * * * [misc]progress: [ 18 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- 1/2) 1/2) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (- (+ 1/2 1/2)) * [exit]simplify: Simplified to (- (+ 1/2 1/2)) * * * * [misc]progress: [ 19 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- 1) 1) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * [exit]simplify: Simplified to (- (+ 1 1)) * [exit]simplify: Simplified to (- (+ 1 1)) * * * * [misc]progress: [ 20 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to (- (- (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) * [exit]simplify: Simplified to (- (- (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) * * * * [misc]progress: [ 22 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ 1 (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (286 enodes) * [exit]simplify: Simplified to (- (- (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) * [exit]simplify: Simplified to (- (- (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) * * * * [misc]progress: [ 23 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (108 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 24 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * * * * [misc]progress: [ 25 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * * [misc]simplify: iters left: 1 (313 enodes) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * * * * [misc]progress: [ 26 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 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 (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 27 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * * [misc]simplify: iters left: 1 (285 enodes) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * * * * [misc]progress: [ 28 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 29 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (- 1) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (- 1) (sqrt (sqrt k))) * [enter]simplify: Simplifying (- (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (- (sqrt (sqrt k))) * [exit]simplify: Simplified to (- (sqrt (sqrt k))) * * * * [misc]progress: [ 30 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [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 (30 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))) * [exit]simplify: Simplified to (* (/ (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 31 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (fabs (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (fabs (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) * * * * [misc]progress: [ 32 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 33 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt 1)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt 1)) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt 1)) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 34 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 35 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 36 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 37 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) * * * * [misc]progress: [ 38 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 39 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt 1)) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt 1)) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 40 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 41 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (sqrt k)))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 42 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 43 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) * * * * [misc]progress: [ 44 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 45 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt 1)) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt 1)) * [exit]simplify: Simplified to (/ 1 (sqrt 1)) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 46 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 47 / 108 ] 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 (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 48 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 49 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) * * * * [misc]progress: [ 50 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 51 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt 1)) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt 1)) * [exit]simplify: Simplified to (/ 1 (sqrt 1)) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 52 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 53 / 108 ] 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 (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 54 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 108 ] 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: [ 56 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 57 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (26 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 58 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (fabs (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (fabs (cbrt (sqrt k)))) * * * * [misc]progress: [ 59 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 60 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt 1)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt 1)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt 1)) (sqrt (sqrt k))) * * * * [misc]progress: [ 61 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 62 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (sqrt k))) 1) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * * * * [misc]progress: [ 63 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (/ 1 (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (/ 1 (sqrt (sqrt k))))) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (/ 1 (sqrt (sqrt k))))) * * * * [misc]progress: [ 64 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (/ 1 (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ 1 (sqrt (sqrt k))))) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ 1 (sqrt (sqrt k))))) * * * * [misc]progress: [ 65 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 66 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 67 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 68 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 69 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* 2 PI) n)) * [exit]simplify: Simplified to (log (* (* 2 PI) n)) * * * * [misc]progress: [ 70 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* n PI)) * [exit]simplify: Simplified to (pow (exp 2) (* n PI)) * * * * [misc]progress: [ 71 / 108 ] 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 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) * [exit]simplify: Simplified to (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) * [enter]simplify: Simplifying (cbrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* 2 PI) n)) * [exit]simplify: Simplified to (cbrt (* (* 2 PI) n)) * * * * [misc]progress: [ 72 / 108 ] 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 (18 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (170 enodes) * [exit]simplify: Simplified to (pow (* (* n PI) 2) 3) * [exit]simplify: Simplified to (pow (* (* n PI) 2) 3) * * * * [misc]progress: [ 73 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) * * * * [misc]progress: [ 74 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 75 / 108 ] 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 (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 76 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 77 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 78 / 108 ] 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: [ 79 / 108 ] 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: [ 80 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 81 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (5 enodes) * [exit]simplify: Simplified to (- (log (sqrt (sqrt k)))) * [exit]simplify: Simplified to (- (log (sqrt (sqrt k)))) * * * * [misc]progress: [ 82 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (13 enodes) * * [misc]simplify: iters left: 2 (17 enodes) * * [misc]simplify: iters left: 1 (30 enodes) * [exit]simplify: Simplified to (- (log (sqrt (sqrt k)))) * [exit]simplify: Simplified to (- (log (sqrt (sqrt k)))) * * * * [misc]progress: [ 83 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (exp (/ 1 (sqrt (sqrt k)))) * [exit]simplify: Simplified to (exp (/ 1 (sqrt (sqrt k)))) * * * * [misc]progress: [ 84 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) * [enter]simplify: Simplifying (cbrt (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt (sqrt k)))) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt (sqrt k)))) * * * * [misc]progress: [ 85 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (sqrt (sqrt k))) * * * * [misc]progress: [ 86 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (sqrt k)))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (sqrt k)))) * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (sqrt k)))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt (sqrt k)))) * * * * [misc]progress: [ 87 / 108 ] 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 (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (- (sqrt (sqrt k))) * [exit]simplify: Simplified to (- (sqrt (sqrt k))) * * * * [misc]progress: [ 88 / 108 ] simplifiying candidate # * * * * [misc]progress: [ 89 / 108 ] 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: [ 90 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) 1) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [exit]simplify: Simplified to (sqrt (sqrt k)) * * * * [misc]progress: [ 91 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 92 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (fabs (cbrt (sqrt k)))) * * * * [misc]progress: [ 93 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 94 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt 1)) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt 1)) * [exit]simplify: Simplified to (/ 1 (sqrt 1)) * * * * [misc]progress: [ 95 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (sqrt k)))) * * * * [misc]progress: [ 96 / 108 ] 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: [ 97 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (118 enodes) * * [misc]simplify: iters left: 4 (384 enodes) * [exit]simplify: Simplified to (/ (+ (+ (* (* (* 1/8 (pow n 1/2)) (pow (* 2 PI) 1/2)) (* (* (log (* 2 PI)) (log (* 2 PI))) (* k k))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* 2 PI) 1/2))) (* (pow (* 2 PI) 1/2) (pow n 1/2)))) (- (* (* (pow (* 2 PI) 1/2) (pow n 1/2)) (* (log (* 2 PI)) (* (* (* k k) (log n)) 1/4))) (* (* 1/2 k) (* (* (pow (* 2 PI) 1/2) (pow n 1/2)) (+ (log n) (log (* 2 PI))))))) (sqrt k)) * * * * [misc]progress: [ 98 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (293 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k)) * * * * [misc]progress: [ 99 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (312 enodes) * [exit]simplify: Simplified to (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k)) * * * * [misc]progress: [ 100 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 101 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (/ 1 (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 6) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 4) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 4) (pow k 2))))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 102 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (/ 1 (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 6) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 4) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 4) (pow k 2))))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 103 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 104 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 105 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 106 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (- (+ (* +nan.0 (/ 1 k)) (- (+ +nan.0 (- (* +nan.0 k)))))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 107 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k)))))))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 108 / 108 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k)))))))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 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) +nan.0)) , with alts (#) * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (sqrt k) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]points: Sampling 8000 additional inputs, on iter 0 have 0 / 8000 * * * * [misc]points: Computing exacts on every 500 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 250 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 125 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 62 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 31 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 15 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 8000 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 6460 additional inputs, on iter 1 have 1540 / 8000 * * * * [misc]points: Computing exacts on every 403 of 6460 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 201 of 6460 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 100 of 6460 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 50 of 6460 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 25 of 6460 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 12 of 6460 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 6460 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 6460 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 6460 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 5252 additional inputs, on iter 2 have 2748 / 8000 * * * * [misc]points: Computing exacts on every 328 of 5252 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 164 of 5252 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 82 of 5252 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 41 of 5252 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 20 of 5252 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 5252 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 5252 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 5252 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 5252 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4261 additional inputs, on iter 3 have 3739 / 8000 * * * * [misc]points: Computing exacts on every 266 of 4261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 133 of 4261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 66 of 4261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 33 of 4261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 16 of 4261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 4261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 4261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 4261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 4261 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 3454 additional inputs, on iter 4 have 4546 / 8000 * * * * [misc]points: Computing exacts on every 215 of 3454 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 107 of 3454 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 53 of 3454 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 26 of 3454 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 13 of 3454 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 3454 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 3454 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 3454 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 2763 additional inputs, on iter 5 have 5237 / 8000 * * * * [misc]points: Computing exacts on every 172 of 2763 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 86 of 2763 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 43 of 2763 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 21 of 2763 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 2763 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 2763 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 2763 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2763 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 2238 additional inputs, on iter 6 have 5762 / 8000 * * * * [misc]points: Computing exacts on every 139 of 2238 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 69 of 2238 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 34 of 2238 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 17 of 2238 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 2238 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 2238 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 2238 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2238 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 1844 additional inputs, on iter 7 have 6156 / 8000 * * * * [misc]points: Computing exacts on every 115 of 1844 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 57 of 1844 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 28 of 1844 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 14 of 1844 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 1844 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 1844 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1844 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 1486 additional inputs, on iter 8 have 6514 / 8000 * * * * [misc]points: Computing exacts on every 92 of 1486 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 46 of 1486 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 23 of 1486 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 11 of 1486 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 1486 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 1486 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1486 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 1198 additional inputs, on iter 9 have 6802 / 8000 * * * * [misc]points: Computing exacts on every 74 of 1198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 37 of 1198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 18 of 1198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 9 of 1198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 1198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 1198 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1198 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 966 additional inputs, on iter 10 have 7034 / 8000 * * * * [misc]points: Computing exacts on every 60 of 966 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 30 of 966 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 15 of 966 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 966 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 966 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 966 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 806 additional inputs, on iter 11 have 7194 / 8000 * * * * [misc]points: Computing exacts on every 50 of 806 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 25 of 806 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 12 of 806 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 806 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 806 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 806 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 662 additional inputs, on iter 12 have 7338 / 8000 * * * * [misc]points: Computing exacts on every 41 of 662 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 20 of 662 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 662 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 662 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 662 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 662 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 556 additional inputs, on iter 13 have 7444 / 8000 * * * * [misc]points: Computing exacts on every 34 of 556 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 17 of 556 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 556 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 556 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 556 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 556 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 444 additional inputs, on iter 14 have 7556 / 8000 * * * * [misc]points: Computing exacts on every 27 of 444 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 13 of 444 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 444 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 444 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 444 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 359 additional inputs, on iter 15 have 7641 / 8000 * * * * [misc]points: Computing exacts on every 22 of 359 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 11 of 359 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 5 of 359 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 359 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 359 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 300 additional inputs, on iter 16 have 7700 / 8000 * * * * [misc]points: Computing exacts on every 18 of 300 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 9 of 300 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 300 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 300 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 300 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 251 additional inputs, on iter 17 have 7749 / 8000 * * * * [misc]points: Computing exacts on every 15 of 251 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 251 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 251 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 251 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 196 additional inputs, on iter 18 have 7804 / 8000 * * * * [misc]points: Computing exacts on every 12 of 196 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 6 of 196 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 196 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 196 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 155 additional inputs, on iter 19 have 7845 / 8000 * * * * [misc]points: Computing exacts on every 9 of 155 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 155 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 155 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 155 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 121 additional inputs, on iter 20 have 7879 / 8000 * * * * [misc]points: Computing exacts on every 7 of 121 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 121 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 121 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 97 additional inputs, on iter 21 have 7903 / 8000 * * * * [misc]points: Computing exacts on every 6 of 97 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 97 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 97 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 70 additional inputs, on iter 22 have 7930 / 8000 * * * * [misc]points: Computing exacts on every 4 of 70 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 70 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 70 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 53 additional inputs, on iter 23 have 7947 / 8000 * * * * [misc]points: Computing exacts on every 3 of 53 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 53 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 40 additional inputs, on iter 24 have 7960 / 8000 * * * * [misc]points: Computing exacts on every 2 of 40 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 40 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 31 additional inputs, on iter 25 have 7969 / 8000 * * * * [misc]points: Computing exacts for 31 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 24 additional inputs, on iter 26 have 7976 / 8000 * * * * [misc]points: Computing exacts for 24 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 20 additional inputs, on iter 27 have 7980 / 8000 * * * * [misc]points: Computing exacts for 20 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 15 additional inputs, on iter 28 have 7985 / 8000 * * * * [misc]points: Computing exacts for 15 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 14 additional inputs, on iter 29 have 7986 / 8000 * * * * [misc]points: Computing exacts for 14 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 12 additional inputs, on iter 30 have 7988 / 8000 * * * * [misc]points: Computing exacts for 12 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 10 additional inputs, on iter 31 have 7990 / 8000 * * * * [misc]points: Computing exacts for 10 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 10 additional inputs, on iter 32 have 7990 / 8000 * * * * [misc]points: Computing exacts for 10 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 9 additional inputs, on iter 33 have 7991 / 8000 * * * * [misc]points: Computing exacts for 9 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 5 additional inputs, on iter 34 have 7995 / 8000 * * * * [misc]points: Computing exacts for 5 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 5 additional inputs, on iter 35 have 7995 / 8000 * * * * [misc]points: Computing exacts for 5 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 5 additional inputs, on iter 36 have 7995 / 8000 * * * * [misc]points: Computing exacts for 5 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 37 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 38 have 7997 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 39 have 7997 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 40 have 7999 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [exit]points: Sampled 8000 points with exact outputs