* [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: Computing exacts on every 8 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: Setting MPFR precision to 832 * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision * * * * [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 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 204 additional inputs, on iter 1 have 52 / 256 * * * * [misc]points: Computing exacts on every 12 of 204 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 204 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 204 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 204 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 169 additional inputs, on iter 2 have 87 / 256 * * * * [misc]points: Computing exacts on every 10 of 169 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 169 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 169 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 169 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 123 additional inputs, on iter 3 have 133 / 256 * * * * [misc]points: Computing exacts on every 7 of 123 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 123 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 123 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 104 additional inputs, on iter 4 have 152 / 256 * * * * [misc]points: Computing exacts on every 6 of 104 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 104 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 104 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 82 additional inputs, on iter 5 have 174 / 256 * * * * [misc]points: Computing exacts on every 5 of 82 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 82 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 82 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 62 additional inputs, on iter 6 have 194 / 256 * * * * [misc]points: Computing exacts on every 3 of 62 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 62 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 54 additional inputs, on iter 7 have 202 / 256 * * * * [misc]points: Computing exacts on every 3 of 54 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 54 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 42 additional inputs, on iter 8 have 214 / 256 * * * * [misc]points: Computing exacts on every 2 of 42 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 42 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 35 additional inputs, on iter 9 have 221 / 256 * * * * [misc]points: Computing exacts on every 2 of 35 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 35 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 10 have 225 / 256 * * * * [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 29 additional inputs, on iter 11 have 227 / 256 * * * * [misc]points: Computing exacts for 29 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 26 additional inputs, on iter 12 have 230 / 256 * * * * [misc]points: Computing exacts for 26 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 13 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 14 additional inputs, on iter 14 have 242 / 256 * * * * [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 13 additional inputs, on iter 15 have 243 / 256 * * * * [misc]points: Computing exacts for 13 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 11 additional inputs, on iter 16 have 245 / 256 * * * * [misc]points: Computing exacts for 11 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 17 have 246 / 256 * * * * [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 18 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 9 additional inputs, on iter 19 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 20 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 21 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 5 additional inputs, on iter 22 have 251 / 256 * * * * [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 23 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 24 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 25 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 26 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 27 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 28 have 255 / 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 256 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 (55 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 / 3 ] rewriting at (2 1) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 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 (* (* n 2) PI)) in k * [misc]taylor: Taking taylor expansion of (* (* n 2) PI) in k * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [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 (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (* (* 2 n) PI) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 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 (* (* n 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* n 2) PI) in n * [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]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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 (* (* n 2) PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 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 (* (* n 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* n 2) PI) in n * [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]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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 (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 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) 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 (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 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 (- 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 (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 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 (* (* (/ 1 n) 2) PI)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 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 (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (* (/ 2 n) PI) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 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 (* (* (/ 1 n) 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 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 (* 1 2) into 2 * [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) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 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 (* (* (/ 1 n) 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 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 (* 1 2) into 2 * [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) (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 (+ (* 1 0) (* 0 2)) 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 (- (/ 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 (+ (* 1 0) (+ (* 0 0) (* 0 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 (- (+ (* (/ 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 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 (* (* (/ 1 (- n)) 2) PI)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 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 (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (* (/ -2 n) PI) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 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 (* (* (/ 1 (- n)) 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 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 (* -1 2) into -2 * [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) (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 (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 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 (* (* (/ 1 (- n)) 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 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 (* -1 2) into -2 * [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) (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 (+ (* -1 0) (* 0 2)) 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) 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 (+ (* -1 0) (+ (* 0 0) (* 0 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) 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 (- 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 / 3 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* (* n 2) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* n 2) PI) in n * [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]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (* n 2) PI) in n * [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]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* (/ 1 n) 2) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 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) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 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 (* 1 2) into 2 * [misc]backup-simplify: Simplify (* 2 PI) 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 (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 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 (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 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)) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 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 (* -1 2) into -2 * [misc]backup-simplify: Simplify (* -2 PI) 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 (+ (* -1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) 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 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 3 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 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 (* (* n 2) PI)) in k * [misc]taylor: Taking taylor expansion of (* (* n 2) PI) in k * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [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 (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (* (* 2 n) PI) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* PI (* n 2)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 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 (* (* n 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* n 2) PI) in n * [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]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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 (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 n) (log (* 2 PI)))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 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 (* (* n 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* n 2) PI) in n * [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]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 2) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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 (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 n) (log (* 2 PI)))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k * [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]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 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) 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]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 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 (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 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 (- 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]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* -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))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 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 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* 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 (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 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))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 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 (* (* (/ 1 n) 2) PI)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 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 (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (* (/ 2 n) PI) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]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 n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 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 (* (* (/ 1 n) 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 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 (* 1 2) into 2 * [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) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 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 (* (* (/ 1 n) 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 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 (* 1 2) into 2 * [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) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) 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 (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 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 (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 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)))))) (pow k 3)))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 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 (* (* (/ 1 (- n)) 2) PI)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 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 (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (* (/ -2 n) PI) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) * [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 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 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 (* (* (/ 1 (- n)) 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 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 (* -1 2) into -2 * [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) (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 (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)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 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 (* (* (/ 1 (- n)) 2) PI)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 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 (* -1 2) into -2 * [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) (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 (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)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k * [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]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) 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 (+ (* -1 0) (* 0 2)) 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) 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]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) 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 (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) 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 (- 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]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) 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 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +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: simplifying candidates * * * * [misc]progress: [ 1 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* n 2) PI)) (/ (- 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 (145 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) (sqrt k))) * * * * [misc]progress: [ 4 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* n 2) PI) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (* (* n 2) PI) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 6 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n 2) PI) (/ 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 (* n (* PI 2)) (/ k 2)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 7 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (- 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 (cbrt (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 8 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (- 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 (sqrt (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 9 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- 1 k) 2) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (12 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 10 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to (/ 1 2) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n 2) PI) (- 1 k)) (/ 1 2)) (sqrt k))) * * * * [misc]progress: [ 11 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow (* n 2) (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 12 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))))) * * * * [misc]progress: [ 34 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k)))))) * * * * [misc]progress: [ 35 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* (* n 2) PI) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (302 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 36 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 37 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (204 enodes) * * [misc]simplify: iters left: 1 (325 enodes) * [exit]simplify: Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 39 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 43 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))))) * * * * [misc]progress: [ 44 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 45 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow (* n 2) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * [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)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow (* n 2) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 46 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 47 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 48 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k)))) * * * * [misc]progress: [ 49 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 50 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 51 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (12 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 (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k)))) * * * * [misc]progress: [ 52 / 74 ] 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))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k))))) * * * * [misc]progress: [ 53 / 74 ] 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))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 54 / 74 ] 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 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 55 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 56 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 57 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 58 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (cbrt (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 59 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 60 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt k) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to (sqrt k) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1) (sqrt k))) * * * * [misc]progress: [ 61 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* n 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))) * * * * [misc]progress: [ 62 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 63 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 64 / 74 ] simplifiying candidate # * * * * [misc]progress: [ 65 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n 2) PI) (/ 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 (* (* PI n) 2) (/ 1 2)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))) * * * * [misc]progress: [ 66 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (- (fma (* (log (* PI 2)) (log (* PI 2))) (* (* (* k k) 1/8) (* (pow n 1/2) (pow (* PI 2) 1/2))) (fma (* (* (log n) (log n)) (* (* k k) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))) (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) 1/2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (- (fma (* (log (* PI 2)) (log (* PI 2))) (* (* (* k k) 1/8) (* (pow n 1/2) (pow (* PI 2) 1/2))) (fma (* (* (log n) (log n)) (* (* k k) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))) (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) 1/2))) (sqrt k))) * * * * [misc]progress: [ 67 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (274 enodes) * [exit]simplify: Simplified to (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) (sqrt k))) * * * * [misc]progress: [ 68 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (280 enodes) * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) * * * * [misc]progress: [ 69 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* 2 (* n PI)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 70 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* 2 (* n PI)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 71 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (* 2 (* n PI)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 72 / 74 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 73 / 74 ] 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)))))) (pow k 3)))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 74 / 74 ] 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]simplify: Simplified (2) to (λ (k n) +nan.0) * * * [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 2 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 2 1) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]backup-simplify: Simplify (pow PI 1/2) into (pow PI 1/2) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log 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 PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 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 PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n 2))) 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 2)) in k * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [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 (/ (pow (* 2 n) 1/2) +nan.0) into (* +nan.0 (sqrt (* n 2))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log 2) (log n))) into (* 1/2 (* (- 1 k) (+ (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log 2) (log n))) into (* 1/2 (* (- 1 k) (+ (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log 2) (log n))) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log 2) (log n))) into (* 1/2 (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of 1/4 in k * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (log (/ 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 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)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k -1/4)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 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)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log 2) (log n)))) into (- (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log 2) (log n)))) (* 0 (+ (log 2) (log n)))) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) 0) (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (pow k -1/4))) into (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) * [misc]backup-simplify: Simplify (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) into (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) 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) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log 2) (log n)))) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) 0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 0) (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow k -1/4)))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))))) * [misc]backup-simplify: Simplify (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) (* k 1)) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)))) into (- (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 7) 1/4))) (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (pow k 3) 1/4))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2))) 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) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 2 n))))) * [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 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 2 n))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 2 n))))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (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) (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) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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) 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) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log 2) (log n))) into (* -1 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log 2) (log n)))) into (* -1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k * [misc]taylor: Taking taylor expansion of 1/4 in k * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (log 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 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)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))))) 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 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (* 0 (pow k 1/4))) 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 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 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)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) 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 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 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)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) 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) (log (/ 1 n)))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 k) (- (log 2) (log (/ 1 n)))))) (pow (/ 1 k) 1/4)) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -2 n))))) * [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 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -2 n))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -2 n))))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -2) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt (sqrt (/ -1 k)))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -2) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt (sqrt (/ -1 k)))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) 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 -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (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) (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) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -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 0) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -2) (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) * [misc]backup-simplify: Simplify (* (sqrt +nan.0) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt +nan.0)) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (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 (+ (* -1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 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)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) (/ 0 (sqrt (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +nan.0)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt +nan.0)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt +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 (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 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)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) (/ 0 (sqrt (sqrt (/ -1 k))))) (* 0 (/ 0 (sqrt (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (- (- +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 (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (pow (sqrt +nan.0) 3)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (pow (sqrt +nan.0) 3)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -2) (log (/ 1 (- n))))))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -2) (log (/ 1 (- n))))))) (pow (sqrt +nan.0) 3)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -2) (log (/ 1 (- n))))))) (sqrt +nan.0)))) (* (/ 1 (- k)) 1)) (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -2) (log (/ 1 (- n))))))) (sqrt +nan.0)))) into (- (* (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (* (sqrt +nan.0) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n 2))) 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 2)) in k * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [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 (/ (pow (* 2 n) 1/2) +nan.0) into (* +nan.0 (sqrt (* n 2))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [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 (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log 2) (log n))) into (* 1/2 (* (- 1 k) (+ (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log PI)) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log 2) (log n))) into (* 1/2 (* (- 1 k) (+ (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log PI)) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4))) into (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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 (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log 2) (log n))) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log 2) (log n))) into (* 1/2 (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (log 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 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [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 (/ (* (pow (* 1 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 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)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow PI 1/2)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 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)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 0) (* -1 (log PI))) into (- (log PI)) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log PI))) (* 0 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log 2) (log n)))) into (- (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log 2) (log n)))) (* 0 (+ (log 2) (log n)))) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) +nan.0) (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) 0)) into (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) into (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 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 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log PI))) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log 2) (log n)))) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow PI 1/2)))) into (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) +nan.0) (* (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI)))))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))))))))) * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 2 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 2 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 2 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 2 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log 2) (log n))))) (pow (/ 1 k) 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log PI))) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log 2) (log n)))) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) (pow PI 1/2))))) into (- (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow (log n) 2))) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 3)) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (log n))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 3)) (sqrt PI))) (* 1/8 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n)))) (sqrt PI))))))))))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) +nan.0) (+ (* (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI)))))))) +nan.0) (* (- (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow (log n) 2))) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 3)) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (log n))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 3)) (sqrt PI))) (* 1/8 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n)))) (sqrt PI))))))))))))) 0)))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))))))))) (* k 1)) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) k) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (* (log n) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k)) (sqrt PI)))))))))))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2))) 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) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 2 n))))) * [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 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 2 n))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 2 n))))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [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 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log PI)) into (* 1/2 (* (- 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log PI)) into (* 1/2 (* (- 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4))) into (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log 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 (/ 1 k)) (log PI)) 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (* -1 (log PI)) into (* -1 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (log PI))) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (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) (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) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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) 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) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log 2) (log n))) into (* -1 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log 2) (log n)))) into (* -1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 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)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) 0) (* 0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 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)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 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)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (pow k 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log 2) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log 2) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log 2) (log (/ 1 n))))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 3)))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -2 n))))) * [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 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -2 n))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -2 n))))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [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 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -2) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt (sqrt (/ -1 k)))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) into (* 1/2 (* (+ (/ 1 k) 1) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (sqrt (/ -1 k)))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -2) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (sqrt (sqrt (/ -1 k)))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) into (* 1/2 (* (+ (/ 1 k) 1) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (sqrt (/ -1 k)))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))) * [misc]backup-simplify: Simplify (* (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k)))))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log 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) 1) (log PI)) 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (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) (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) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -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 0) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -2) (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (sqrt (sqrt (/ -1 k))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 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)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) (/ 0 (sqrt (sqrt (/ -1 k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) 0) (* 0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (sqrt (sqrt (/ -1 k))))) (* 0 (/ 0 (sqrt (sqrt (/ -1 k))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 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)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) (/ 0 (sqrt (sqrt (/ -1 k))))) (* 0 (/ 0 (sqrt (sqrt (/ -1 k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -2) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -2) (log (/ 1 (- n)))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -2) (log (/ 1 (- n)))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -2) (log (/ 1 (- n))))))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))) (- (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [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 (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [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 (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (* +nan.0 (sqrt PI)) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [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 (- (/ (* -1/2 (* (log PI) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [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 (- (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) k) (+ (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (* (* +nan.0 (sqrt PI)) (/ 1 k)))) into (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))) (- (* +nan.0 (sqrt PI))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [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 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [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 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (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 (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 5)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (pow (sqrt +nan.0) 5)))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (pow (sqrt +nan.0) 3)))) (/ 1 k)) (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (sqrt +nan.0)))) into (- (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 5) (pow k 2))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [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 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [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 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (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 (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 5)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (pow (sqrt +nan.0) 5)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (pow (sqrt +nan.0) 3)))) (/ 1 (- k))) (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (sqrt +nan.0)))) into (- (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 5) (pow k 2))))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (/ k 2)) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (pow PI (/ k 2)) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 5 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (- 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 (cbrt (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (pow PI (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 6 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (- 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 (sqrt (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (pow PI (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 7 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- 1 k) 2) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (12 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (pow PI 1) (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 8 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to (/ 1 2) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (pow PI (- 1 k)) (/ 1 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 9 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (460 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 20 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (126 enodes) * * [misc]simplify: iters left: 2 (460 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 21 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n 2) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * [exit]simplify: Simplified to (- (/ (log (* n 2)) (/ 2 (- 1 k))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (/ (log (* n 2)) (/ 2 (- 1 k))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 22 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (pow (* n 2) (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (169 enodes) * * [misc]simplify: iters left: 1 (186 enodes) * [exit]simplify: Simplified to (* (/ (pow (* n 2) (/ (- 1 k) 2)) (* (sqrt (sqrt k)) (sqrt k))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (cbrt (* (/ (pow (* n 2) (/ (- 1 k) 2)) (* (sqrt (sqrt k)) (sqrt k))) (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 25 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (12 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 k) 2)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (cbrt (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 2 (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 30 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (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 (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (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 2 (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 31 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (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 2 (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 32 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) * * [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 (/ (- 1 k) 2)) (sqrt 1)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [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))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 33 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (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 2 (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 34 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [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))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 35 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [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 (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 36 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [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 (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 37 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt (sqrt (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 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [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 (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 38 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 39 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt (sqrt (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 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [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 (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 40 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 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 (43 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 41 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [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 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 42 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [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 (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [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 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 43 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [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 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [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 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 44 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1)) * * [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 (* n 2) (/ (- 1 k) 2))) (sqrt 1)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 45 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [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 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [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 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 46 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (sqrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (sqrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 47 / 201 ] 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)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 1 k) 2)) (cbrt (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 (/ (pow (* n 2) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (pow (* n 2) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 48 / 201 ] 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)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ 1 (fabs (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (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 (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ 1 (fabs (cbrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 49 / 201 ] 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)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (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 (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 50 / 201 ] 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)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ 1 (sqrt 1)) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ 1 (sqrt 1)) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 51 / 201 ] 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)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (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 (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 52 / 201 ] 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 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* 1 (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* 1 (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 53 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 54 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 56 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 57 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 58 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 59 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt 1)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 60 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 61 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ (- 1 k) 2)) 1) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 62 / 201 ] simplifiying candidate # * [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)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow 2 (/ (- 1 k) 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 63 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 64 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (sqrt (pow (* n 2) (/ (- 1 k) 2))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 65 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 66 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n 2) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (pow (* n 2) (/ 1 2)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 67 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 68 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 69 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k)) (pow PI (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k)) (pow PI (/ (- 1 k) 2))) 1)) * * * * [misc]progress: [ 70 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 71 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (288 enodes) * [exit]simplify: Simplified to (- (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log (* n 2)) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log (* n 2)) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 72 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (251 enodes) * [exit]simplify: Simplified to (+ (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 73 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (216 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))))) * * * * [misc]progress: [ 74 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (288 enodes) * [exit]simplify: Simplified to (- (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log (* n 2)) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log (* n 2)) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 75 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (251 enodes) * [exit]simplify: Simplified to (+ (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 76 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (216 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))))) * * * * [misc]progress: [ 77 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (209 enodes) * [exit]simplify: Simplified to (+ (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 78 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (171 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))))) * * * * [misc]progress: [ 79 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * [exit]simplify: Simplified to (- (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))))) * * * * [misc]progress: [ 80 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (433 enodes) * [exit]simplify: Simplified to (- (* (+ (log (* n 2)) (log PI)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log (* n 2)) (log PI)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 81 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (307 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (* n 2)) (log PI))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (/ (- 1 k) 2) (+ (log (* n 2)) (log PI))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 82 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * [exit]simplify: Simplified to (+ (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) (- (/ (* (log PI) (- 1 k)) 2) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) (- (/ (* (log PI) (- 1 k)) 2) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 83 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 84 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 85 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (* (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (pow (* n 2) (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (173 enodes) * [exit]simplify: Simplified to (* (/ (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow (* n 2) (/ (- 1 k) 2)))) (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow (* n 2) (/ (- 1 k) 2)))) (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 86 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (* (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (pow (* n 2) (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (156 enodes) * [exit]simplify: Simplified to (* (/ (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow (* n 2) (/ (- 1 k) 2)))) (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3)) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (* (pow (* n 2) (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow (* n 2) (/ (- 1 k) 2)))) (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3)))) * * * * [misc]progress: [ 87 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (153 enodes) * [exit]simplify: Simplified to (* (pow (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) 3) (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt k) (sqrt (sqrt k))) (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (pow (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) 3) (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt k) (sqrt (sqrt k))) (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 88 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (* (* (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (128 enodes) * * [misc]simplify: iters left: 3 (391 enodes) * [exit]simplify: Simplified to (* (pow (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) 3) (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3)) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (pow (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) 3) (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3)))) * * * * [misc]progress: [ 89 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 90 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 91 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 92 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n 2) (/ (- 1 k) 2)) (pow PI (/ (- 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 PI (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow PI (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (* (sqrt (sqrt k)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (sqrt k) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow (* n 2) (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 93 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 94 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [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 (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 95 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [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 (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 96 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 97 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))))) * * * * [misc]progress: [ 98 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 99 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt 1))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 100 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 101 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) 1)) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 102 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 103 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))))) * * * * [misc]progress: [ 104 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 105 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 106 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 107 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (sqrt (pow PI (/ (- 1 k) 2))) 1)) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 108 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 109 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))))) * * * * [misc]progress: [ 110 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 111 / 201 ] simplifiying candidate # * [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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ 1 (sqrt 1))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 112 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 113 / 201 ] simplifiying candidate # * [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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ 1 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 114 / 201 ] simplifiying candidate # * [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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 115 / 201 ] 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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (pow PI (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))) * * * * [misc]progress: [ 116 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (cbrt (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [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 (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (cbrt (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (cbrt (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))) (* (cbrt (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 117 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 118 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (12 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 k) 2)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 119 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (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 (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt (sqrt k)))) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 120 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 121 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) * * [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 (/ (- 1 k) 2)) (sqrt 1)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 122 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 123 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 124 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 125 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 126 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt (sqrt (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 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 127 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1))) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 128 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (sqrt (sqrt (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 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow (* n 2) (/ (- 1 k) 2))))) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 129 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 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 (43 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (pow (* n 2) (/ (- 1 k) 2)))) (* (/ (cbrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 130 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 131 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [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 (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 132 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [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 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 133 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1)) * * [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 (* n 2) (/ (- 1 k) 2))) (sqrt 1)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt 1)) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 134 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [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 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 135 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* n 2) (/ (- 1 k) 2))) (* (/ (sqrt (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 136 / 201 ] 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)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 137 / 201 ] 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)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (fabs (cbrt (sqrt k)))) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 138 / 201 ] 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)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt (sqrt k)))) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 139 / 201 ] 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)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt 1)) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 140 / 201 ] 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)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt (sqrt k)))) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 141 / 201 ] 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 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 142 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 143 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n 2) (/ (- 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 (* n 2) (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow (* n 2) (/ (- 1 k) 2)) (* (/ 1 (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 144 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 145 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n 2) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (* (pow PI (/ (- 1 k) 2)) (pow (* n 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 146 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 147 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 148 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 149 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 150 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (174 enodes) * * [misc]simplify: iters left: 1 (388 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (exp (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 151 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (175 enodes) * [exit]simplify: Simplified to (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (exp (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 152 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 153 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 154 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (167 enodes) * * [misc]simplify: iters left: 1 (184 enodes) * [exit]simplify: Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (cbrt (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 155 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 156 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 157 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 158 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 159 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 160 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))) * * * * [misc]progress: [ 161 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 162 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt 1) (cbrt (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt 1) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 163 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 164 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 165 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (13 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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 166 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [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 PI (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))) * * * * [misc]progress: [ 167 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 168 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1)) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 169 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 170 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (sqrt (pow PI (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (sqrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (sqrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 171 / 201 ] 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)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 172 / 201 ] 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)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (fabs (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (fabs (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))))) * * * * [misc]progress: [ 173 / 201 ] 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)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 174 / 201 ] 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)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (sqrt 1)) (/ (pow PI (/ (- 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))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (sqrt 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 175 / 201 ] 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)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 176 / 201 ] 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 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* 1 (/ (pow PI (/ (- 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))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (* 1 (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 177 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 178 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 179 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 180 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 181 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k)))))) * * * * [misc]progress: [ 182 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 183 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ (- 1 k) 2)) (sqrt 1)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 184 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 185 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ (- 1 k) 2)) 1) (sqrt (sqrt k))))) * * * * [misc]progress: [ 186 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (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 (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (cbrt (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 187 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow PI (/ (- 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 PI (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (sqrt (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 188 / 201 ] simplifiying candidate # * * * * [misc]progress: [ 189 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (/ 1 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow PI (/ 1 2)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ 1 2)) (* (sqrt (sqrt k)) (pow PI (/ k 2)))))) * * * * [misc]progress: [ 190 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (336 enodes) * [exit]simplify: Simplified to (fma (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8) (fma (* 1/2 (log PI)) (* (- k) (sqrt PI)) (sqrt PI))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (fma (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8) (fma (* 1/2 (log PI)) (* (- k) (sqrt PI)) (sqrt PI))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 191 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (log PI)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (266 enodes) * [exit]simplify: Simplified to (pow (pow PI 1/2) (- 1 k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (pow PI 1/2) (- 1 k)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 192 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (log PI)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (266 enodes) * [exit]simplify: Simplified to (pow (pow PI 1/2) (- 1 k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (pow PI 1/2) (- 1 k)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 193 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 7) 1/4))) (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (pow k 3) 1/4))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (326 enodes) * [exit]simplify: Simplified to (+ (fma (pow (pow k 7) 1/4) (* (* 1/8 (* (pow n 1/2) (pow 2 1/2))) (+ (* (log n) (log n)) (* (log 2) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (pow (/ 1 k) 1/4))) (- (* (* (pow (pow k 7) 1/4) 1/4) (* (* (log 2) (log n)) (* (pow n 1/2) (pow 2 1/2)))) (* (* 1/2 (pow (pow k 3) 1/4)) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n)))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (+ (fma (pow (pow k 7) 1/4) (* (* 1/8 (* (pow n 1/2) (pow 2 1/2))) (+ (* (log n) (log n)) (* (log 2) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (pow (/ 1 k) 1/4))) (- (* (* (pow (pow k 7) 1/4) 1/4) (* (* (log 2) (log n)) (* (pow n 1/2) (pow 2 1/2)))) (* (* 1/2 (pow (pow k 3) 1/4)) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n)))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 194 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (* (exp (* 1/2 (* (- 1 k) (- (log 2) (log (/ 1 n)))))) (pow (/ 1 k) 1/4)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (* (pow (/ 1 k) 1/4) (exp (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (pow (/ 1 k) 1/4) (exp (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 195 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (* (sqrt +nan.0) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 196 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) k) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (* (log n) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k)) (sqrt PI)))))))))))))))))))))))))))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 197 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 3)))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 198 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (pow k 2))) (- (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -2) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log PI))))))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 199 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))) (- (* +nan.0 (sqrt PI))))))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) +nan.0)) * * * * [misc]progress: [ 200 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 5) (pow k 2))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) +nan.0)) * * * * [misc]progress: [ 201 / 201 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 5) (pow k 2))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) +nan.0)) * * * [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 2 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 2 1) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]backup-simplify: Simplify (pow PI 1/2) into (pow PI 1/2) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log 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 PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 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 PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n 2))) 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 2)) in k * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) 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]taylor: Taking taylor expansion of (pow (* n 2) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n 2))) 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 2)) in k * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* 0 1) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 n))) 1) 1)))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (+ (* 0 (* 1/2 (log (* 2 n)))) (* +nan.0 1)) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (pow (* 2 n) 1/2) (- +nan.0)) into (* +nan.0 (sqrt (* n 2))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log 2) (log n))) into (* 1/2 (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log 2) (log n)) k))) into (exp (* 1/2 (* (+ (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (pow k 1/4) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) into (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log 2) (log n)))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) into (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log 2) (log n))) into (* 1/2 (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log 2) (log n)) k))) into (exp (* 1/2 (* (+ (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (pow k 1/4) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) into (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log 2) (log n)))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) into (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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 (+ (log 2) (log n)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log 2) (log n))) into (* 1/2 (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log 2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log 2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 0) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 1) (* 0 0)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log 2) (log n))) (* 0 0)) into (+ (* 1/2 (log 2)) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log 2) (log n)))) 1) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) 1/4) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of 1/4 in k * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (log (/ 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) * [misc]backup-simplify: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (* 0 (exp (* 1/2 (* (+ (log 2) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k -1/4)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (log 2) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log 2)) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (/ (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) 0) (* (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))) (pow k -1/4))) into (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) * [misc]backup-simplify: Simplify (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) into (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))))) 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) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log 2) (log n))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) 1)) (* (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))) (/ (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) 0) (+ (* (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))) 0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)))))) (pow k -1/4)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))))) * [misc]backup-simplify: Simplify (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))))) into (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) (* k 1)) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)))) into (- (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 7) 1/4))) (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (pow k 3) 1/4))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) 2))) 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) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 2 n)))) into (pow (/ 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2))) 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]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) 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) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) into (exp (* 1/2 (/ (log (/ 2 n)) k))) * [misc]backup-simplify: Simplify (* (sqrt +nan.0) (exp (* 1/2 (/ (log (/ 2 n)) k)))) into (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (pow (/ 2 n) 1/2) (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (sqrt +nan.0))) into (* (/ 1 (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (sqrt +nan.0))) (sqrt (/ 2 n))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (pow (/ 1 k) 1/4) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) into (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (pow (/ 1 k) 1/4) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) into (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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 (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log 2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log 2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log 2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (/ (- (log 2) (log n)) 1) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (pow k 1/4) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/4 (log k))) in k * [misc]taylor: Taking taylor expansion of (* 1/4 (log k)) in k * [misc]taylor: Taking taylor expansion of 1/4 in k * [misc]backup-simplify: Simplify 1/4 into 1/4 * [misc]taylor: Taking taylor expansion of (log 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 (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) * [misc]backup-simplify: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) into (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) into (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (* 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))))) 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 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 0) (* 0 (pow k 1/4))) 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 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (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 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))))) 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 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) 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 (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))))) 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 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log 2) (log (/ 1 n))) (/ 1 k))))) (pow (/ 1 k) 1/4)) into (* (/ (exp (* 1/2 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k)))) (pow (/ 1 k) 1/4)) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ -2 n)))) into (pow (/ -2 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2))) 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]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ -2 n))) into (* -1/2 (log (/ -2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) into (exp (* -1/2 (/ (log (/ -2 n)) k))) * [misc]backup-simplify: Simplify (* (sqrt +nan.0) (exp (* -1/2 (/ (log (/ -2 n)) k)))) into (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (pow (/ -2 n) 1/2) (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (sqrt +nan.0))) into (* (/ 1 (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (sqrt +nan.0))) (sqrt (/ -2 n))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (sqrt (/ -1 k))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k))))) into (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (sqrt (/ -1 k))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k))))) into (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log -2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log -2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -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 (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log -2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log -2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log -2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -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]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -2) (log n)) 1) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log -2) (log n))) into (* -1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) 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 -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify (sqrt +nan.0) into (sqrt +nan.0) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt +nan.0)) into (/ (* (exp (* 1/2 (- (log -2) (log n)))) (sqrt +nan.0)) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (- (log -2) (log n)))) (sqrt +nan.0)) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (* (exp (* 1/2 (- (log -2) (log n)))) (sqrt +nan.0)) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (sqrt (/ -1 k))) 0) (* 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k))))) (+ (* (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt +nan.0))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt +nan.0))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt +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 (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (sqrt (/ -1 k))) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k))))) (+ (* (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))))) (* 0 (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (- (- +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 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt +nan.0)))) (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (pow (sqrt +nan.0) 3))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt +nan.0)))) (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (pow (sqrt +nan.0) 3))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt +nan.0)))) (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (pow (sqrt +nan.0) 3))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ 1 (- n)))))) (* (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k))))) (sqrt +nan.0)))) (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ 1 (- n)))))) (* (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k))))) (pow (sqrt +nan.0) 3))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ 1 (- n)))))) (* (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k))))) (sqrt +nan.0))))) (* (/ 1 (- k)) 1)) (/ (* (exp (* 1/2 (- (log -2) (log (/ 1 (- n)))))) (sqrt +nan.0)) (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k)))))))) into (- (/ (* (exp (* 1/2 (- (log -2) (log (/ -1 n))))) (sqrt +nan.0)) (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k)))) (+ (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (pow (sqrt +nan.0) 3) (pow k 2))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (sqrt +nan.0) (pow k 2))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (sqrt +nan.0) k))))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n 2))) 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 2)) in k * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) 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]taylor: Taking taylor expansion of (pow (* n 2) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n 2))) 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 2)) in k * [misc]taylor: Taking taylor expansion of (* n 2) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n 2) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* 0 1) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 n))) 1) 1)))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (+ (* 0 (* 1/2 (log (* 2 n)))) (* +nan.0 1)) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (pow (* 2 n) 1/2) (- +nan.0)) into (* +nan.0 (sqrt (* n 2))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [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 (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log 2) (log n))) into (* 1/2 (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log 2) (log n)) k))) into (exp (* 1/2 (* (+ (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (pow k 1/4) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) into (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log 2) (log n)))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) into (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log PI)) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log 2) (log n))) into (* 1/2 (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* n 2) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* n 2))) 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 2)) in n * [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 (+ (* 0 0) (* 1 2)) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log 2) (log n)) k))) into (exp (* 1/2 (* (+ (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (pow k 1/4) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) into (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log 2) (log n)))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) into (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log PI)) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4))) into (* (/ (* (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (* (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (- 1 k) (log PI))))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (- 1 k) (log PI))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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 (+ (log 2) (log n)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log 2) (log n))) into (* 1/2 (+ (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (log 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 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log 2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log 2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (log 2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (+ (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (* (+ (log 2) (log n)) 0) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 1) (* 0 0)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log 2) (log n))) (* 0 0)) into (+ (* 1/2 (log 2)) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow PI 1/2)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) 1) into (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt 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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (* 0 (exp (* 1/2 (* (+ (log 2) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (log 2) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 0) (* -1 (log PI))) into (- (log PI)) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log PI))) (* 0 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* -1/2 (* (log PI) (sqrt PI)))) (* 0 (pow PI 1/2))) into (- (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))) * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log 2)) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (- (/ (- (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))) 1) (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) (/ (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) +nan.0) (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) 0)) into (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) into (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 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 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log PI))) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* 0 (* -1/2 (* (log PI) (sqrt PI)))) (* 0 (pow PI 1/2)))) into (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log 2) (log n))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) 1) (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) 1)) (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) (/ (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1)))) into (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) +nan.0) (* (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI)))))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))))))))) * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4)) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 2 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 2 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 2 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 2 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 2 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 2 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 2 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 2 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (log 2) (log n)) k)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4))) (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (pow k 1/4)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (+ (log 2) (log n)))) (exp (* 1/2 (* (+ (log 2) (log n)) k)))) (pow (/ 1 k) 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log PI)))) (pow (/ 1 k) 1/4))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log PI))) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* 0 (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* 0 (* -1/2 (* (log PI) (sqrt PI)))) (* 0 (pow PI 1/2))))) into (- (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 3)) (sqrt PI)))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log 2) (log n))) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 3) 6)) (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) * [misc]backup-simplify: Simplify (- (/ (- (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 3)) (sqrt PI)))) 1) (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) (/ (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) 1)) (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) 1)) (* (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI)))))))) (/ (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow (log n) 2))) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 3)) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (log n))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 3)) (sqrt PI))) (* 1/8 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n)))) (sqrt PI))))))))))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI)))))) +nan.0) (+ (* (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI)))))))) +nan.0) (* (- (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow (log n) 2))) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 3)) (sqrt PI))) (+ (* 1/16 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (log n))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (+ (* 1/48 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 3)) (sqrt PI))) (* 1/8 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n)))) (sqrt PI))))))))))))) 0)))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log PI) 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (sqrt PI)))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log PI)) (sqrt PI)))))))))) (* k 1)) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI)))))) into (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) k) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (* (log n) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k)) (sqrt PI)))))))))))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) 2))) 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) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 2 n)))) into (pow (/ 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2))) 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]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) 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) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) 2) into (/ 2 n) * [misc]backup-simplify: Simplify (log (/ 2 n)) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) into (exp (* 1/2 (/ (log (/ 2 n)) k))) * [misc]backup-simplify: Simplify (* (sqrt +nan.0) (exp (* 1/2 (/ (log (/ 2 n)) k)))) into (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (pow (/ 2 n) 1/2) (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (sqrt +nan.0))) into (* (/ 1 (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (sqrt +nan.0))) (sqrt (/ 2 n))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [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 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (pow (/ 1 k) 1/4) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) into (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log PI)) into (* 1/2 (* (- 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) 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) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* 1 2) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (pow (/ 1 k) 1/4) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) into (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log PI)) into (* 1/2 (* (- 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) * [misc]backup-simplify: Simplify (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4))) into (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log 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 (/ 1 k)) (log PI)) 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (* -1 (log PI)) into (* -1 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (log PI))) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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 (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log 2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log 2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log 2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 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]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (/ (- (log 2) (log n)) 1) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (* 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) 0) (* 0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)))) 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 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (* 0 (exp (* 1/2 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (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 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (- (log 2) (log n))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (pow (/ 1 k) 1/4))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4))) (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow (/ 1 k) 1/4)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (pow k 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow k 1/4)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (- (log 2) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (exp (* 1/2 (- (log 2) (log n))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (/ (- (log 2) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (/ (- (log 2) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (exp (* 1/2 (- (log 2) (log (/ 1 n)))))) (exp (* 1/2 (/ (- (log 2) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (pow k 3)))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (pow k 2)))) (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) k)))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ -2 n)))) into (pow (/ -2 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2))) 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]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ -1 n) 2) into (/ -2 n) * [misc]backup-simplify: Simplify (log (/ -2 n)) into (log (/ -2 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ -2 n))) into (* -1/2 (log (/ -2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) into (exp (* -1/2 (/ (log (/ -2 n)) k))) * [misc]backup-simplify: Simplify (* (sqrt +nan.0) (exp (* -1/2 (/ (log (/ -2 n)) k)))) into (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (pow (/ -2 n) 1/2) (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (sqrt +nan.0))) into (* (/ 1 (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (sqrt +nan.0))) (sqrt (/ -2 n))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [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 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (sqrt (/ -1 k))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k))))) into (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) into (* 1/2 (* (+ (/ 1 k) 1) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (sqrt (/ -1 k)))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) (/ 1 2)) (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) 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)) 2)) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 2) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (sqrt (/ -1 k))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k))))) into (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log PI)) into (* 1/2 (* (+ (/ 1 k) 1) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (sqrt (/ -1 k)))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))) * [misc]backup-simplify: Simplify (* (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k)))))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (/ -1 k)))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log 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) 1) (log PI)) 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log -2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log -2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -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 (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log -2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log -2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log -2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -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]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -2) (log n)) 1) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log -2) (log n))) into (* -1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) into (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) into (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (sqrt (sqrt (/ -1 k))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (sqrt (/ -1 k))) 0) (* 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k))))) (+ (* (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) 0) (* 0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) 0) (* 0 (exp (* 1/2 (- (log -2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) (+ (* (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (sqrt (sqrt (/ -1 k))))) (* 0 (/ 0 (sqrt (sqrt (/ -1 k))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (sqrt (/ -1 k))))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (sqrt (/ -1 k))) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k))))) (+ (* (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))))) (* 0 (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (sqrt (/ -1 k)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (sqrt (/ 1 (sqrt (/ -1 k))))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt (/ 1 (sqrt (/ -1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (- (log -2) (log n))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) (+ (* (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) (* (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log n))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ 1 (- n))))))) (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ 1 (- n))))))) (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ 1 (- n))))))) (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ -1 n)))))) (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (pow k 2)))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) k)))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [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 (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [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 (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (* +nan.0 (sqrt PI)) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [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 (- (/ (* -1/2 (* (log PI) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [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 (- (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) k) (+ (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (* (* +nan.0 (sqrt PI)) (/ 1 k)))) into (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))) (- (* +nan.0 (sqrt PI))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [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 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) * [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 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (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 (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 5)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log PI)))) (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (pow (sqrt +nan.0) 5)))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (pow (sqrt +nan.0) 3)))) (/ 1 k)) (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log PI)))) (sqrt +nan.0)))) into (- (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 5) (pow k 2))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [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 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) * [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 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) * [misc]backup-simplify: Simplify (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (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 (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 5)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log PI)))) (pow (sqrt +nan.0) 5)))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (pow (sqrt +nan.0) 5)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (pow (sqrt +nan.0) 3)))) (/ 1 (- k))) (/ (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log PI)))) (sqrt +nan.0)))) into (- (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 5) (pow k 2))))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (/ k 2)) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (pow PI (/ k 2)) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 5 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (- 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 (cbrt (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow (pow PI (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 6 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (- 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 (sqrt (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow (pow PI (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 7 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- 1 k) 2) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (12 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow (pow PI 1) (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 8 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to (/ 1 2) * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow (pow PI (- 1 k)) (/ 1 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 9 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 20 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 21 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (- (/ 1 2) (/ k 2)) (log (* n 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 22 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ 1 2)) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (353 enodes) * [exit]simplify: Simplified to (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 23 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 24 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 25 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (186 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (- (/ 1 2) (/ k 2)) (log (* n 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 26 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n 2)) (/ 1 2)) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (353 enodes) * [exit]simplify: Simplified to (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 27 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * [exit]simplify: Simplified to (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 28 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * [exit]simplify: Simplified to (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (log (* n 2)) (- (/ 1 2) (/ k 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 29 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (405 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (- (/ 1 2) (/ k 2)) (log (* n 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 30 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n 2) (/ 1 2))) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (339 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n 2))) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (exp (- (* (- (/ 1 2) (/ k 2)) (log (* n 2))) (log (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 31 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ 1 2))) (* (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))) (* (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))) (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (122 enodes) * * [misc]simplify: iters left: 3 (483 enodes) * [exit]simplify: Simplified to (* (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) (/ (/ (pow (* n 2) (/ 1 2)) (sqrt k)) (* (pow (* n 2) (/ k 2)) (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (cbrt (* (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) (/ (/ (pow (* n 2) (/ 1 2)) (sqrt k)) (* (pow (* n 2) (/ k 2)) (sqrt (sqrt k)))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 34 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ 1 2))) (* (* (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (442 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (* (sqrt k) (pow (* n 2) (/ k 2)))) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (cbrt (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (* (sqrt k) (pow (* n 2) (/ k 2)))) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 35 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 36 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 37 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (/ (pow 2 (/ 1 2)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow 2 (/ 1 2)) (pow (* n 2) (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (pow (* n 2) (/ k 2))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (/ (pow 2 (/ 1 2)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 40 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ 1 2))) (cbrt (pow (* n 2) (/ 1 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (/ 1 2))) (/ (cbrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (* (cbrt (pow (* n 2) (/ 1 2))) (/ (cbrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (* (cbrt (pow (* n 2) (/ 1 2))) (cbrt (pow (* n 2) (/ 1 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 41 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ (sqrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 42 / 194 ] 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))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * [exit]simplify: Simplified to (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 43 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 44 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 45 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 46 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n 2) (/ k 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow (* n 2) (/ k 2)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* n 2) (/ k 2))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 47 / 194 ] 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)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (/ (pow n (/ 1 2)) (/ (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) (pow 2 (/ 1 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 48 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n 2) (/ 1 2))) (cbrt (pow (* n 2) (/ 1 2)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (/ 1 2))) (cbrt (pow (* n 2) (/ 1 2)))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (/ (* (cbrt (pow (* n 2) (/ 1 2))) (cbrt (pow (* n 2) (/ 1 2)))) (/ (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) (cbrt (pow (* n 2) (/ 1 2))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 49 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* n 2) (/ 1 2))) * * [misc]simplify: iters left: 4 (7 enodes) * * [misc]simplify: iters left: 3 (10 enodes) * [exit]simplify: Simplified to (sqrt (pow (* n 2) (/ 1 2))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (* (/ (sqrt (pow (* n 2) (/ 1 2))) (/ (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) (sqrt (pow (* n 2) (/ 1 2))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 50 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 51 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 52 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 53 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (pow (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) 1)) * * * * [misc]progress: [ 54 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * * [misc]simplify: iters left: 3 (470 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 56 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (125 enodes) * * [misc]simplify: iters left: 3 (434 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))))) * * * * [misc]progress: [ 57 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (359 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 58 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * * [misc]simplify: iters left: 3 (470 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 59 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (125 enodes) * * [misc]simplify: iters left: 3 (434 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))))) * * * * [misc]progress: [ 60 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (359 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 61 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (131 enodes) * * [misc]simplify: iters left: 3 (467 enodes) * [exit]simplify: Simplified to (+ (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 62 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (122 enodes) * * [misc]simplify: iters left: 3 (429 enodes) * [exit]simplify: Simplified to (+ (- (/ (* (- 1 k) (log PI)) 2) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (/ (* (- 1 k) (log PI)) 2) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 63 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (354 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log PI) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log PI) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 64 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (351 enodes) * [exit]simplify: Simplified to (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (log (* n 2)) (/ k 2) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (log (* n 2)) (/ k 2) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 65 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (312 enodes) * [exit]simplify: Simplified to (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (/ k 2) (log (* n 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (/ k 2) (log (* n 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 66 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (256 enodes) * [exit]simplify: Simplified to (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (/ k 2) (log (* n 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (/ k 2) (log (* n 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 67 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * * [misc]simplify: iters left: 3 (470 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 68 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (125 enodes) * * [misc]simplify: iters left: 3 (434 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))))) * * * * [misc]progress: [ 69 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (359 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 70 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * * [misc]simplify: iters left: 3 (470 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 71 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (125 enodes) * * [misc]simplify: iters left: 3 (434 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (* (- 1 k) (log PI)) 2))))) * * * * [misc]progress: [ 72 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (112 enodes) * * [misc]simplify: iters left: 3 (359 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 73 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (131 enodes) * * [misc]simplify: iters left: 3 (467 enodes) * [exit]simplify: Simplified to (+ (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 74 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (122 enodes) * * [misc]simplify: iters left: 3 (429 enodes) * [exit]simplify: Simplified to (+ (- (/ (* (- 1 k) (log PI)) 2) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (/ (* (- 1 k) (log PI)) 2) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 75 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (354 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log PI) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log PI) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 76 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (111 enodes) * * [misc]simplify: iters left: 3 (351 enodes) * [exit]simplify: Simplified to (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (log (* n 2)) (/ k 2) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (log (* n 2)) (/ k 2) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 77 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (312 enodes) * [exit]simplify: Simplified to (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (/ k 2) (log (* n 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (/ k 2) (log (* n 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 78 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (* (log (* n 2)) (/ 1 2)) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (256 enodes) * [exit]simplify: Simplified to (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (/ k 2) (log (* n 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (fma (/ (- 1 k) 2) (log PI) (- (/ (log (* n 2)) 2) (log (sqrt (sqrt k))))) (fma (/ k 2) (log (* n 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 79 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (452 enodes) * [exit]simplify: Simplified to (- (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (- 1 k) (/ 2 (log PI))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (- 1 k) (/ 2 (log PI))))))) * * * * [misc]progress: [ 80 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (415 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 81 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (339 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 82 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (129 enodes) * * [misc]simplify: iters left: 3 (452 enodes) * [exit]simplify: Simplified to (- (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (- 1 k) (/ 2 (log PI))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (- 1 k) (/ 2 (log PI))))))) * * * * [misc]progress: [ 83 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (415 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 84 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (* (log (* n 2)) (/ k 2)))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (339 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (/ (- 1 k) (/ 2 (log PI))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 85 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (114 enodes) * * [misc]simplify: iters left: 3 (351 enodes) * [exit]simplify: Simplified to (+ (- (/ (* (- 1 k) (log PI)) 2) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (/ (* (- 1 k) (log PI)) 2) (log (sqrt (sqrt k)))) (- (* (/ (- 1 k) 2) (log (* n 2))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 86 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (314 enodes) * [exit]simplify: Simplified to (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 87 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (+ (log (sqrt (sqrt k))) (log (pow (* n 2) (/ k 2))))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (251 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (- 1 k) (/ 2 (log PI))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (- 1 k) (/ 2 (log PI))))))) * * * * [misc]progress: [ 88 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (294 enodes) * [exit]simplify: Simplified to (+ (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 89 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (256 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (- 1 k) (/ 2 (log PI))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (/ (- 1 k) (/ 2 (log PI))))))) * * * * [misc]progress: [ 90 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (pow (* n 2) (/ 1 2))) (log (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (208 enodes) * [exit]simplify: Simplified to (+ (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 91 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (195 enodes) * [exit]simplify: Simplified to (+ (- (/ (log PI) (/ 2 (- 1 k))) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (+ (- (/ (log PI) (/ 2 (- 1 k))) (log (sqrt (sqrt k)))) (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 92 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (496 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log PI) (log (* n 2)))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (/ (- 1 k) 2) (+ (log PI) (log (* n 2)))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 93 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log PI) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (- (* (log (* n 2)) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) (- (log (sqrt (sqrt k))) (* (log PI) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 94 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 95 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 96 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (* (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ 1 2))) (* (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))) (* (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))) (pow (* n 2) (/ k 2))))) (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (61 enodes) * * [misc]simplify: iters left: 4 (252 enodes) * [exit]simplify: Simplified to (* (/ (/ (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2))) (/ (sqrt k) (pow (* n 2) (/ 1 2)))) (* (* (sqrt k) (pow (* n 2) (/ k 2))) (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))))) (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (/ (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2))) (/ (sqrt k) (pow (* n 2) (/ 1 2)))) (* (* (sqrt k) (pow (* n 2) (/ k 2))) (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))))) (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 97 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (* (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ 1 2))) (* (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))) (* (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))) (pow (* n 2) (/ k 2))))) (* (* (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (60 enodes) * * [misc]simplify: iters left: 4 (228 enodes) * [exit]simplify: Simplified to (* (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3) (/ (* (/ (pow (* n 2) (/ 1 2)) (sqrt k)) (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2)))) (* (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))) (* (pow (* n 2) (/ k 2)) (sqrt (sqrt k)))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3) (/ (* (/ (pow (* n 2) (/ 1 2)) (sqrt k)) (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2)))) (* (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))) (* (pow (* n 2) (/ k 2)) (sqrt (sqrt k)))))))) * * * * [misc]progress: [ 98 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (* (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ 1 2))) (* (* (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (63 enodes) * * [misc]simplify: iters left: 4 (241 enodes) * [exit]simplify: Simplified to (* (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (pow (* n 2) (/ k 2)) (sqrt (sqrt k)))) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow (* n 2) (/ 1 2)) (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (pow (* n 2) (/ k 2)) (sqrt (sqrt k)))) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow (* n 2) (/ 1 2)) (sqrt k))))))) * * * * [misc]progress: [ 99 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (* (* (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ 1 2))) (* (* (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (* (* (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (59 enodes) * * [misc]simplify: iters left: 4 (215 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k)))) (/ (* (pow (* n 2) (/ k 2)) (sqrt k)) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))))) (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3)) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k)))) (/ (* (pow (* n 2) (/ k 2)) (sqrt k)) (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))))) (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3)))) * * * * [misc]progress: [ 100 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (55 enodes) * * [misc]simplify: iters left: 4 (187 enodes) * [exit]simplify: Simplified to (* (pow (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* n 2) (/ k 2))) 3) (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt k) (sqrt (sqrt k))) (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (pow (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* n 2) (/ k 2))) 3) (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt k) (sqrt (sqrt k))) (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 101 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (* (* (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (51 enodes) * * [misc]simplify: iters left: 4 (160 enodes) * [exit]simplify: Simplified to (* (pow (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* n 2) (/ k 2))) 3) (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3)) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (pow (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* n 2) (/ k 2))) 3) (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) 3)))) * * * * [misc]progress: [ 102 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 103 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 104 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 105 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n 2) (/ 1 2)) (pow PI (/ (- 1 k) 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 (* n 2) (/ 1 2)) (pow PI (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* n 2) (/ 1 2)) (pow PI (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (* (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (17 enodes) * [exit]simplify: Simplified to (* (pow (* n 2) (/ k 2)) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow (* n 2) (/ 1 2)) (pow PI (/ (- 1 k) 2))) (* (pow (* n 2) (/ k 2)) (sqrt k)))) * * * * [misc]progress: [ 106 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 107 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [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 (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 108 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [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 (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 109 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 110 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))))) * * * * [misc]progress: [ 111 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 112 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt 1))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 113 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 114 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) 1)) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 115 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 116 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))))) * * * * [misc]progress: [ 117 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 118 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 119 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 120 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) 1)) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 121 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 122 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))))) * * * * [misc]progress: [ 123 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 124 / 194 ] simplifiying candidate # * [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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ 1 (sqrt 1))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 125 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 126 / 194 ] simplifiying candidate # * [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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ 1 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 127 / 194 ] simplifiying candidate # * [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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 128 / 194 ] 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))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (pow PI (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))) * * * * [misc]progress: [ 129 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (cbrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (cbrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (cbrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))))) (* (cbrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 130 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* n 2) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* n 2) (/ k 2)))) (* (sqrt (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 131 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (* (/ (pow 2 (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 132 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n 2) (/ 1 2))) (cbrt (pow (* n 2) (/ 1 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n 2) (/ 1 2))) (/ (cbrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* n 2) (/ 1 2))) (/ (cbrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k)))) (* (/ (cbrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 133 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n 2) (/ 1 2))) (sqrt (sqrt k))) (* (/ (sqrt (pow (* n 2) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 134 / 194 ] 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))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 135 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 136 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n 2) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (pow (* n 2) (/ 1 2)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow (* n 2) (/ 1 2)) (* (/ 1 (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 137 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 138 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n 2) (/ 1 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow (* n 2) (/ 1 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow (* n 2) (/ 1 2)))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))) * * * * [misc]progress: [ 139 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 140 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 141 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 142 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 143 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (174 enodes) * * [misc]simplify: iters left: 1 (388 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (exp (- (* (/ (- 1 k) 2) (log PI)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 144 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (175 enodes) * [exit]simplify: Simplified to (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (exp (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))))) * * * * [misc]progress: [ 145 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 146 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 147 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (167 enodes) * * [misc]simplify: iters left: 1 (184 enodes) * [exit]simplify: Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (cbrt (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* (sqrt (sqrt k)) (sqrt k)) (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 148 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 149 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 150 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 151 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 152 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 153 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (fabs (cbrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))) * * * * [misc]progress: [ 154 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 155 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt 1) (cbrt (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt 1) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 156 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 157 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 158 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * * [misc]simplify: iters left: 6 (13 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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 159 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [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 PI (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))) * * * * [misc]progress: [ 160 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 161 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1)) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 162 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 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 PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 163 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (sqrt (pow PI (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (sqrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [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 (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (sqrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 164 / 194 ] 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)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 165 / 194 ] 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)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (fabs (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (fabs (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))))) * * * * [misc]progress: [ 166 / 194 ] 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)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 167 / 194 ] 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)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (sqrt 1)) (/ (pow PI (/ (- 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))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (sqrt 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 168 / 194 ] 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)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * * [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 PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))) * * * * [misc]progress: [ 169 / 194 ] 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 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* 1 (/ (pow PI (/ (- 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))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (* 1 (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 170 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 171 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 172 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 173 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 174 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (cbrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (pow PI (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k)))))) * * * * [misc]progress: [ 175 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 176 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (pow PI (/ (- 1 k) 2)) (sqrt 1)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 177 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt (sqrt k))) * * [misc]simplify: iters left: 3 (4 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) * * * * [misc]progress: [ 178 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (pow PI (/ (- 1 k) 2)) 1) (sqrt (sqrt k))))) * * * * [misc]progress: [ 179 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (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 (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (cbrt (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 180 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow PI (/ (- 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 PI (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (sqrt (pow PI (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (sqrt (pow PI (/ (- 1 k) 2))))))) * * * * [misc]progress: [ 181 / 194 ] simplifiying candidate # * * * * [misc]progress: [ 182 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (/ 1 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow PI (/ 1 2)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow PI (/ 1 2)) (* (sqrt (sqrt k)) (pow PI (/ k 2)))))) * * * * [misc]progress: [ 183 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (336 enodes) * [exit]simplify: Simplified to (fma (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8) (fma (* 1/2 (log PI)) (* (- k) (sqrt PI)) (sqrt PI))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (fma (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8) (fma (* 1/2 (log PI)) (* (- k) (sqrt PI)) (sqrt PI))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 184 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (log PI)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (266 enodes) * [exit]simplify: Simplified to (pow (pow PI 1/2) (- 1 k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow (pow PI 1/2) (- 1 k)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 185 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (log PI)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (266 enodes) * [exit]simplify: Simplified to (pow (pow PI 1/2) (- 1 k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (pow (pow PI 1/2) (- 1 k)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 186 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 7) 1/4))) (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (pow k 3) 1/4))))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (117 enodes) * * [misc]simplify: iters left: 4 (326 enodes) * [exit]simplify: Simplified to (+ (fma (pow (pow k 7) 1/4) (* (* 1/8 (* (pow n 1/2) (pow 2 1/2))) (+ (* (log n) (log n)) (* (log 2) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (pow (/ 1 k) 1/4))) (- (* (* (pow (pow k 7) 1/4) 1/4) (* (* (log 2) (log n)) (* (pow n 1/2) (pow 2 1/2)))) (* (* 1/2 (pow (pow k 3) 1/4)) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n)))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (+ (fma (pow (pow k 7) 1/4) (* (* 1/8 (* (pow n 1/2) (pow 2 1/2))) (+ (* (log n) (log n)) (* (log 2) (log 2)))) (* (* (pow n 1/2) (pow 2 1/2)) (pow (/ 1 k) 1/4))) (- (* (* (pow (pow k 7) 1/4) 1/4) (* (* (log 2) (log n)) (* (pow n 1/2) (pow 2 1/2)))) (* (* 1/2 (pow (pow k 3) 1/4)) (* (* (pow n 1/2) (pow 2 1/2)) (+ (log 2) (log n)))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 187 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (exp (* 1/2 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k)))) (pow (/ 1 k) 1/4)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (190 enodes) * [exit]simplify: Simplified to (* (* (pow (/ 1 k) 1/4) (* (pow 2 1/2) (pow n 1/2))) (pow (* (pow 2 1/2) (pow n 1/2)) (- k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (* (pow (/ 1 k) 1/4) (* (pow 2 1/2) (pow n 1/2))) (pow (* (pow 2 1/2) (pow n 1/2)) (- k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 188 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ (* (exp (* 1/2 (- (log -2) (log (/ -1 n))))) (sqrt +nan.0)) (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k)))) (+ (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (pow (sqrt +nan.0) 3) (pow k 2))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (sqrt +nan.0) (pow k 2))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log -2) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (sqrt +nan.0) k))))))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))) * * * * [misc]progress: [ 189 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) k) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log PI) (* (log n) (pow k 2)))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log PI) 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (sqrt PI))) (- (* +nan.0 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k)) (sqrt PI)))))))))))))))))))))))))))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 190 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (pow k 3)))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (pow k 2)))) (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log PI))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) k)))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 191 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ -1 n)))))) (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (pow k 2)))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (- (log -2) (log (/ -1 n)))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) k)))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 192 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))) (- (* +nan.0 (sqrt PI))))))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) +nan.0)) * * * * [misc]progress: [ 193 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 5) (pow k 2))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) +nan.0)) * * * * [misc]progress: [ 194 / 194 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 3) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (* (pow (sqrt +nan.0) 5) (pow k 2))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) +nan.0)) * * * [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) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 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 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: [ 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 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: simplifying candidates * * * * [misc]progress: [ 1 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))))) * * * * [misc]progress: [ 4 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* 2 PI) n) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (* (* 2 PI) n) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2))))) * * * * [misc]progress: [ 6 / 88 ] simplifiying candidate # * [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)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))))) * * * * [misc]progress: [ 7 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (- 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 (cbrt (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))) * * * * [misc]progress: [ 8 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (- 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 (sqrt (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))) * * * * [misc]progress: [ 9 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- 1 k) 2) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (12 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 10 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 2) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (5 enodes) * [exit]simplify: Simplified to (/ 1 2) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2)))) * * * * [misc]progress: [ 11 / 88 ] 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)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))))) * * * * [misc]progress: [ 12 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- 1/2) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 23 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (- 1) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 24 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 35 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (cbrt (sqrt k)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 36 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (sqrt k)) * * [misc]simplify: iters left: 2 (3 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 37 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt k) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to (sqrt k) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 38 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * [exit]simplify: Simplified to (fma (log (* (* n PI) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n PI) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))))) * * * * [misc]progress: [ 42 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * [exit]simplify: Simplified to (fma (log (* (* n PI) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n PI) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))))) * * * * [misc]progress: [ 43 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (302 enodes) * [exit]simplify: Simplified to (fma (log (* 2 (* n PI))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* 2 (* n PI))) (/ (- 1 k) 2) (- (log (sqrt k)))))) * * * * [misc]progress: [ 44 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 45 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 46 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 47 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 48 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 49 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * * [misc]simplify: iters left: 2 (329 enodes) * * [misc]simplify: iters left: 1 (470 enodes) * [exit]simplify: Simplified to (* (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) * * * * [misc]progress: [ 50 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 51 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 52 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 53 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (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)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* PI (* 2 n)) (/ 1 2)) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 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 (* (* 2 PI) n) (/ k 2)) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (pow (* PI (* 2 n)) (/ 1 2)) (* (pow (* (* 2 PI) n) (/ k 2)) (sqrt k)))) * * * * [misc]progress: [ 54 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 88 ] simplifiying candidate # * [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)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) * * * * [misc]progress: [ 56 / 88 ] simplifiying candidate # * [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 (* (* n 2) PI) (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 57 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 58 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (pow (* (* n PI) 2) (/ (- 1 k) 2)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* n PI) 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 59 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 60 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 61 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 62 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 63 / 88 ] simplifiying candidate # * [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)) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))) * * * * [misc]progress: [ 64 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (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)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 65 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 66 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 67 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 68 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 69 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 70 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 71 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 72 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 73 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 74 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 75 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 76 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 77 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) * * [misc]simplify: iters left: 6 (37 enodes) * * [misc]simplify: iters left: 5 (108 enodes) * * [misc]simplify: iters left: 4 (367 enodes) * [exit]simplify: Simplified to (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (- (fma (* (log (* PI 2)) (log (* PI 2))) (* (* (* k k) 1/8) (* (pow n 1/2) (pow (* PI 2) 1/2))) (fma (* (* (log n) (log n)) (* (* k k) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))) (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) 1/2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (- (fma (* (log (* PI 2)) (log (* PI 2))) (* (* (* k k) 1/8) (* (pow n 1/2) (pow (* PI 2) 1/2))) (fma (* (* (log n) (log n)) (* (* k k) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))) (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) 1/2))))) * * * * [misc]progress: [ 78 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (274 enodes) * [exit]simplify: Simplified to (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (* (pow n (- 1/2 (* 1/2 k))) (pow (* 2 PI) (- 1/2 (* 1/2 k)))))) * * * * [misc]progress: [ 79 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (280 enodes) * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * * [misc]progress: [ 80 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 k)) (- (+ +nan.0 (- (* +nan.0 k)))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 81 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 82 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* +nan.0 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 83 / 88 ] 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]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 84 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 85 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 86 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 2 (* n PI)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 87 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 2 (* n PI)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 88 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 2 (* n PI)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (15 enodes) * * [misc]simplify: iters left: 1 (17 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * * * [misc]progress: adding candidates to table * [misc]progress: [Phase 3 of 3] Extracting. * * [misc]regime: Finding splitpoints for: (# # # # # # # # # # #) * * * [misc]regime-changes: Trying 4 branch expressions: (n (* (* 2 PI) n) k (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * * * [misc]regimes: Trying to branch on n from (# # # # # # # # # # #) * * * * [misc]regimes: Trying to branch on (* (* 2 PI) n) from (# # # # # # # # # # #) * * * * [misc]regimes: Trying to branch on k from (# # # # # # # # # # #) * * * * [misc]regimes: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (# # # # # # # # # # #) * * * [misc]regime: Found split indices: #